(In)validity of large N orientifold equivalence

Laurence G. Yaffe; Mithat Unsal

REVIEW

(In)validity of large N orientifold equivalence

Mithat Unsal, Laurence G. Yaffe

High Energy Physics - Theory · Submitted 25 Aug 2006 · 47 references

Pith's verdict: A clean, honest corrective: the SYM/QCD(AS) orientifold equivalence is dead at small S^1 radius, and the authors say plainly that they don't know about R^4.

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arXiv IDhep-th/0608180 (version 3)

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CitationLaurence G. Yaffe, Mithat Unsal. "(In)validity of large N orientifold equivalence." arXiv:hep-th/0608180 (2006). https://pith.science/paper/SWLHP5C4

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Editor's note

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The thing to know: this paper kills the Armoni-Shifman-Veneziano orientifold equivalence in the one regime where anyone can actually compute. On R^3 x S^1 with small circumference and periodic fermions, the one-loop Wilson-line potential for QCD(AS) has two degenerate minima at Omega = ±i, exchanged by charge conjugation, while the SYM potential vanishes identically by supersymmetry. So C breaks in QCD(AS) and not in SYM, the ground state sits outside the neutral sector, and the equivalence has nothing to say about vacuum observables. The computation is a straightforward adaptation of Gross-Pisarski-Yaffe (Appendix A is careful and complete), and the two-minimum structure is protected parametrically: the barrier is O(N^2/L^4) and corrections are O(g^2 N^2/L^4), so at small L it survives. I checked the minimization logic and it holds — the coincident-eigenvalue subspace simultaneously minimizes the gluon term and maximizes the fermion term, so the global minimum is where they say it is. The companion observation that chiral symmetry is unbroken at small L, opposite to SYM, is a nice independent diagnostic and follows from the same Omega = ±i background shifting the KK frequencies by a half-integer. The daughter-daughter framing via SO(2N) projections is a reorganization of their own [15] machinery rather than new mathematics, but it is the right way to see why the twisted sector was always there and why its existence alone was never the issue. The paper is unusually explicit about what it does not know: the abstract's last sentence, Section 4, and the summary all say the large-L and R^4 realizations are open. (The classifier's 'no limitations found' is simply wrong; the authors state them repeatedly.) Two soft spots, both minor. First, 'fails' in the abstract is a touch stronger than the body, which correctly says the neutral-sector equivalence still holds kinematically but generates no useful information when C is broken — the distinction matters and the body gets it right. Second, the Section 6 rebuttal of the string-theory argument is argument rather than computation; it is clearly labeled as such and I think it is correct, but it is the least checkable part of the paper. Neither touches the central result. This is for people working on large-N equivalences, orbifold/orientifold projections, or the Armoni-Shifman-Veneziano program specifically; outsiders will find it narrow. It deserves referees, and I would expect them to pass it with light revisions.

Referee report

Significance

The paper makes a clear, checkable, and physically consequential point: a widely discussed large-N equivalence is not a theorem but a conditional statement whose validity depends on symmetry realization, and in a regime where the dynamics is under analytic control the condition fails. The strengths are substantial. The one-loop computation is explicit and reproducible, and I verified the internal arithmetic: the O(N) constant in Eq. (3.4) reproduces the vacuum energy in Eq. (3.8), and the high-temperature potential Eq. (3.9) reproduces both Eq. (3.10) and the Stefan-Boltzmann result quoted below it. The paper is also candid about what it does not establish, stating repeatedly that the R^4 and large-L symmetry realizations are unknown, and it draws an explicit and useful parallel with the Z2 orbifold case of Ref. [16]. The prediction that C is spontaneously broken for L << Lambda^{-1}, with order parameter Im tr Omega = ±i, is falsifiable by lattice simulation at small volume with periodic boundary conditions, and the authors flag the existing small-lattice study of Ref. [30] as not having tested it. This is a well-posed contribution that sharpens the conditions under which large-N'

Major objections (1)

[Section 3, Eqs. (3.4)-(3.7)] The load-bearing step is the assertion, just below Eq. (3.6), that higher-order corrections 'are small perturbations which cannot change the conclusion that the effective potential has two distinct gauge-inequivalent minima.' As written this rests on the perturbative smallness of g^2(1/L) alone, which is the weakest link a skeptical reader will press on. The argument can be made considerably more robust with one added sentence, and I recommend the authors add it: the two minima at Omega = ±i are exactly degenerate by the unbroken C symmetry of the potential, so no correction of any order, perturbative or non-perturbative, can lift the degeneracy; what must survive is only the O(N^2/L^4) barrier separating them, and non-perturbative effects on R^3 x S^1 at small L are exponentially suppressed relative to that barrier. Stated this way, the conclusion does not depend on perturbation theory at all, only on the exact C symmetry plus the existence of a barrier at leading order. I also note that the O(N) constant term in Eq. (3.4) shifts the potential uniformly and cannot affect the location of the minima, which the text says but could state more prominently.

Minor objections (5)

[Abstract and Section 1 vs. Sections 2 and 6] The abstract states that 'this large N equivalence fails for sufficiently small radius,' and Section 1 says the 'previously asserted large N equivalence between SYM and QCD(AS) is false.' The body is more precise: Section 2 explains that the kinematic neutral-sector mapping still holds, and Section 6 states that 'large N equivalence between theories does not mean equality.' Since what actually fails is the applicability of the neutral-sector mapping to vacuum expectation values and connected correlators when the ground state lies outside the neutral sector, I suggest the abstract and the Section 1 summary say so explicitly, e.g. 'the equivalence yields no predictions for vacuum observables,' to avoid a reader concluding that the C-even correlator identities themselves are being withdrawn.
[Footnote 13] The footnote correctly notes that Omega = ±i lies in SU(N) only when N is a multiple of 4, and that for other N the vacuum is the center element closest to ±i, with an O(1) vacuum-energy discrepancy relative to U(N). It would help to state explicitly that the C-breaking order parameter survives this restriction, i.e. that Im tr Omega / N = sin(2 pi k/N) = 1 - O(1/N^2) for the nearest center element, so that the nonzero expectation value and hence the C-breaking conclusion are unaffected for all N > 2. As written, a reader may wonder whether the order parameter itself is degraded, not merely the energy.
[Section 3, 'Compactification on T^3 x R'] The claim that the effective potential of Ref. [26] has eight-fold degenerate minima corresponding to Wilson lines equal to ±i along each torus direction, and that this implies spontaneous breaking of both the (Z2)^3 center symmetry and charge conjugation in the N -> infinity limit, is the authors' own interpretation of a result obtained elsewhere. Since this is a published source the result itself is supported, but a brief display of the relevant terms, or a one-line explanation of why the eight-fold degeneracy is not an artifact of the Born-Oppenheimer approximation at finite N, would let the reader verify the interpretation without consulting Ref. [26].
[Section 5] The Goldstone-boson counting argument, that only (1/2) n_f (n_f + 1) - 1 of the n_f^2 - 1 Goldstone bosons of multi-flavor QCD(AS) are C-even and this matches the adjoint-fermion count, is a nice consistency check and deserves to be stated as such explicitly, since it is the kind of matching that would fail if the neutral-sector mapping were incorrect.
[Footnotes 13 and 20, and References] A few typographical corrections: footnote 13 reads 'Change conjugation symmetry in SU(N) QCD(AS)' where 'Charge' is intended; footnote 20 contains a stray comma in 'the theory,. Therefore'; and the title of Ref. [25] is given as 'A insight on the proof...' rather than 'An insight...'. The figure 2 caption would also read more cleanly if the normalization were stated as 'after subtracting the O(N) constant and dividing by N(N-1)/(pi^2 L^4)'.

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The paper

The paper claims

The paper argues that the claimed large-$N$ equivalence between supersymmetric Yang-Mills theory and QCD with an antisymmetric-tensor fermion fails on a small circle, because charge conjugation breaks spontaneously in the QCD-like theory.

The reading

The paper asks whether large-$N$ QCD with one fermion in the two-index antisymmetric (or symmetric) representation is equivalent, in its bosonic sector, to $N=1$ supersymmetric Yang-Mills theory. That proposed match matters because it would let known supersymmetric results predict non-perturbative QCD quantities such as the vacuum energy and chiral condensate, up to $1/N$ corrections. The authors argue that the match fails when the theory is put on $R^3$ times $S^1$ with a sufficiently small circle and periodic fermions, because the QCD-like theory spontaneously breaks charge conjugation while the supersymmetric theory does not. They also show that the QCD-like theory keeps chiral symmetry unbroken at small radius, the opposite of what happens in supersymmetric Yang-Mills. The large-radius or decompactified case remains undecided.

What carries the argument

The argument turns on the Wilson line around the compact direction: the path-ordered phase picked up by a test charge circling the $S^1$. In a constant diagonal background, the one-loop effective potential is the logarithm of a ratio of functional determinants of the covariant Laplacian, with gauge-boson and ghost contributions in the adjoint representation and fermion contributions in the two-index antisymmetric or symmetric representation. The competition between these contributions produces a double well in the phase of the Wilson line. Charge conjugation sends $Omega$ to $Omega^dagger$, exchanging the two minima and making the imaginary part of $operatorname{tr}Omega$ an order parameter for spontaneous symmetry breaking. The same background shifts the allowed fermion frequencies by a half-integer, gapping all Kaluza-Klein fermion modes and leaving chiral symmetry unbroken at small radius. In the supersymmetric theory the adjoint Majorana fermion cancels the gauge contribution at one loop, so the potential vanishes and the symmetry realization is different.

Extended reading notes

Core claim

The central claim is that the proposed large-$N$ orientifold equivalence is not valid in general: it fails for QCD with an antisymmetric or symmetric tensor fermion compactified on $R^3$ times $S^1$ at sufficiently small circumference. The authors compute the one-loop effective potential for the Wilson line wrapping the circle. For QCD(AS), the potential has two degenerate global minima at $v = pi/2$ and $v = 3pi/2$, corresponding to $Omega = pm i$ times the unit matrix. Charge conjugation acts by complex conjugation, sending $Omega$ to $Omega^dagger$, and exchanges these two minima, so the order parameter $langle operatorname{Im}operatorname{tr}Omega angle$ is nonzero, $pm i + O(g^2)$. Thus the ground state lies outside the charge-conjugation-even sector to which the proposed equivalence is supposed to apply. For $N=1$ supersymmetric Yang-Mills, the one-loop potential vanishes identically; non-perturbatively the Wilson-line eigenvalues spread uniformly around the circle, leaving charge conjugation unbroken. The paper also finds a nonvanishing leading $O(N^2)$ vacuum energy for QCD(AS), unlike supersymmetric Yang-Mills, and an unbroken discrete chiral symmetry at small radius. The same conclusion is reported for small $T^3$ times $R$ compactifications.

Load-bearing premise

The load-bearing premise is that at sufficiently small circumference the gauge coupling is weak enough that the one-loop two-minimum structure of the Wilson-line potential survives all higher-order and non-perturbative corrections, so the spontaneous breaking of charge conjugation is reliable.

Editorial extensions

If this is right

The asserted large-$N$ orientifold equivalence cannot be a general theorem independent of spacetime volume or dimension: it fails on small $R^3$ times $S^1$ and on small $T^3$ times $R$.
Predictions for QCD(AS/S) drawn from supersymmetric Yang-Mills, such as a vanishing leading vacuum energy, a matching chiral condensate, or degenerate parity doublets, do not follow in the small-radius phase with broken charge conjugation.
Any useful version of the equivalence must be restricted to phases in which charge conjugation is unbroken in both theories; at sufficiently high temperature both theories preserve charge conjugation and chiral symmetry, so the equivalence can apply there within the neutral sectors.
The phase diagram of QCD(AS/S) must contain one or more transitions separating a high-temperature charge-conjugation-invariant deconfined phase from a low-temperature small-volume phase with broken charge conjugation.
For multiple fermion flavors, the same small-radius charge-conjugation breaking occurs, and only the charge-conjugation-even Goldstone bosons can match the adjoint-fermion theory.

Reading between the lines

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

A two-loop or non-perturbative calculation that removed the double well in the small-circle Wilson-line potential would reopen the equivalence in that regime, so the qualitative conclusion depends on the one-loop minimum surviving corrections when the coupling is small.
A lattice study measuring $operatorname{Im}operatorname{tr}Omega$ or other charge-conjugation-odd Wilson loops as a function of circle size and temperature would directly test whether a large-radius charge-conjugation-invariant phase exists.
If charge conjugation remains broken all the way to $R^4$, the orientifold equivalence would have no useful vacuum predictions at all; if it is restored beyond some critical radius, the equivalence could still be useful in the large-radius confining phase, but only for charge-conjugation-even operators.
The parallel with orbifold projections suggests that orientifold equivalences should be treated as phase-dependent statements about neutral sectors, not as dualities between whole theories.

Original abstract

It has been argued that the bosonic sectors of supersymmetric SU(N) Yang-Mills theory, and of QCD with a single fermion in the antisymmetric (or symmetric) tensor representation, are equivalent in the $N\to\infty$ limit. If true, this correspondence can provide useful insight into properties of real QCD (with fundamental representation fermions), such as predictions [with O(1/N) corrections] for the non-perturbative vacuum energy, the chiral condensate, and a variety of other observables. Several papers asserting to have proven this large N ``orientifold equivalence'' have appeared. By considering theories compactified on $R^3 \times S^1$, we show explicitly that this large N equivalence fails for sufficiently small radius, where our analysis is reliable, due to spontaneous symmetry breaking of charge conjugation symmetry in QCD with an antisymmetric (or symmetric) tensor representation fermion. This theory is also chirally symmetric for small radius, unlike super-Yang-Mills. The situation is completely analogous to large-N equivalences based on orbifold projections: simple symmetry realization conditions are both necessary and sufficient for the validity of the large N equivalence. Whether these symmetry realization conditions are satisfied depends on the specific non-perturbative dynamics of the theory under consideration. Unbroken charge conjugation symmetry is necessary for validity of the large N orientifold equivalence. Whether or not this condition is satisfied on $R^4$ (or $ R^3 \times S^1$ for sufficiently large radius) is not currently known.

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, 7,131 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.89 · human participants 0.01 · controlled comparison 0.21 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.84 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

It has been argued that the bosonic sectors of supersymmetric SU(N) Yang-Mills theory, and of QCD with a single fermion in the antisymmetric (or symmetric) tensor representation, are equivalent in the $N\to\infty$ limit. If true, this correspondence can provide useful insight into properties of real QCD (with fundamental representation fermions), such as predictions [with O(1/N) corrections] for the non-perturbative vacuum energy, the chiral condensate, and a variety of other observables. Several papers asserting to have proven this large N ``orientifold equivalence'' have appeared. By considering theories compactified on $R^3 \times S^1$, we show explicitly that this large N equivalence fails for sufficiently small radius, where our analysis is reliable, due to spontaneous symmetry breaking of charge conjugation symmetry in QCD with an antisymmetric (or symmetric) tensor representation fermion. This theory is also chirally symmetric for small radius, unlike super-Yang-Mills. The situation is completely analogous to large-N equivalences based on orbifold projections: simple symmetry realization conditions are both necessary and sufficient for the validity of the large N equivalence. Whether these symmetry realization conditions are satisfied depends on the specific non-perturbative dynamics of the theory under consideration. Unbroken charge conjugation symmetry is necessary for validity of the large N orientifold equivalence. Whether or not this condition is satisfied on $R^4$ (or $ R^3 \times S^1$ for sufficiently large radius) is not currently known.

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	It has been argued that the bosonic sectors of supersymmetric SU(N) Yang-Mills theory, and of QCD with a single fermion in the antisymmetric (or symmetric) tensor representation, are equivalent in the $N\to\infty$ limit.	background 1.00	0.04	0.04	hedged possibility 0.44
s1	If true, this correspondence can provide useful insight into properties of real QCD (with fundamental representation fermions), such as predictions [with O(1/N) corrections] for the non-perturbative vacuum energy, the chiral condensate, and a variety of other observables.	background 0.94	0.05	0.03	hedged possibility 0.95
s2	Several papers asserting to have proven this large N ``orientifold equivalence'' have appeared.	background 0.99	0.04	0.02	asserted 0.90
s3	By considering theories compactified on $R^3 \times S^1$, we show explicitly that this large N equivalence fails for sufficiently small radius, where our analysis is reliable, due to spontaneous symmetry breaking of charge conjugation symmetry in QCD with an antisymmetric (or symmetric) tensor representation fermion.	result 0.93	0.95	0.90	asserted 1.00
s4	This theory is also chirally symmetric for small radius, unlike super-Yang-Mills.	result 0.98	0.74	0.06	asserted 1.00
s5	The situation is completely analogous to large-N equivalences based on orbifold projections: simple symmetry realization conditions are both necessary and sufficient for the validity of the large N equivalence.	interpretation 0.93	0.52	0.21	asserted 1.00
s6	Whether these symmetry realization conditions are satisfied depends on the specific non-perturbative dynamics of the theory under consideration.	interpretation 0.88	0.21	0.09	asserted 0.97
s7	Unbroken charge conjugation symmetry is necessary for validity of the large N orientifold equivalence.	result 0.53	0.66	0.51	asserted 1.00
s8	Whether or not this condition is satisfied on $R^4$ (or $ R^3 \times S^1$ for sufficiently large radius) is not currently known.	gap 0.62	0.13	0.09	asserted 0.62

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

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

levels run

P abstract

not run

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

Figures

**Figure 1.** Z2 projections of SO(2N) N = 1 super-Yang-Mills theory, yielding either U(N) SYM, or U(N) QCD(AS). Both daughter theories have a charge conjugation symmetry which is a remnant of a Z2 gauge transformation in the parent theory; hence both daughter theories have twisted sectors corresponding to charge conjugation odd states. and a Majorana gluino λ. The parent theory has a discrete Z4N−4 chiral symmetry,8 which is the non-anomalous remnant of U(1)R symmetry. This Z4N−4 symmetry is spontaneously broken down to the Z2 of (−1)F (corresponding to fermion number modulo two) by the…

**Figure 2.** The one loop effective potential in QCD(AS/S), minus the irrelevant O(N) additive constant and divided by N(N−1)/(π 2L 4 ), as a function of the phase v of the Wilson line (when all eigenvalues coincide). There are two minima at v = π/2 and 3π/2. These two minima are exchanged by charge conjugation C, indicating that C breaks spontaneously in QCD(AS) on R 3 × S 1 when the circumference L is small compared to Λ−1 . For N = 1 SYM, the one loop potential identically vanishes. If L ≪ Λ −1 , so that g 2 (1/L) ≪ 1, then higher order corrections to the effective potential are small

**Figure 3.** Chiral condensates of N = 1 SYM (left) and QCD(AS/S) (right), for L ≪ Λ −1 . The N = 1 SYM theory has N chirally asymmetric vacuum states in which the fermion condensate hλλi has a non-zero magnitude and a phase equal to an integer multiple of 2π/N. In contrast, QCD(AS/S) has a chirally symmetric phase with vanishing chiral condensate. space is lifted by instanton and monopole contributions [37]. A nonperturbative superpotential is generated, and it provides a repulsive interaction between eigenvalues. Consequently, as shown in a nice treatment by Davies et al. [38, 39], in the…

**Figure 4.** Schematic phase diagram of U(N) N = 1 SYM (left) and QCD(AS/S) (right) as a function of temperature T and compactification size L of one spatial direction. N = 1 super-Yang-Mills has a confining low temperature phase in which the discrete chiral symmetry is spontaneously broken, and a deconfined high temperature phase with unbroken chiral symmetry. Charge conjugation is unbroken in both phases. QCD(AS/S) has multiple confining low temperature phases. For sufficiently small radius, L < LC, it spontaneously breaks charge conjugation symmetry. For sufficiently large radius, L > Lχ, it…

Figures reproduced from arXiv:hep-th/0608180 by the authors.

References

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View on Pith Pith review arXiv 2003
[40]

E. T. Tomboulis and L. G. Yaﬀe, Absence of chiral symmetry breaking at high temperatures , Phys. Rev. Lett. 52 (1984) 2115

View on Pith 1984
[41]

E. T. Tomboulis and L. G. Yaﬀe, Finite temperature SU (2) lattice gauge theory , Commun. Math. Phys. 100 (1985) 313

View on Pith 1985
[42]

N. Weiss, The wilson line in ﬁnite temperature gauge theories , Phys. Rev. D25 (1982) 2667

View on Pith 1982
[43]

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View on Pith 1981
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F. Sannino, Higher representations: Conﬁnement and large N , Phys. Rev. D72 (2005) 125006, [hep-th/0507251]

View on Pith Pith review arXiv 2005
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C. Alexandrou et. al. , The deconﬁnement phase transition in one-ﬂavor QCD , Phys. Rev. D60 (1999) 034504, [ hep-lat/9811028]

View on Pith Pith review arXiv 1999
[46]

A. Armoni, A. Gorsky, and M. Shifman, SpontaneousZ(2) symmetry breaking in the orbifold daughter of N = 1 super-Yang-Mills theory, fractional domain walls and vacu um structure , Phys. Rev. D72 (2005) 105001, [ hep-th/0505022]

View on Pith Pith review arXiv 2005
[47]

I. Bena, E. Gorbatov, S. Hellerman, N. Seiberg, and D. Shih, A note on (meta)stable brane conﬁgurations in MQCD , hep-th/0608157. – 23 –

View on Pith Pith review arXiv

Forward citations

Cited by 19 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
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Compactifying 4d gauge theories on a small T^2 with 't Hooft flux gives a calculable center-vortex description that reproduces confinement, chiral symmetry breaking, and vacuum structure, conjecturally connected to R^4.
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Adapting Rains's hyperbolic limit of elliptic hypergeometric integrals, the paper shows the Di Pietro-Komargodski high-temperature formula holds only when an effective potential for the gauge holonomies is positive se...
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If large-N QCD with adjoint fermions has both volume independence and a Hagedorn spectrum, it must develop an emergent fermionic symmetry that pairs bosonic and fermionic states.
The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
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On a small circle, QCD with adjoint fermions Higgses most simple gauge groups only partially, and neutral bion molecules generate Borel-plane singularities of order N closer to the origin than four-dimensional instant...

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A duality is established between 2d XY-spin models with Z_p symmetry-breaking perturbations and 4d SU(2) gauge theories with adjoint fermions on a small circle near the deconfinement temperature.
Non-perturbative volume-reduction of large-N QCD with adjoint fermions
hep-lat 2009-06 accept novelty 7.0 of 10

The single-site reduced large-N gauge theory with one adjoint Wilson fermion keeps its (Z_N)^4 center symmetry across a wide range of quark masses, including near the critical hopping parameter, so volume reduction is...
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A double-trace deformation of SU(N) Yang-Mills stabilizes center symmetry at all compactification radii, yielding both a valid single-site large-N reduced model and, at small N and small radius, an analytically solvab...
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A brane configuration in type 0B string theory is proposed as the UV completion of U(Nc) QCD3, yielding a Seiberg dual that reproduces the bosonization and symmetry-breaking phases.
Microscopic Structure of Magnetic Bions
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For SU(2) gauge theory with four massless adjoint Weyl fermions on a small circle, the next-to-leading semiclassical calculation makes the confinement mass gap an increasing function of the circle size.
Universality of Phases in QCD and QCD-like Theories
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In the large-Nc limit the phase diagrams of QCD at finite isospin density and of SO(2Nc) and Sp(2Nc) gauge theories at finite baryon density coincide, and outside the BEC-BCS crossover they also match ordinary QCD at ...
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Large-N volume independence extends to conformal gauge theories: with unbroken center symmetry, compactification radii drop out of leading large-N observables, so a conformal theory keeps its infinite correlation leng...
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Lattice simulation of SU(3) with two adjoint Dirac flavors finds four center-symmetry phases as the compactified dimension shrinks, with an intermediate deconfined phase separating the large- and small-volume confined...
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Volume independence in large Nc gauge theories is recast as orbifold equivalence and combined with orientifold equivalence to relate infinite-volume QCD(AS) to a single-site matrix model of QCD(Adj).
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For every simple gauge group except SU(2), softly broken N=1 super Yang-Mills on a small circle undergoes a first-order transition as the gaugino mass grows, mirroring thermal deconfinement in pure Yang-Mills.
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For Nf = 2 QCD on Nt = 4 lattices, the Roberge-Weiss endpoint is first order at small and large quark masses and second order for intermediate masses, with tricritical masses am = 0.043(5) and am = 0.72(8).
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How the literature uses it

43 arXiv papers cite this in 70 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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States a conflicting result 2 papers

We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to N=1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory.

Exact Results in Non-Supersymmetric Large N Orientifold Field Theories · 0.87
Therefore, regarding orientifold planar equivalence, we argue that in the one-loop approximation C-breaking in QCD(AS/S,+) resulting from the application of PBC to fermions does not invalidate the large N equivalence with QCD(Adj,-).

Phase diagrams of SU(N) gauge theories with fermions in various representations · 0.81

Papers citing it · 51 sentences without a confident label

Uses its method or tool 2 papers

The proof is based on the orientifold planar equivalence as formulated in terms of the coherent states [ref] .

Domain Walls and Metastable Vacua in Hot Orientifold Field Theories · Introduction · 0.96
An easy way to see this is to evaluate the one-loop Coleman–Weinberg effective potential induced by quantum fluctuations by using the background field method (e.g. [ref] ).

QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations · Appendix: Center stabilization · 0.98

Cites it as support 1 paper

At the same time, the validity of planar equivalence with $=1$ SQCD at large $N$ requires [ref] the absence of closed string tachyons.

Non-Supersymmetric Seiberg Duality, Orientifold QCD and Non-Critical Strings · Embedding in string theory · 0.99

Cites it as background 15 papers

A necessary and sufficient condition for the equivalence to hold is the non-breaking of charge conjugation symmetry [ref] (this condition is equivalent to the absence of closed string tachyons in the string realisation of the theory [ref] ).

Lattice Study of Planar Equivalence: The Quark Condensate · Introduction · 0.82
Interesting examples of equivalences are: (i) those relating a theory on an infinite lattice to a theory on a finite-size lattice, or even on a single-site lattice, (unitary matrix model) [ref] ; or (ii) in the continuum, relating a theory on $^d$ to a theory compactified on $^d-k ×(S^1)^k$; or (iii) equivalences relating a supersymmetric theory to a non-supersymmetric one [ref] .

New Methods in QFT and QCD: From Large-N Orbifold Equivalence to Bions and Resurgence · Large-$N$ Orbifold and Orientifold Equivalences · 0.84
Going back to the correspondence with the critical properties of $SU(3)$ lattice gauge theories, switching the sign of $h$ is like turning the boundary conditions of dynamical fermions in the temporal direction from anti-periodic to periodic: fermions are not thermal any more and the Euclidean temporal direction can then be viewed as a compactified spatial direction; the effective coupling to the Polyakov line changes sign, so that the Polyakov line tends to align along one of the complex center elements below a given compactification radius, thus breaking spontaneously the residual charge symmetry (see Refs. [ref] for early lattice studies of the associated transition, which has been studied in the context of orientfold planar equivalence [ref] ).

The three-dimensional, three state Potts model in a negative external field · Introduction · 0.84

Discussion

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