Mirror Symmetry in Three Dimensional Gauge Theories

K. Intriligator; N. Seiberg

REVIEW

Mirror Symmetry in Three Dimensional Gauge Theories

K. Intriligator, N. Seiberg

High Energy Physics - Theory · Submitted 28 Jul 1996 · 16 references

Pith's verdict: The paper that invented three-dimensional N=4 mirror symmetry; the A_n and D_n dual pairs are real derivations, the E-series is a clearly-labelled proposal dressed up slightly too strongly in the abstract.

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arXiv IDhep-th/9607207 (version 1)

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CitationK. Intriligator, N. Seiberg. "Mirror Symmetry in Three Dimensional Gauge Theories." arXiv:hep-th/9607207 (1996). https://pith.science/paper/WAAHEKXM

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Editor's note

read the letter

This is the paper that started 3d N=4 mirror symmetry, and it earns that place. The core observation is clean and, in hindsight, obvious in the way good ideas are: the Coulomb branch of a Kronheimer quiver is quantum-corrected while the Higgs branch is not, so a dual description that swaps the two branches turns a one-loop computation in one theory into a classical statement in the other. The FI parameters of one side become the mass parameters of the other, and the U(1) gauge factors carry a hidden global symmetry that is only visible at the fixed point. That last point — that visible and hidden global symmetries get exchanged — is the part I find most useful and it is argued properly in the introduction, not just asserted. The A_n case is worked through honestly: the classical Higgs metric of the U(1)^{n-1} quiver in (3.5)-(3.6) is matched against the one-loop Coulomb metric of U(1) with n electrons in (3.9)-(3.10), and the n=2 case against Eguchi-Hanson versus Taub-NUT. That is a genuine two-sided comparison of distinct Lagrangians, not a restatement, and the tables in section 2 are consistent throughout. The D_n case gets the one-dimensional branches matched and the rest is flagged as expected. The E_6,7,8 section is a proposal: no dual is exhibited, and the identification of the Coulomb branch with the exceptional instanton moduli space rests on the dimension count C_2(G)-1 plus the assumed breaking patterns. The authors say so — section 5 states plainly that the dual theories are unknown — so the record's 'no limitations found' is wrong; the gap is acknowledged in the text. What I would flag is the abstract's 'we show' for small E_8 instantons against the body's 'we argue' and 'it is expected'. That is a mild overclaim, not a fatal one, and it is the only place the paper's framing outruns its argument. One correction to the reader's report: one-loop exactness of the Coulomb metric is not the weak premise, it is cited to [3,4] and is a known result. The real gap is the uncomputed D_n and E_n identifications, exactly as the stress-test says. Read it for the framework and the A_n derivation; treat the E-series as a well-motivated conjecture. It deserves referees.

Referee report

Significance

If the duality holds, this is a foundational result. It gives the first field-theoretic realization of mirror symmetry in three dimensions, identifies the Coulomb branch of a quiver with an instanton moduli space, and supplies a local quantum field theory for small E6,7,8 instantons, which is not known to exist in four, five or six dimensions. The geometric reading in the introduction, in which the duality becomes mirror symmetry of a Calabi-Yau compactified on a circle, is a clean and influential observation. The paper deserves credit for not resting on dimension counting alone in the A-series: the classical Higgs metric (3.5)-(3.6) and the one-loop Coulomb metric (3.7)-(3.8) are written explicitly and compared two-sidedly with the U(1)-with-n-electrons metrics (3.9)-(3.10), and the n=2 case is worked out completely as Eguchi-Hanson versus Taub-NUT in (3.1)-(3.4). That is a genuine derivation rather than a restatement, and it is the strongest part of the paper.

Major objections (1)

[Abstract and §5] The abstract states (abstract:s4) that 'we show that in three dimensions small E8 instantons in string theory are described by a local quantum field theory', but §5 supports this only with the dimension count dim = C_2(E8) - 1 = 29 and with the symmetry-breaking pattern E8 -> E7 with massless moduli in 1/2(56) + 1, phrased as what 'we want the Coulomb branch to reflect' rather than as a computed property of K_E8. No Coulomb-branch metric is computed for any E-series quiver, no dual theory is exhibited, and the section itself says 'it is not known what the dual theories are'. The body is appropriately hedged ('we argue', 'it is expected'), so the mismatch is one of claim strength rather than of hidden error, but the E8 statement is a headline claim and the abstract's 'we show' outruns the argument given. Either supply one independent check, for instance the one-loop Coulomb-branch metric of K_E6 compared against the known E6 one-instanton metric, or 't Hooft anomaly matching for the hidden E8 global symmetry, or recalibrate the abstract to 'we argue' and label the E-series identification in §5 explicitly as a conjecture supported by dimension and zero-mode counting.

Minor objections (6)

[§4] The (2n-3)-dimensional Coulomb branch of K_SO(2n) is stated to be 'expected to coincide' with the Higgs branch of SU(2) with n quarks, and neither metric is computed; the check actually performed is the one-dimensional D_n ALE matching together with the symmetry-breaking pattern SO(2n) -> SO(2n-4) x SU(2) with 1/2(2n-4,2) + (1,1). That is a good but partial substitute, and the status of the SO(2n) duality should be stated at the same level of confidence as the E-series, not left to a single 'expected'.
[§3.2, Eqs. (3.7)-(3.8)] The text identifies (3.8) with the multi-monopole metrics of ref. [16] and separately with the moduli space of an SU(n) instanton, without relating the two. A sentence explaining that the g_cl^{-2} = 0 limit of (3.8) removes the constant term from the harmonic function and yields the A_{n-1} ALE space, which is the SU(n) one-instanton moduli space modulo R^4 translations, would close the logic for the reader.
[§2, Eq. (2.1)] The hypersurface equations, in particular the SO(2r) case X_1^2 + X_2^2 X_3 + X_3^{r-1} = B_G, should be checked against ref. [13], and the scaling weights of X_1, X_2, X_3 under the degree-one scaling of the zeta parameters should be stated explicitly so that the reader can verify the degrees c_a(G) quoted in the following sentence.
[§2, table of d_H, d_C, #m, #zeta] The table does not state that d_H and d_C are in quaternionic units; footnote 5 says so, but the table is read on its own and should carry the same statement in its caption.
[§3.2 and ref. [15]] The citation of [15] for the Higgs branch of U(1) with n electrons being the SU(n) instanton moduli space should specify that this is instanton number one and modulo R^4 translations, so that the dimension n-1 matches the d_C entry in the table.
[Whole manuscript] The supplied text has broken ligatures and inter-word spacing throughout (for example 'g roup', 'Q uantum', 'd ual', 'th e', 'ﬁxed'); the final version should be checked for these before typesetting.

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The paper

The paper claims

A pair of three-dimensional gauge theories can describe the same long-distance physics, with one theory's Higgs branch playing the role of the other's Coulomb branch, and one theory's quantum corrections reappearing as classical data in its

The reading

The paper argues that certain three-dimensional gauge theories with eight supercharges come in dual pairs that meet at the same interacting fixed point, and that the duality acts like a mirror: the Higgs branch of one theory is the Coulomb branch of the other, mass terms trade places with Fayet-Iliopoulos parameters, and two global rotation symmetries swap. The concrete carriers are the quiver gauge theories Kronheimer built to construct the ALE spaces $C^2/Γ_G$ as hyper-Kahler quotients: the Higgs branch is the ALE space, and the authors claim the quantum-corrected Coulomb branch is the moduli space of a single $G$-instanton. This matters because it turns a gravitational statement (ALE instantons) and a gauge statement (instantons of the corresponding $ADE$ group) into two descriptions of one fixed point, and because the Coulomb branch is where quantum effects live in one description and where they vanish in the other, so the duality explains why the two computations agree. The checkable cases are $K_{SU(n)} = U(1)^{n-1}$ dual to $U(1)$ with $n$ electrons, and $K_{SO(2n)}$ dual to $SU(2)$ with $n$ quarks. The $E_6$, $E_7$ and $E_8$ quivers are then claimed to give new fixed points, with the $E_8$ case supplying a local field theory whose long-distance limit is the small $E_8$ instanton.

What carries the argument

Kronheimer's hyper-Kahler quotient: the quiver group $K_G$ and its adjacently charged hypermultiplets, whose Higgs branch is the ALE space $C^2/Γ_G$ and whose $r$ Fayet-Iliopoulos parameters are exactly the blow-up modes resolving the orbifold to $C^2/Γ_H$ for $H$ obtained from $G$ by adjoint Higgsing. The load-bearing calculational step is the one-loop correction to the Coulomb branch metric, eq. (3.8), which produces the multi-centre Taub-NUT geometry with centres at the mass parameters; this is what lets the authors identify the Coulomb branch with an instanton moduli space rather than merely count its dimension. The dimension count $C_2(G)-1$ (the dual Coxeter number minus one, matching the instanton moduli space after removing $R^4$ translations) and the assumed symmetry-breaking patterns $E_6 → SU(6)$, $E_7 → SO(12)$, $E_8 → E_7$ with the stated massless spectra carry the $E$-series cases.

Extended reading notes

Core claim

For each simply laced group $G$, take the quiver gauge theory $K_G = (∏_i U(n_i))/U(1)$ read off the extended Dynkin diagram, with hypermultiplets on the links. Its Higgs branch is exactly $C^2/Γ_G$, the ALE space, and is protected from quantum corrections because the gauge coupling sits in a background superfield of type $(1+3,1)$ under $SU(2)_L × SU(2)_R$ and so can only enter the Coulomb branch. The paper's claim is that the Coulomb branch, classically $(R^3 × S^1)^{C_2(G)-1}$, is corrected by quantum effects into the moduli space of one $G$-instanton, with the origin the zero-size instanton, and that at the origin the two branches meet at an interacting renormalization-group fixed point carrying an accidental global $G$ symmetry visible only at long distance. The duality then says the fixed point has a second description in which the two branches are exchanged, so the quantum-corrected Coulomb branch of one theory is the classical Higgs branch of the other, and the $r$ Fayet-Iliopoulos parameters of one are the $r$ independent mass parameters of the dual. The authors verify the metric matching explicitly for $G = SU(n)$: the multi-Taub-NUT metric computed at one loop in (3.8) coincides with the multi-monopole metric of the literature and, after sending the classical coupling to infinity and relabelling $ζ_i → m'_i$, with the Higgs-branch metric of $U(1)$ with $n$ electrons.

Load-bearing premise

The load-bearing premise is that a single one-loop computation gives the exact Coulomb-branch metric, so that the Coulomb branch can be identified with the $G$-instanton moduli space; this is shown explicitly only for $G = SU(n)$, is stated as an expectation for $SO(2n)$, and for $E_6$, $E_7$, $E_8$ rests on the dimension count $C_2(G)-1$ together with the assumed symmetry-breaking patterns.

Editorial extensions

If this is right

The $E_6$, $E_7$ and $E_8$ quivers flow to interacting fixed points in three dimensions whose Coulomb branches are the moduli spaces of the corresponding exceptional instantons, giving new strongly coupled theories with no known Lagrangian dual.
Small $E_8$ instantons in string theory acquire a local quantum field theory description in three dimensions, something not known in four, five or six dimensions.
The duality exchanges visible and hidden global symmetries: the manifest flavour symmetry of one description appears as an accidental symmetry generated at long distance in the other, with the Cartan part visible as the conserved current $*F$ of each gauge $U(1)$ factor.
Compactifying a mirror pair of Calabi-Yau spaces on circles of inverse radii gives two three-dimensional theories that become indistinguishable, so the gauge-theory duality reproduces mirror symmetry of the Calabi-Yau pair.
Turning on Fayet-Iliopoulos parameters breaks $K_G$ to $K_H$ for $H$ adjointly embedded in $G$, and the duality survives in the low-energy theory, giving a nested family of dual pairs.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the Coulomb branch really is the one-instanton moduli space for every simply laced $G$, the statement should be extendable to $k$ instantons by taking $k$ units of the relevant magnetic charge, which would predict a family of fixed points whose Coulomb branches are multi-instanton moduli spaces and whose dimensions grow with $k$.
The metric matching is a statement about hyper-Kahler geometry that can be tested independently of the gauge theory: the Coulomb-branch metric for $K_{SO(2n)}$ should equal the $D_n$ ALE metric in the limit where the classical coupling is taken to infinity, and for the exceptional groups it should equal the known one-instanton metrics on the corresponding moduli spaces.
Because the duality is claimed only as a long-distance statement, with both sides free at short distance, the natural place to look for a sharp test is a protected quantity that survives the limit, such as the spectrum of BPS states or the anomaly coefficients of the accidental global symmetry.
The exchange of Fayet-Iliopoulos parameters with mass parameters suggests the hidden symmetry's rank equals the number of $U(1)$ factors, so the $E_8$ quiver should exhibit a hidden rank-8 symmetry whose Cartan subgroup is directly measurable as the eight conserved currents.

Original abstract

We discuss non-trivial fixed points of the renormalization group with dual descriptions in $N=4$ gauge theories in three dimensions. This new duality acts as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories. Quantum effects on the Coulomb branch arise classically on the Higgs branch of the dual theory. We present examples of dual theories whose Higgs/Coulomb branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space of instantons of the corresponding $ADE$ gauge group. In particular, we show that in three dimensions small $E_8$ instantons in string theory are described by a local quantum field theory.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,239 input tokens, $0.0002 reported.

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The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We discuss non-trivial fixed points of the renormalization group with dual descriptions in $N=4$ gauge theories in three dimensions. This new duality acts as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories. Quantum effects on the Coulomb branch arise classically on the Higgs branch of the dual theory. We present examples of dual theories whose Higgs/Coulomb branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space of instantons of the corresponding $ADE$ gauge group. In particular, we show that in three dimensions small $E_8$ instantons in string theory are described by a local quantum field theory.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We discuss non-trivial fixed points of the renormalization group with dual descriptions in $N=4$ gauge theories in three dimensions.	contribution 0.87	0.69	0.17	asserted 0.78
s1	This new duality acts as mirror symmetry, exchanging the Higgs and Coulomb branches of the theories.	interpretation 0.55	0.64	0.51	asserted 1.00
s2	Quantum effects on the Coulomb branch arise classically on the Higgs branch of the dual theory.	interpretation 0.61	0.46	0.18	asserted 1.00
s3	We present examples of dual theories whose Higgs/Coulomb branch are the ALE spaces and whose Coulomb/Higgs branches are the moduli space of instantons of the corresponding $ADE$ gauge group.	contribution 0.60	0.79	0.22	asserted 1.00
s4	In particular, we show that in three dimensions small $E_8$ instantons in string theory are described by a local quantum field theory.	result 0.86	0.88	0.24	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.82.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (16)

[16]

K. Lee, E. Weinberg, P. Yi, “The Moduli Space of Many BPS M onopoles for Arbitrary Gauge Groups,” hep-th/9602167. 13

View on Pith Pith review arXiv
[1]

A. Sen, “ F -Theory And Orientifolds,” hep-th/9605150

View on Pith Pith review arXiv
[2]

T. Banks, M. Douglas, and N. Seiberg, “Probing F -Theory With Branes,” hep- th/9605199

View on Pith
[3]

N. Seiberg, “IR Dynamics on Branes and Space-Time Geomet ry,” hep-th/9606017

View on Pith Pith review arXiv
[4]

N. Seiberg and E. Witten, “Gauge Dynamics and Compactiﬁc ation to Three Dimen- sions,” hep-th/9607163

View on Pith Pith review arXiv
[5]

N. Seiberg and E. Witten, “Electric-Magnetic Duality, M onopole Condensation, And Conﬁnement In N = 2 Supersymmetric Yang-Mills Theory,” Nucl. Phys. B426 (1994) 19, hep-th/9407087

View on Pith Pith review arXiv 1994
[6]

N. Seiberg and E. Witten, “Monopoles, Duality, And Chira l Symmetry Breaking In N = 2 Supersymmetric QCD,” Nucl. Phys. B431 (1994) 484, hep-th/9408099

View on Pith Pith review arXiv 1994
[7]

N. Seiberg, “Naturalness Versus Supersymmetric Non-re normalization Theorems,” Phys.Lett. B318 (1993) 469, hep-ph/9309335

View on Pith Pith review arXiv 1993
[8]

P.C. Argyres, M.R. Plesser and N. Seiberg, “The Moduli Sp ace of Vacua of N = 2 SUSY QCD and Duality in N = 1 SUSY QCD,” hep-th/9603042

View on Pith Pith review arXiv
[9]

N. Seiberg, “Electric-Magnetic Duality in Supersymmet ric Non-Abelian Gauge The- ories,” Nucl.Phys. B435 (1995) 129, hep-th/9411149

View on Pith Pith review arXiv 1995
[10]

D.R. Morrison and M.R. Plesser, “Towards Mirror Symmet ry as Duality for Two Dimensional Abelian Gauge Theories,” hep-th/9508107

View on Pith Pith review arXiv
[11]

A.M. Polyakov, “Quark Conﬁnement And The Topology of Ga uge Groups,” Nucl. Phys. B234 (1983) 269

View on Pith 1983
[12]

P.B. Kronheimer, Jour. Diﬀerential Geometry, 29 (1989) 665

View on Pith 1989
[13]

S. Katz and D.R. Morrison, Jour. Alg. Geom. 1 (1992) 449 and references therein

View on Pith 1992
[14]

T. Eguchi, P. Gilkey, and A. Hanson, Phys. Rep. 66 (1980) 213

View on Pith 1980
[15]

M.R. Douglas, “Branes Within Branes,” hep-th/9512077

View on Pith Pith review arXiv

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Boundary Chiral Algebras and Holomorphic Twists
hep-th 2020-04 accept novelty 7.0 of 10

In the holomorphic twist of 3d N=2 theories, bulk local operators form a commutative chiral algebra with a shifted Poisson bracket and a degree-1 stress tensor, while boundary operators form a module over it whose exp...
Instantons from Blow-up
hep-th 2019-08 conditional novelty 7.0 of 10

The instanton partition function of many 4d N=2 and 5d N=1 gauge theories is fully determined by the perturbative part via generalized Nakajima-Yoshioka blowup equations.
Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling
hep-th 2018-10 conditional novelty 7.0 of 10

A stable-intersection rule for brane webs yields a classification of the infinite-coupling Higgs branch of 5d SU(N_c) SQCD with N_f flavors and Chern-Simons level k, revealing up to three components.
Dual Boundary Conditions in 3d SCFT's
hep-th 2017-12 conditional novelty 7.0 of 10

Matching pairs of half-BPS boundary conditions are proposed for particle-vortex, level-rank, SQED/XYZ, and Aharony dualities, each checked by boundary anomaly matching and by identities between half-indices.
A Symmetry Breaking Scenario for QCD$_3$
hep-th 2017-06 conditional novelty 7.0 of 10

For 2k < N_f < N_*(N,k), SU(N)_k with N_f fundamental fermions is conjectured to break U(N_f) spontaneously to U(N_f/2+k) x U(N_f/2-k), with a Wess-Zumino term fixed by N.
A one-dimensional theory for Higgs branch operators
hep-th 2016-10 conditional novelty 7.0 of 10

A 1d Gaussian theory coupled to a matrix model computes 2- and 3-point functions of Higgs branch operators in 3d N=4 SCFTs, fixing parameters left free by earlier bootstrap work.
Level/rank Duality and Chern-Simons-Matter Theories
hep-th 2016-07 accept novelty 7.0 of 10

Coupling level/rank-dual Chern-Simons Lagrangians to background fields with the right counterterms fixes spin-structure and framing-anomaly puzzles and generates new topological and Chern-Simons-matter dualities.
A Duality Web in 2+1 Dimensions and Condensed Matter Physics
hep-th 2016-06 conditional novelty 7.0 of 10

Assuming one boson-fermion duality, the paper derives a connected web of 2+1-dimensional dualities, including a properly quantized fermion-fermion duality, and relates them to 3+1-dimensional S-duality.
Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
hep-th 2016-03 conditional novelty 7.0 of 10

Half-BPS boundary conditions in 3d N=4 gauge theories are shown to produce modules for quantized Higgs- and Coulomb-branch algebras, and a 2d compactification is proposed as the physical origin of symplectic duality.
Deformations of Superconformal Theories
hep-th 2016-02 conditional novelty 7.0 of 10

A symmetry-and-unitarity classification determines which relevant, marginal, and irrelevant supersymmetry-preserving deformations exist for superconformal field theories in three to six dimensions, and which theories ...
Mirror Symmetry And Loop Operators
hep-th 2015-06 conditional novelty 7.0 of 10

Wilson loops in 3d N=4 theories map under mirror symmetry to Vortex loops whose 1d quiver data encodes the original gauge representation, checked by exact S^3 matrix model computations.
Coulomb branch Hilbert series and Hall-Littlewood polynomials
hep-th 2014-03 conditional novelty 7.0 of 10

The Coulomb branch Hilbert series of T_rho(G) theories with background magnetic fluxes is conjectured to equal a Hall-Littlewood polynomial times an explicit prefactor, supported by residue and low-rank checks.
Monopole operators and Hilbert series of Coulomb branches of 3d N = 4 gauge theories
hep-th 2013-09 accept novelty 7.0 of 10

A sum over dressed monopole operators computes the Hilbert series, and hence the chiral ring, of the Coulomb branch of any good or ugly 3d N=4 gauge theory.
3d dualities from 4d dualities
hep-th 2013-05 conditional novelty 7.0 of 10

Every four-dimensional Seiberg duality, compactified on a circle and deformed by an instanton-generated monopole superpotential, descends to a three-dimensional duality, and real-mass flows from these reproduce known ...
Aspects of 3d N=2 Chern-Simons-Matter Theories
hep-th 2013-05 accept novelty 7.0 of 10

The Witten index of 3d N=2 Chern-Simons-matter theories with generic real masses is given by a shifted WZW level counting formula and is invariant under phase transitions.
On Three Dimensional Quiver Gauge Theories and Integrability
hep-th 2013-04 conditional novelty 7.0 of 10

The vacuum moduli space of a 3d N=4 quiver on a circle equals an intersection of two Lagrangian submanifolds in the moduli space of flat connections on a punctured torus, and 3d mirror symmetry becomes bispectral dual...
K-Decompositions and 3d Gauge Theories
hep-th 2013-01 conditional novelty 7.0 of 10

A hypersimplicial K-decomposition of ideal triangulations yields octahedron gluing equations that construct framed flat PGL(K,C) moduli spaces and candidate 3d N=2 theories T_K[M].
IIB Duals of D=3 N=4 Circular Quivers
hep-th 2012-10 accept novelty 7.0 of 10

Explicit type-IIB AdS4 backgrounds are built for the 3d N=4 SCFTs of circular quivers, and a large-L limit is shown to reproduce M-theory on AdS4 x S7/(Z_k x Z_k-hat).
General Argyres-Douglas Theory
hep-th 2012-04 conditional novelty 7.0 of 10

Compactifying the six-dimensional (2,0) A_{N-1} theory on a sphere with irregular singularities yields a classified family of Argyres-Douglas theories whose Seiberg-Witten curves, scaling dimensions, and central charg...
Conifold Transitions in M-theory on Calabi-Yau Fourfolds with Background Fluxes
hep-th 2012-03 accept novelty 7.0 of 10

For M-theory on a Calabi-Yau fourfold, conifold transitions survive background G-flux precisely when the canonical bundle of the singular curve splits into two line bundles, and a new class of mixed horizontal/vertica...
Comments on 3d Seiberg-like dualities
hep-th 2011-08 accept novelty 7.0 of 10

New Seiberg-like dualities are proposed for three-dimensional N=2 Yang-Mills-Chern-Simons theories with unitary gauge groups and arbitrary chiral matter, derived from Aharony duality by real mass deformations and chec...
Chern-Simons Theory and S-duality
hep-th 2011-06 conditional novelty 7.0 of 10

The paper identifies the ℏ → -4π²/ℏ symmetry of complex Chern-Simons theory with N=4 super-Yang-Mills S-duality, and mapping class group actions with N=2 S-duality, checking the dictionary on punctured-torus examples.
3D-partition functions on the sphere: exact evaluation and mirror symmetry
hep-th 2011-05 conditional novelty 7.0 of 10

An explicit closed-form expression for the sphere partition function of the T(SU(N)) quiver tail is derived and used to verify 3D mirror symmetry for infinite families of theories.
A Duality Appetizer
hep-th 2011-03 conditional novelty 7.0 of 10

The N=2 SU(2) Chern-Simons theory at level 1 with one adjoint chiral multiplet is conjectured to be dual to a single free massless chiral multiplet, supported by matching sphere partition functions and superconformal indices.
Off-shell supergravity-matter couplings in three dimensions
hep-th 2011-01 accept novelty 7.0 of 10

The authors solve the Bianchi identities of 3D N-extended conformal supergravity to dimension 3/2 and construct off-shell matter couplings, including new projective-superspace formulations for N=3 and N=4.
Notes on SUSY Gauge Theories on Three-Sphere
hep-th 2010-12 accept novelty 7.0 of 10

The one-loop contribution of a chiral multiplet with arbitrary R-charge q to the S^3 partition function is the double sine function s_{b=1}(i - iq - l sigma), extending the Kapustin-Willett-Yaakov formula beyond canon...
Mirrors of 3d Sicilian theories
hep-th 2010-07 accept novelty 7.0 of 10

The 3d N=4 theories from compactifying 6d (2,0) theories on a punctured Riemann surface times a circle have mirror duals that are star-shaped quiver gauge theories.
Nonperturbative Tests of Three-Dimensional Dualities
hep-th 2010-03 accept novelty 7.0 of 10

Exact three-sphere partition functions of mirror-symmetric three-dimensional gauge theories agree, and the ABJM theory at unit Chern-Simons level matches the mirror of N=8 super-Yang-Mills, giving nonperturbative evid...
Towards M2-brane Theories for Generic Toric Singularities
hep-th 2008-09 conditional novelty 7.0 of 10

Several N=2 Chern-Simons quiver theories are constructed whose moduli spaces are toric Calabi-Yau four-folds with no (3+1)-dimensional parent, verified by explicit toric-diagram computation.
Quantum critical transport, duality, and M-theory
hep-th 2007-01 accept novelty 7.0 of 10

The N=8 SU(N) superconformal Yang-Mills theory in 2+1 dimensions obeys an exact relation K_L K_T = N^3/(18 pi^2) between longitudinal and transverse current correlators at all frequencies and momenta, derived from the...
Superconformal Chern-Simons Theories
hep-th 2004-11 conditional novelty 7.0 of 10

Explicit scale-invariant Chern-Simons matter Lagrangians exist for N=1 and N=2 supersymmetry, but no N=8 version exists within the assumed adjoint-matter, single-gauge-group framework.
SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry
hep-th 2003-07 conditional novelty 7.0 of 10

Three-dimensional conformal field theories with a U(1) symmetry carry a natural SL(2,Z) action, generated by gauging the background field and by shifting its Chern-Simons level, and this action is dual to SL(2,Z) elec...

See all 127 Pith citations

How later papers used it

290 later papers cite it

Evidence: substantial. 287 of the citing papers share no author with it, and 18 of those carry a confident label from Pith's citation classifier.

Pith read 40 of the 460 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

3 later papers by other authors are listed below: 1 built on it and 2 used its method or tool.

Builds on it 1 of 4 papers with this label

Generalized this paper's mirror duality for U(N_c) with adjoint and 2 flavors, proposing a mirror dual for U(N_c) with adjoint and a generic number N_f flavors.

A tale of exceptional 3d dualities (2018) · 0.96 · paraphrased: the licence does not allow quoting

Uses its method or tool 2 of 9 papers with this label

Found the desired theory by applying 3d mirror symmetry from this paper, since it already knew how to realize X as a Higgs branch.

Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants (2020) · 0.85 · paraphrased: the licence does not allow quoting
Obtained the magnetic quiver by applying mirror symmetry from this paper to the reduction of the original theory to three dimensions.

Probing 7-branes on Orbifolds (2022) · 0.81 · paraphrased: the licence does not allow quoting

How the literature uses it

275 arXiv papers cite this in 436 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 232 sentences without a confident label

Builds on it 2 papers

We extend the correspondence between the Coulomb branch of ADE quivers [ref] and the moduli space of ADE instantons, first pointed out for one instanton in [ref] and then generalized to higher instanton number in [ref] .

Coulomb Branch and The Moduli Space of Instantons · Introduction · 0.93
GIT being a recipe for realising 3D mirror symmetry, [ref] , we show how it can be suitably extended for cases where mirror duals are not necessarily in a 1-to-1 correspondence.

Factorisation Homology for Class $\cal S$ Theories · Introduction · 0.84

Uses its method or tool 9 papers

Following [ref] , we realise this UV completion by constructing the sigma model as the Coulomb branch of a gauge theory.

The Partonic Nature of Instantons · Partons in the $CP^1$ Sigma Model · 0.89
These monopole deformations can be systematically analyzed (see [ref] ) using local 3d mirror symmetry [ref] , allowing us to trade monopole operators for polynomial interactions in elementary fields.

D2-brane probes of non-toric cDV threefolds via monopole superpotentials · Introduction · 0.98
We then provide two checks of the validity of our results: * Using a letter counting argument, combined with an analysis of the gauge-invariance conditions, we can reproduce to arbitrary order the series expansion of the Hilbert series; * Combining three-dimensional mirror symmetry [ref] applied to the ADHM quiver and the monopole formula [ref] , our results can be cross-checked through the computation of the Coulomb branch Hilbert series of the mirror theory.

Non-Connected Gauge Groups and the Plethystic Program · Introduction · 0.92

Compares with it 3 papers

(For $n=2$, $T(SU(n))$ coincides with one of the main examples in [ref] .)

S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory · Introduction · 0.89
The dualities we propose bear a strong resemblance to the recently established $𝒩=2$ mirror dualities[We actually expect that our dualities arise from supersymmetry breaking mass deformations of the $𝒩=2$ dualities of [ref] , but an in-depth study of the RG flow from the $𝒩=2$ to the non-supersymmetric dualities goes beyond the scope of this paper.] of [ref] , which themselves arise from suitably chosen mass deformations of $𝒩=4$ mirror pairs [ref] .

Planar Abelian Duals of Chern-Simons QCD · Introduction and Summary · 0.83
The pattern of dualities that emerges looks very similar to the dual theories one finds in supersymmetric gauge theories, where these dualties are known as “mirror symmetry" [ref] .

More Abelian Dualities in 2+1 Dimensions · Introduction · 0.81

Cites it as support 2 papers

This hyperKähler structure is required by supersymmetry and is sufficient to ensure that there are no further corrections to the action: the one-loop result is exact [ref] .

The Partonic Nature of Instantons · A UV Completion of the Sigma Model · 0.99
A recent results that corroborates this expectation appeared recently in [ref] , where it is shown that $4d$ mirror symmetry dualities [ref] (and hence $3d$ mirror symmetry dualities [ref] ) can be proven using only Intriligator-Pouliot (IP) duality, relating theories with $Usp$ gauge group and fundamental matter.

S-confinements from deconfinements · Introduction and summary · 1.00

Cites it as background 161 papers

It turns out that different phases appear in different regimes of the theory: * For $2k≥N_f$, the two phases of the theory are $SU(N)_k±N_f/2$, with a single phase transition between them [ref] . * For $2k < N_f < N_⋆(N,k)$, where the theory is strongly coupled, the following phase diagram was proposed in [ref] : When the fermion masses are large, the phases are still $SU(N)_k±N_f/2$.

$QCD_3$ Dualities and the F-Theorem · Phases of $QCD_3$ · 0.89
In particular abelian mirror symmetry [ref] by definition maps a topological symmetry $U(1)_J$ in one theory to a flavor symmetry in the dual theory.

Exact results for vortex loop operators in 3d supersymmetric theories · Abelian mirror symmetry · 0.92
These tools include the SUSY dualities between certain 2+1D theories known as mirror symmetry [ref] .[More recent developments may be found in [ref] .] We focus on one example of this duality (which we refer to as mirror symmetry for convenience).

Bosonization and Mirror Symmetry · Mirror symmetry and its deformations · 0.83

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [16]

K. Lee, E. Weinberg, P. Yi, “The Moduli Space of Many BPS M onopoles for Arbitrary Gauge Groups,” hep-th/9602167. 13

View on Pith Pith review arXiv

[2] [1]

A. Sen, “ F -Theory And Orientifolds,” hep-th/9605150

View on Pith Pith review arXiv

[3] [2]

T. Banks, M. Douglas, and N. Seiberg, “Probing F -Theory With Branes,” hep- th/9605199

View on Pith

[4] [3]

N. Seiberg, “IR Dynamics on Branes and Space-Time Geomet ry,” hep-th/9606017

View on Pith Pith review arXiv

[5] [4]

N. Seiberg and E. Witten, “Gauge Dynamics and Compactiﬁc ation to Three Dimen- sions,” hep-th/9607163

View on Pith Pith review arXiv

[6] [5]

N. Seiberg and E. Witten, “Electric-Magnetic Duality, M onopole Condensation, And Conﬁnement In N = 2 Supersymmetric Yang-Mills Theory,” Nucl. Phys. B426 (1994) 19, hep-th/9407087

View on Pith Pith review arXiv 1994

[7] [6]

N. Seiberg and E. Witten, “Monopoles, Duality, And Chira l Symmetry Breaking In N = 2 Supersymmetric QCD,” Nucl. Phys. B431 (1994) 484, hep-th/9408099

View on Pith Pith review arXiv 1994

[8] [7]

N. Seiberg, “Naturalness Versus Supersymmetric Non-re normalization Theorems,” Phys.Lett. B318 (1993) 469, hep-ph/9309335

View on Pith Pith review arXiv 1993

[9] [8]

P.C. Argyres, M.R. Plesser and N. Seiberg, “The Moduli Sp ace of Vacua of N = 2 SUSY QCD and Duality in N = 1 SUSY QCD,” hep-th/9603042

View on Pith Pith review arXiv

[10] [9]

N. Seiberg, “Electric-Magnetic Duality in Supersymmet ric Non-Abelian Gauge The- ories,” Nucl.Phys. B435 (1995) 129, hep-th/9411149

View on Pith Pith review arXiv 1995

[11] [10]

D.R. Morrison and M.R. Plesser, “Towards Mirror Symmet ry as Duality for Two Dimensional Abelian Gauge Theories,” hep-th/9508107

View on Pith Pith review arXiv

[12] [11]

A.M. Polyakov, “Quark Conﬁnement And The Topology of Ga uge Groups,” Nucl. Phys. B234 (1983) 269

View on Pith 1983

[13] [12]

P.B. Kronheimer, Jour. Diﬀerential Geometry, 29 (1989) 665

View on Pith 1989

[14] [13]

S. Katz and D.R. Morrison, Jour. Alg. Geom. 1 (1992) 449 and references therein

View on Pith 1992

[15] [14]

T. Eguchi, P. Gilkey, and A. Hanson, Phys. Rep. 66 (1980) 213

View on Pith 1980

[16] [15]

M.R. Douglas, “Branes Within Branes,” hep-th/9512077

View on Pith Pith review arXiv