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Adding baryonic superpotential terms drives a 4d SU(N) model from a mixed phase to a non-Abelian free magnetic phase, and the construction descends to new 3d and 2d dualities.

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2026-08-03 17:07 UTC pith:VE2W3O6H

load-bearing objection New 3d SU/SO dualities are solid and worth proving; the new 2d dualities rest on 4d index checks the paper skips, so the paper is conditionally acceptable. the 6 major comments →

arxiv 2512.10495 v2 pith:VE2W3O6H submitted 2025-12-11 hep-th

Six Easy Pieces: interplays among dualities in 4d, 3d and 2d

Antonio Amariti , Pietro Glorioso , Chiara Mascherpa , Andrea Zanetti This is my paper
classification hep-th
keywords supersymmetric gauge theorieselectric-magnetic dualitymixed phasetensor deconfinementbaryonic deformationssuperconformal index3d and 2d dualitiessymplectic and orthogonal gauge groups
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies four-dimensional supersymmetric SU(N) gauge theories with N+1 fundamentals, five antifundamentals, and a conjugate antisymmetric tensor, which earlier work found to flow to a mixed phase: a low-energy spectrum split between an interacting sector and a free magnetic sector. Its central claim is that adding certain baryonic superpotential terms, irrelevant in the ultraviolet but dangerously irrelevant along the renormalization-group flow, erases the interacting sector and sends the theory to a non-Abelian free magnetic phase, described by a dual symplectic USp(2) gauge theory. The main construction is tensor deconfinement, replacing the antisymmetric tensor by a strongly coupled auxiliary gauge group and then dualizing the original SU(N) node, yielding intermediate dualities between SU(N) and USp(2M) SQCD. Only these intermediate dualities admit the reduction to 2d, while the 3d reduction, through circle compactification, freezing of mass parameters, and the duplication formula for hyperbolic Gamma functions, produces new dualities between SU(N) with a symmetric tensor plus monopole superpotential and SO(N−1), SO(N), or SO(N+1) SQCD. A reader will care because the paper turns a subtle mixed-phase behavior into an ordinary electric/magnetic duality and exports that structure to lower dimensions, where some of the resulting 2d dualities are new.

Core claim

The paper claims that each of the six baryonic deformations (three for SU(2n), three for SU(2n+1)) drives the low-energy theory from the mixed phase of the undeformed model to a non-Abelian free magnetic phase. The final magnetic description is a USp(2) symplectic gauge theory with vector matter and singlet fields, reached through an intermediate SU(N) ↔ USp(2M) duality with 2M+6 fundamentals. That intermediate duality is obtained by two routes: canonical deconfinement of the conjugate antisymmetric through a symplectic node, or a non-canonical route that introduces a second SU(N) node and follows the Higgsing triggered by the baryonic deformation. The 4d claims are checked against the super

What carries the argument

Tensor deconfinement: replace a two-index tensor of one gauge group by mesons and baryons of an auxiliary gauge group that is assumed to s-confine, i.e. confine with a non-trivial superpotential at a higher scale, so the original group acts as a flavor symmetry. This is the move that turns the antisymmetric-tensor models into ordinary SQCD with an extra node, and it is reused in 3d, where the symmetric tensor is deconfined by an SO(N−1), SO(N), or SO(N+1) node. The other workhorse is the duplication formula for hyperbolic Gamma functions, an identity that converts antisymmetric-tensor one-loop factors on a squashed three-sphere into symmetric-tensor factors and maps the dual symplectic group

Load-bearing premise

The load-bearing premise is that the four-dimensional superconformal-index identities for the baryon-deformed dualities are correct even though the paper omits them (Section 2.1.1 after Eq. (2.6) and Section 2.2.1 after Eq. (2.31)), and that the omitted index evaluation for the alternative deconfinement route (Section 2.1.2) also goes through; the 3d and 2d reductions inherit their validity from these 4d identities, and only the 3d dualities receive an independent proof.

What would settle it

Compute the superconformal-index identity for the SU(4) model with the baryonic deformation (2.2), comparing the electric index against the claimed USp(2) magnetic dual with eight fundamentals, using the elliptic hypergeometric beta integral; an exact or numerical mismatch at low orders in the fugacity expansion would falsify the 4d duality and, because the reduction chain starts there, the derived 2d dualities as well.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the six baryonic deformations are dangerously irrelevant as claimed, each mixed-phase electric theory acquires an infrared-free magnetic description, so the final endpoint is an ordinary electric/magnetic pair rather than a split interacting-plus-free phase.
  • The intermediate SU(N) ↔ USp(2M) dualities, not the final USp(2) phase, are the ones that admit a twisted compactification to 2d with non-negative integer R-charges; this pins down which 4d models can serve as parents of 2d dualities.
  • The 2d reduction of the SU(2n) model with deformation (2.2) yields a family of dualities between SU(2n) with a conjugate antisymmetric and USp(2n−2) gauge theories containing chiral and Fermi matter with specified J-terms; some of these dualities had appeared before, while others are new.
  • The 3d reduction, after freezing mass parameters and applying the duplication formula, produces unified dualities for generic N between SU(N) with a symmetric tensor plus monopole superpotential and SO(N−1), SO(N), or SO(N+1) SQCD; these are re-derived by tensor deconfinement in Section 4.7, so they do not depend on the omitted 4d index steps.
  • Further dualizing the 3d orthogonal duals gives SO(3) gauge theories with vectors, matching the direct reduction of the 4d USp(2) phase, so the 3d web closes consistently.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • A natural next step, not taken here, is to evaluate explicitly one of the omitted superconformal-index identities for a small-rank example; that would convert the 'straightforward' assertion into a proof and independently certify the 2d chain, which currently inherits its validity from the 4d identity.
  • The same baryon-deformation logic would likely apply to the larger-flavor mixed-phase models mentioned in the introduction; the paper itself points to increasing the number of fundamentals and antifundamentals as the route toward 4d SU/orthogonal dualities, of which the 3d ones found here would be the reduction.
  • One specific gap the paper flags is that it could not find a 4d parent for a known 2d gauge/Landau-Ginzburg duality with N+2 fundamentals and a conjugate antisymmetric; this suggests the flavor-count threshold for realizing that 2d duality from 4d lies just above the models studied here.
  • The 3d proof via SO deconfinement is self-contained, so the 3d dualities are the most secure output; if the 4d index checks were later completed and passed, the same proof could be rerun in reverse to turn the 4d claims into a theorem.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

6 major / 4 minor

Summary. The paper studies 4d N=1 SU(N) gauge theories with N+1 fundamentals, five antifundamentals, and a conjugate antisymmetric tensor, which were previously shown to be in a mixed phase. It proposes that the baryonic deformations (2.1)-(2.3) and (2.26)-(2.28) drive these theories to a non-Abelian free magnetic phase, with intermediate USp(2M) SQCD dualities that can be reduced to 2d and 3d. In 3d, after freezing mass parameters and applying the duplication formula, the paper proposes new dualities between SU(N) with a symmetric tensor plus monopole superpotential and SO(N-1), SO(N), or SO(N+1) SQCD, and provides a tensor-deconfinement proof in Section 4.7. In 2d it recovers known dualities and proposes new SU/USp dualities, though the detailed analysis is largely restricted to one deformation.

Significance. If the central 4d index identities are valid, the paper provides a coherent web of dualities across 4d, 3d, and 2d. Its strengths include explicit 3d sphere partition function identities, a systematic use of the duplication formula, and an independent deconfinement argument for the new 3d dualities. The paper does not rely on numerical fitting and formulates its claims in a falsifiable way. However, the 4d superconformal index identities that seed the lower-dimensional reductions are not shown, and the 2d dualities are not independently derived. These gaps make the overall claim conditional rather than self-contained.

major comments (6)
  1. [Section 2.1.1 after Eq. (2.6); Section 2.2.1 after Eq. (2.31)] The 4d superconformal index identities that establish the dualities are asserted but not displayed. The text says "The derivation is straightforward and we skip the details." These identities are load-bearing: the 3d reductions in Section 4 are obtained from them (e.g., Eqs. (4.1), (4.10), (4.15), (4.26), (4.34)) and the 2d dualities in Section 3 rely on the same 4d parent. Please provide the explicit elliptic hypergeometric identities, at least in an appendix, or give an independent derivation. This is the central missing support for the paper's main claims.
  2. [Section 2.1.2, Eqs. (2.16)-(2.18)] The Higgs-flow evaluation of the superconformal index is omitted, with a reference to [36] and the statement that the details are "identical to the ones extensively discussed in [36]." Since the alternative deconfinement is used to confirm the canonical result, a precise map of variables and contour-pinching steps should be given, or the corresponding identity should be written out. As it stands, this is an unverified check.
  3. [Section 4.7, Cases I-III] The independent proof of the new 3d dualities assumes without demonstration that "the SU(N) gauge group is confining" after deconfining the symmetric tensor. This step is load-bearing because it is the only independent support for the 3d dualities, and it is not evident which known confining duality is being invoked. Please identify the precise SU(N) confining duality (field content, superpotential, and operator map) or provide a proof.
  4. [Sections 2.1.2 and 2.2.2] The alternative deconfinement is explicitly described as "ad hoc" and the Higgsing operator is chosen to reproduce the expected USp(2M) dual. This makes the derivation circular if it is presented as evidence for the duality. It is acceptable as a consistency check, but the text should state this explicitly and should not present the alternative route as an independent derivation. The canonical deconfinement in Sections 2.1.1 and 2.2.1 should carry the logical weight.
  5. [Section 3, Eq. (3.1)] The detailed 2d analysis is carried out only for SU(2n) with deformation (2.2). The text says "The generalization to the other SU(2n) and SU(2n+1) models is straightforward and we leave the analysis to the interested reader." Yet the abstract and introduction claim new 2d dualities more broadly. Please either state the final dualities for the remaining deformations or restrict the claim to the case actually analyzed.
  6. [Section 4.6] The opening line of Section 4.6 says the 4d parent has superpotential W = \tilde A^{n-1}\tilde Q_5, which does not match any of the deformations (2.26)-(2.28). Later in the same section the final superpotential is written as \tilde S^{2n-1}\tilde Q_1^2\tilde Q_2^2, so the intended 4d parent is unclear. Please correct this inconsistency, since it affects the identification of the 3d duality being derived.
minor comments (4)
  1. [Introduction, Section 2] There are several typos and grammatical slips: "a-mazimization" should be "a-maximization"; "in addition fo flippers" should be "in addition to flippers"; "avoding" should be "avoiding". The phrase "ad hoc" appears repeatedly; a less colloquial term would be more appropriate in a formal paper.
  2. [Notation and formatting] The unified duality tables in Section 4 use notation such as "1 □ □˜S" and "□ □˜S" that is not defined before first use. Please add a short explanation of the table notation.
  3. [Section 3] The paper relies on same-author results [15] and [40] for the 2d LG dualities used as building blocks. This is not a defect, but the places where these external results are essential should be flagged more explicitly, especially because the derived dualities are claimed to be new.
  4. [Section 2.2.3] The comparison with the literature for the odd-rank case is compressed; a formula or reference number for the dual superpotential of [20,24] would help the reader verify the operator map.

Circularity Check

2 steps flagged

No definitional circularity, but the new 2d dualities are conditional on an unproven 4d index identity and are assembled from same-author 2d results; the 3d chain is independently supported.

specific steps
  1. self citation load bearing [Section 3.3, second [V,X] case ('2n fundamental and 3 antifundamental chirals')]
    "In this case, the SU(2n) theory is dual to the LG model discussed in Appendix A.1 of [40] and in the dual phase the constraint forbidding the axial symmetry for the USp(2n−2) model is lifted."

    This step is load-bearing for the new 2d SU/USp dualities: the SU(2n)→LG duality is imported from [40], a previous paper with overlapping authors (Amariti, Glorioso, Mantegazza, Morgante, Zanetti), and the deconfinement of the antisymmetric is likewise quoted from [15] (same four authors as the present work). The paper does not reproduce or independently verify these 2d dualities here; it uses them as the engine that produces the claimed new dual phase. If [15]/[40] were unsound, the new [V,X] dualities would not be established. This is self-citation doing load-bearing work, though not a definitional equivalence: the 3d section later gives an independent deconfinement proof.

  2. other [Section 3, introductory paragraph before table (3.1)]
    "Supposing the 4d index matches across a duality, the choice of non-negative Rcharges restricts the matching of the 2d elliptic genera to the zero flux sector. The matching of the 2d elliptic genera then follows from the matching of the 4d twisted indices in the zero flux sector. On the other hand, proving the matching of the elliptic genera by independent arguments provides additional support to our assumption of a matching between the 4d indices."

    The 2d dualities are presented as derived, but the derivation is explicitly conditional on an unstated 4d superconformal-index identity. In Sections 2.1.1 and 2.2.1 that identity is asserted with 'The derivation is straightforward and we skip the details', and Section 2.1.2 defers the pole evaluation to [36]. The text here calls the 4d matching an 'assumption' and treats an independent 2d proof only as 'additional support'. Thus the new 2d dualities are not independent first-principles results; they inherit the status of the unproven 4d input. This is a load-bearing gap rather than a definitional circularity.

full rationale

There is no numerical fitting, no fitted parameter renamed as a prediction, and no step that reduces to its own definition by construction. The central 3d SU/SO dualities receive an independent derivation in Section 4.7 via tensor deconfinement from the external ortho-symplectic confining duality of [4], so those claims do not rest on the paper's own conclusions. The 'ad hoc' deconfinements in Section 2 are transparently constructions chosen to reproduce an expected USp(2M) phase; while that weakens their status as independent predictions, it is not circular. The main circularity-adjacent issues are: (i) the 4d superconformal-index identities, which are the base of the 2d and part of the 3d reduction chain, are never displayed and are deferred to 'straightforward' derivations or to a same-author reference [36]; and (ii) the new 2d dualities are assembled from 2d LG and confining dualities taken from [15] and [40], both with overlapping authorship. Because the paper explicitly labels the 4d match an 'assumption' and because the 3d proof is independent, the appropriate score is moderate: some self-citation is load-bearing and some results are conditional, but the derivation is not circular by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 7 axioms · 0 invented entities

No numerical fits to data are involved. The ledger entries are structural choices (auxiliary group ranks, frozen masses, R-charge assignments) chosen by hand to make the deconfinement/reduction produce the claimed dualities. The physical axioms are standard dualities and reduction prescriptions from the literature; the paper does not derive them, and the most important omissions are flagged.

free parameters (3)
  • Auxiliary USp(2m) rank in canonical deconfinement = m = n−2, n−1, n for SU(2n) deformations (2.1)-(2.3); m = n−1, n, n+1 for SU(2n+1) deformations (2.26)-(2.28)
    Chosen by hand per baryonic deformation so that the tensor deconfinement quiver s-confines; not derived from an independent principle, though representation theory fixes it. See Sections 2.1.1 and 2.2.1.
  • Frozen mass assignments in 3d reduction = ν3=τ_S/2, ν4=ω1/2+τ_S/2, ν5=ω2/2+τ_S/2 (Section 4.1); variants in (4.22) and (4.28)
    These specific mass values are chosen so the duplication formula (4.4) converts antisymmetric tensors into symmetric tensors and USp groups into SO groups. The resulting dualities depend on this choice.
  • R-charge assignments in 2d reduction = Assignments such as R(\tilde Q_{4,5})=1, R(Q_{2n+1})=2, R(\tilde Q_5)=2, etc., summarized in table (3.1)
    Discrete choices of non-negative integer R-charges select which 2d dualities emerge: [X,X], [X,V], [V,X], or [V,V]. The paper does not derive these assignments from a uniqueness principle.
axioms (7)
  • domain assumption Seiberg duality for SU(N_c) SQCD and Intriligator-Pouliot duality for USp(2N) are valid.
    Standard 4d N=1 dualities used throughout the deconfinement chains; cited as [21] and [22].
  • domain assumption s-confining and flipped-confining dualities for SU(N) with N+1 flavors and for USp(2N) with 2N+4 flavors are valid.
    Used to confine nodes after deconfinement in Sections 2.1.1 and 2.2.1; not re-derived in this paper.
  • domain assumption Ortho-symplectic confining duality: SO(N) with N+1 vectors and a monopole superpotential confines to a WZ model with symmetric meson S=v^2 and baryons q=v^N.
    External result from [4] used to deconfine the symmetric tensor in the proof of the 3d dualities in Section 4.7.
  • domain assumption ARSW reduction of 4d dualities to 3d sphere partition functions, including KK monopole superpotential corrections, is valid.
    Used for all 3d identities in Section 4; cited as [32].
  • standard math Duplication formula (4.4) for hyperbolic Gamma functions is a valid mathematical identity.
    Used to turn antisymmetric tensors into symmetric tensors and USp groups into SO groups; no physical input beyond its algebraic validity.
  • domain assumption The freezing prescription for mass parameters, and its effect of converting antisymmetric to symmetric tensors and USp to SO, maps 3d dualities beyond the level of partition-function identities.
    Invoked in Sections 4.1-4.6 following [33-35]; the physical interpretation is not proved independently except by the subsequent deconfinement proof.
  • domain assumption Twisted S^2 reduction to 2d with integer non-negative R-charges, together with nonperturbative constraints forbidding axial symmetries, correctly yields 2d N=(0,2) dualities.
    Used in Section 3; cited as [31] and [15,39,40]. The paper itself notes it does not have a pure field-theoretical explanation for those constraints.

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0 comments
read the original abstract

In this paper we consider 4d $\mathcal{N}=1$ $\mathrm{SU}(N)$ gauge theories with $N+1$ fundamentals, five antifundamentals and a conjugate two index antisymmetric tensor. The model has been shown to be in a mixed phase in the IR, splitting in an interacting non-Abelian Coulomb phase and a free magnetic phase. Through tensor deconfinement, we show that baryonic deformations lead to a non-Abelian free magnetic phase. Along the analysis we obtain a duality with symplectic SQCD that can be further reduced to 3d and 2d. In the 3d case the analysis of the three sphere partition function allows one to obtain dualities between $\mathrm{SU}(N)$ with a two index symmetric tensor and $\mathrm{SO}(N)$ theories. On the other hand, in 2d we recover dualities already known in the literature and propose new ones between special unitary and symplectic gauge theories.

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Reference graph

Works this paper leans on

43 extracted references · 39 linked inside Pith

  1. [1]

    Pasquetti and M

    S. Pasquetti and M. Sacchi,From 3ddualities to 2dfree field correlators and back, JHEP11(2019) 081 [1903.10817]

    Pith/arXiv arXiv 2019

  2. [2]

    Benvenuti, I

    S. Benvenuti, I. Garozzo and G. Lo Monaco,Monopoles and dualities in 3dN= 2 quivers,JHEP10(2021) 191 [2012.08556]

    Pith/arXiv arXiv 2021

  3. [3]

    Etxebarria, B

    I.G. Etxebarria, B. Heidenreich, M. Lotito and A.K. Sorout,DeconfiningN= 2 SCFTs or the art of brane bending,JHEP03(2022) 140 [2111.08022]

    Pith/arXiv arXiv 2022

  4. [4]

    Benvenuti and G

    S. Benvenuti and G. Lo Monaco,A toolkit for ortho-symplectic dualities,JHEP09 (2023) 002 [2112.12154]

    Pith/arXiv arXiv 2023

  5. [5]

    Bottini, C

    L.E. Bottini, C. Hwang, S. Pasquetti and M. Sacchi,Dualities from dualities: the sequential deconfinement technique,JHEP05(2022) 069 [2201.11090]

    Pith/arXiv arXiv 2022

  6. [6]

    Bajeot and S

    S. Bajeot and S. Benvenuti,Sequential deconfinement and self-dualities in 4dN= 1 gauge theories,JHEP10(2022) 007 [2206.11364]

    Pith/arXiv arXiv 2022

  7. [7]

    Bajeot and S

    S. Bajeot and S. Benvenuti,4dN= 1 dualities from 5d dualities,JHEP08(2024) 197 [2212.11217]

    Pith/arXiv arXiv 2024

  8. [8]

    Amariti and S

    A. Amariti and S. Rota,3d N=2 SO/USp adjoint SQCD: s-confinement and exact identities,Nucl. Phys. B987(2023) 116068 [2202.06885]

    Pith/arXiv arXiv 2023

  9. [9]

    Amariti, F

    A. Amariti, F. Mantegazza and D. Morgante,Sporadic dualities from tensor deconfinement,JHEP05(2024) 188 [2307.14146]

    Pith/arXiv arXiv 2024

  10. [10]

    Amariti and F

    A. Amariti and F. Mantegazza,A new 4dN= 1 duality from the superconformal index,JHEP06(2024) 206 [2402.00609]

    Pith/arXiv arXiv 2024

  11. [11]

    Jiang, S

    J. Jiang, S. Nawata and J. Zheng,2d dualities from 4d,2407.17350

    Pith/arXiv arXiv

  12. [12]

    Amariti and F

    A. Amariti and F. Mantegazza,Confinement for 3dN= 2SU(N)with a Symmetric tensor,2405.11972

    Pith/arXiv arXiv

  13. [13]

    Benvenuti, R

    S. Benvenuti, R. Comi, S. Pasquetti and M. Sacchi,Deconfinements, Kutasov-Schwimmer dualities andDp[SU(N)]theories,2407.11134

    Pith/arXiv arXiv

  14. [14]

    Hwang and S

    C. Hwang and S. Kim,S-confinement of 3d Argyres-Douglas theories and the Seiberg-like duality with an adjoint matter,2407.11129

    Pith/arXiv arXiv

  15. [15]

    Amariti, P

    A. Amariti, P. Glorioso, C. Mascherpa and A. Zanetti,On the zoology of 2d N= (0,2)dualities gauge theories with antisymmetric matter,2504.16544

    arXiv

  16. [16]

    Amariti, F

    A. Amariti, F. Mantegazza and S. Rota,Rank-two tensors and deconfinement in 3d N= 2SU(N)gauge theories,2504.21654

    Pith/arXiv arXiv

  17. [17]

    Jia and S

    Q. Jia and S. Kim,Classification of monopole deformed 3dN= 2Seiberg-like duality with an adjoint matter,2507.04950

    arXiv

  18. [18]

    Berkooz,The Dual of supersymmetric SU(2k) with an antisymmetric tensor and composite dualities,Nucl

    M. Berkooz,The Dual of supersymmetric SU(2k) with an antisymmetric tensor and composite dualities,Nucl. Phys. B452(1995) 513 [hep-th/9505067]. – 42 –

    Pith/arXiv arXiv 1995

  19. [19]

    M.A. Luty, M. Schmaltz and J. Terning,A Sequence of duals for Sp(2N) supersymmetric gauge theories with adjoint matter,Phys. Rev. D54(1996) 7815 [hep-th/9603034]

    Pith/arXiv arXiv 1996

  20. [20]

    Pouliot,Duality in SUSY SU(N) with an antisymmetric tensor,Phys

    P. Pouliot,Duality in SUSY SU(N) with an antisymmetric tensor,Phys. Lett. B367 (1996) 151 [hep-th/9510148]

    Pith/arXiv arXiv 1996

  21. [21]

    Seiberg,Electric - magnetic duality in supersymmetric nonAbelian gauge theories, Nucl

    N. Seiberg,Electric - magnetic duality in supersymmetric nonAbelian gauge theories, Nucl. Phys. B435(1995) 129 [hep-th/9411149]

    Pith/arXiv arXiv 1995

  22. [22]

    Intriligator and P

    K.A. Intriligator and P. Pouliot,Exact superpotentials, quantum vacua and duality in supersymmetric SP(N(c)) gauge theories,Phys. Lett. B353(1995) 471 [hep-th/9505006]

    Pith/arXiv arXiv 1995

  23. [23]

    Bajeot and S

    S. Bajeot and S. Benvenuti,S-confinements from deconfinements,JHEP11(2022) 071 [2201.11049]

    Pith/arXiv arXiv 2022

  24. [24]

    Terning,Duals for SU(N) SUSY gauge theories with an antisymmetric tensor: Five easy flavors,Phys

    J. Terning,Duals for SU(N) SUSY gauge theories with an antisymmetric tensor: Five easy flavors,Phys. Lett. B422(1998) 149 [hep-th/9712167]

    Pith/arXiv arXiv 1998

  25. [25]

    Csaki, P

    C. Csaki, P. Meade and J. Terning,A Mixed phase of SUSY gauge theories from a maximization,JHEP04(2004) 040 [hep-th/0403062]

    Pith/arXiv arXiv 2004

  26. [26]

    Barnes, K.A

    E. Barnes, K.A. Intriligator, B. Wecht and J. Wright,N=1 RG flows, product groups, and a-maximization,Nucl. Phys. B716(2005) 33 [hep-th/0502049]

    Pith/arXiv arXiv 2005

  27. [27]

    Kutasov, A

    D. Kutasov, A. Parnachev and D.A. Sahakyan,Central charges and U(1)(R) symmetries in N=1 superYang-Mills,JHEP11(2003) 013 [hep-th/0308071]

    Pith/arXiv arXiv 2003

  28. [28]

    Craig, R

    N. Craig, R. Essig, A. Hook and G. Torroba,New dynamics and dualities in supersymmetric chiral gauge theories,JHEP09(2011) 046 [1106.5051]

    Pith/arXiv arXiv 2011

  29. [29]

    Craig, R

    N. Craig, R. Essig, A. Hook and G. Torroba,Phases of N=1 supersymmetric chiral gauge theories,JHEP12(2011) 074 [1110.5905]

    Pith/arXiv arXiv 2011

  30. [30]

    Kutasov, A

    D. Kutasov, A. Schwimmer and N. Seiberg,Chiral rings, singularity theory and electric - magnetic duality,Nucl. Phys. B459(1996) 455 [hep-th/9510222]

    Pith/arXiv arXiv 1996

  31. [31]

    Gadde, S.S

    A. Gadde, S.S. Razamat and B. Willett,On the reduction of 4dN= 1theories on S2,JHEP11(2015) 163 [1506.08795]

    Pith/arXiv arXiv 2015

  32. [32]

    Aharony, S.S

    O. Aharony, S.S. Razamat, N. Seiberg and B. Willett,3d dualities from 4d dualities, JHEP07(2013) 149 [1305.3924]

    Pith/arXiv arXiv 2013

  33. [33]

    H.-C. Kim, M. Kim, S.-S. Kim and G. Zafrir,Superconformal indices for non-Lagrangian theories in five dimensions,JHEP03(2024) 164 [2307.03231]

    Pith/arXiv arXiv 2024

  34. [34]

    Hayashi, S.-S

    H. Hayashi, S.-S. Kim, K. Lee and F. Yagi,Seiberg-Witten curves with O7-planes, JHEP11(2023) 178 [2306.11631]

    Pith/arXiv arXiv 2023

  35. [35]

    S.-S. Kim, X. Li, S. Nawata and F. Yagi,Freezing and BPS jumping,JHEP05 (2024) 340 [2403.12525]

    Pith/arXiv arXiv 2024

  36. [36]

    Amariti, F

    A. Amariti, F. Mantegazza, S. Rota and A. Zanetti,A - BCD dualities,2510.19966. – 43 –

    arXiv

  37. [37]

    Benini and A

    F. Benini and A. Zaffaroni,A topologically twisted index for three-dimensional supersymmetric theories,JHEP07(2015) 127 [1504.03698]

    Pith/arXiv arXiv 2015

  38. [38]

    Closset and I

    C. Closset and I. Shamir,TheN= 1Chiral Multiplet onT 2 ×S 2 and Supersymmetric Localization,JHEP03(2014) 040 [1311.2430]

    Pith/arXiv arXiv 2014

  39. [39]

    Sacchi,New 2dN= (0, 2) dualities from four dimensions,JHEP12(2020) 009 [2004.13672]

    M. Sacchi,New 2dN= (0, 2) dualities from four dimensions,JHEP12(2020) 009 [2004.13672]

    Pith/arXiv arXiv 2020

  40. [40]

    Amariti, P

    A. Amariti, P. Glorioso, F. Mantegazza, D. Morgante and A. Zanetti,Dualities from dualities in 2d N=(0,2),Nucl. Phys. B1018(2025) 117005 [2410.12453]

    arXiv 2025

  41. [41]

    Csaki, M

    C. Csaki, M. Schmaltz and W. Skiba,Confinement in N=1 SUSY gauge theories and model building tools,Phys. Rev. D55(1997) 7840 [hep-th/9612207]

    Pith/arXiv arXiv 1997

  42. [42]

    Aharony, S.S

    O. Aharony, S.S. Razamat, N. Seiberg and B. Willett,3ddualities from 4ddualities for orthogonal groups,JHEP08(2013) 099 [1307.0511]

    Pith/arXiv arXiv 2013

  43. [43]

    Nii,Duality and Confinement in 3dN= 2”chiral”SU(N)gauge theories,Nucl

    K. Nii,Duality and Confinement in 3dN= 2”chiral”SU(N)gauge theories,Nucl. Phys. B939(2019) 507 [1809.10757]. – 44 –

    Pith/arXiv arXiv 2019