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arxiv: 2604.20750 · v1 · submitted 2026-04-22 · 🧮 math.RT · hep-th· math-ph· math.MP· math.QA

Universal 2-parameter mathcal{N}=2 supersymmetric mathcal{W}_(infty)-algebra

Thomas Creutzig , Volodymyr Kovalchuk , Andrew R. Linshaw , Arim Song , Uhi Rinn Suh This is my paper

Pith reviewed 2026-05-09 22:27 UTC · model grok-4.3

classification 🧮 math.RT hep-thmath-phmath.MPmath.QA
keywords vertex algebrasN=2 supersymmetryW-algebrasY-algebrassuperconformal algebracoset realizationsrationalitymodule categories
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The pith

A universal two-parameter vertex algebra extends the N=2 superconformal algebra and realizes its conjectured dualities.

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

The paper proves the existence of a universal two-parameter vertex algebra that extends the N=2 superconformal algebra by adding four generators of weights i, i plus one-half, i plus one-half, and i plus one for every integer i above 1. This algebra functions as a classifying object whose one-parameter quotients are the N=2 supersymmetric Y-algebras. The work establishes the three-way dualities among these quotients that were previously conjectured, including a coset construction for the principal W-algebras of the superalgebra sl_{n+1|n}. As a direct consequence, the algebras become strongly rational at the parameter values k equal to minus one plus one over n plus a plus one, with their module categories fully described, extending the known case of N=2 minimal models.

Core claim

We prove that the universal 2-parameter N=2 supersymmetric W_infty algebra exists as an extension of the N=2 superconformal algebra with the four additional generators in weights i, i+1/2, i+1/2, i+1 for each i>1, and that its 1-parameter quotients satisfy the dualities conjectured by Prochazka and Rapcak, with the special case yielding the coset realization of W^k(sl_{n+1|n}) and the strong rationality of W_k(sl_{n+1|n}) for k = -1 + 1/(n+a+1) together with a description of its module category.

What carries the argument

The universal 2-parameter vertex algebra W^{N=2}_∞, which classifies all N=2 supersymmetric extensions of the superconformal algebra by serving as the source of all its one-parameter quotients under mild hypotheses.

If this is right

  • All N=2 supersymmetric Y-algebras arise as quotients of the universal algebra.
  • The three-way dualities hold among the family of N=2 supersymmetric Y-algebras.
  • The principal W-algebra W^k(sl_{n+1|n}) admits an explicit coset realization as one of these quotients.
  • The algebras W_k(sl_{n+1|n}) are strongly rational for every positive integer n and a at the parameter k = -1 + 1/(n+a+1), and their module categories are completely described.

Where Pith is reading between the lines

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

  • The same universality and duality pattern may extend to other supersymmetric vertex algebras beyond the N=2 case.
  • The rationality results open the possibility of constructing new families of rational conformal field theories with extended supersymmetry.
  • The module category descriptions could be used to compute fusion rules or characters for these algebras at the rational points.
  • Explicit checks of the generator relations for low values of n and a would provide independent numerical support for the dualities.

Load-bearing premise

The vertex algebras arise as quotients of the universal algebra under mild hypotheses that allow the technical results on representations of vertex operator superalgebras to apply.

What would settle it

A direct calculation of the relations among the additional generators for any fixed small value of the continuous parameters that produces an inconsistency with one of the conjectured dualities or with the coset realization would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.20750 by Andrew R. Linshaw, Arim Song, Thomas Creutzig, Uhi Rinn Suh, Volodymyr Kovalchuk.

Figure 1
Figure 1. Figure 1: Structure of the N = 2 diamond generated by v. The coordinate axis correspond the conformal and Heisenberg weights. In this case, the N = 2 diamond degenerates to a bottom left leg in [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Block decomposition of sln+r+1|n+s. As before (5.6), F is a square of an odd nilpotent f (or ˜f), so we have the corresponding SUSY W-algebra Wk N=1(slr+n+1|n+s, f). By Theorem 3.2 the ordinary and SUSY W-superalgebras are related by (6.2) Wk N=1(sln+r+1|n+s, f) ∼= Wk (sln+r+1|n+s, F) ⊗ F(glr|s ) ∼= Wk N=1(sln+r+1|n+s, ˜f). We call such algebras of N = 2 hook-type and Wk N=1(sln+r+1|n+s, f) of SUSY N = 2 h… view at source ↗
Figure 3
Figure 3. Figure 3: Structure of the OPEs between two diamonds W N (z)W M(w). The nodes D∆,h represent the vector subspaces spanned by products W N,α(z)W M,β(w) for α, β ∈ {⊥, ±, ⊤} with ∆ = ∆(WN,α) + ∆(W M,β) and h = h(WN,α) + h(W M,β). For instance, DN+M,0 is spanned only by WN,⊥(z)W M,⊥(w). The down arrows represent an action of H(1), the lines pointing up-left or up-right represent action of G + (0) or G − (0), respective… view at source ↗
read the original abstract

The universal $2$-parameter vertex algebra $\mathcal{W}_{\infty}$ of type $\mathcal{W}(2,3,\dots)$ is a classifying object for vertex algebras of type $\mathcal{W}(2,3,\dots,N)$ for some $N$; under mild hypotheses, all such vertex algebras arise as quotients of $\mathcal{W}_{\infty}$. In 2017, Gaiotto and Rap\v{c}\'ak introduced a family of such vertex algebras called $Y$-algebras, and conjectured that they fall into groups of three that are mutually isomorphic. This is a common generalization of both Feigin-Frenkel duality and the coset realization of principal $\mathcal{W}$-algebras in type $A$, and was proven in 2021 for the simple $Y$-algebras (i.e., one label is zero) by the first and third authors. In this paper, we extend this entire story to the $\mathcal{N}=2$ superconformal setting. First, we prove the 2013 conjecture of Gaberdiel and Candu that there exists a universal $2$-parameter vertex algebra $\mathcal{W}^{\mathcal{N}=2}_{\infty}$ which is an extension of the $\mathcal{N}=2$ superconformal algebra, and has four additional generators in weights $i, i + \frac{1}{2}, i + \frac{1}{2}, i+1$, for each integer $i > 1$. This admits many $1$-parameter quotients which we call $\mathcal{N}=2$ supersymmetric $Y$-algebras, and we prove the dualities among these algebras which were conjectured in 2018 by Prochazka and Rap\v{c}\'ak. A special case is the coset realization of the principal $\mathcal{W}$-algebra $\mathcal{W}^k(\mathfrak{sl}_{n+1|n})$ which was conjectured in 1992 by Ito. As a corollary, we obtain the strong rationality of $\mathcal{W}_k(\mathfrak{sl}_{n+1|n})$ for $k = -1 + \frac{1}{n+a+1}$ for all positive integers $n,a$, and we describe its module category. This generalizes Adamovi\'c's 1999 result on $\mathcal{N}=2$ minimal models, which is the case $n=1$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper constructs the universal 2-parameter vertex algebra W^{N=2}_∞ as an extension of the N=2 superconformal algebra with four additional generators in weights i, i+1/2, i+1/2, i+1 for each i>1, proving the 2013 Gaberdiel-Candu conjecture. It defines N=2 supersymmetric Y-algebras as 1-parameter quotients and establishes the dualities conjectured by Prochazka-Rapcak in 2018, including the coset realization of W^k(sl_{n+1|n}) conjectured by Ito in 1992. Corollaries include strong rationality of W_k(sl_{n+1|n}) for k=-1+1/(n+a+1) and a description of its module category, generalizing Adamović's 1999 result on N=2 minimal models.

Significance. If the results hold, the work supplies a classifying object for vertex algebras of type W(2,3,...,N) in the N=2 supersymmetric setting, generalizing Feigin-Frenkel duality and principal W-algebra cosets. The explicit generators, OPE relations, and parameter-dependent quotients, together with complete arguments for the dualities via coset realizations and representation-theoretic identifications, provide a solid foundation. The rationality corollary and module category description are concrete advances that extend prior results on minimal models.

minor comments (2)
  1. [§1] §1: The introduction invokes several technical results from the representation theory of vertex operator superalgebras; adding one-sentence reminders of the precise statements (with equation numbers from the cited references) would improve readability for readers outside the immediate subfield.
  2. The notation for the two continuous parameters of W^{N=2}_∞ is introduced clearly but could be cross-referenced explicitly in the statements of the duality theorems to avoid any ambiguity when specializing to the Y-algebra quotients.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive report, accurate summary of the main results, and recommendation to accept the manuscript. We are pleased that the referee found the construction of the universal N=2 W_infty algebra, the proof of the Gaberdiel-Candu conjecture, the dualities for the supersymmetric Y-algebras, the coset realization, and the rationality corollaries to be significant advances.

Circularity Check

0 steps flagged

No significant circularity; self-contained algebraic proofs

full rationale

The paper constructs the universal N=2 W_infty algebra explicitly via generators and OPE relations, then proves the Gaberdiel-Candu conjecture and Prochazka-Rapcak dualities through coset realizations, quotient identifications, and representation-theoretic arguments. These steps rely on stated mild hypotheses and external results on vertex operator superalgebras (cited with precise references or proved in the manuscript), not on parameters fitted to the target or self-definitional reductions. The 2021 self-citation is for a prior special case and is not load-bearing for the new existence and duality proofs. The derivation chain is independent and does not collapse to its inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 2 invented entities

The central claims rest on the introduction of a new 2-parameter universal algebra whose existence is proved, together with standard axioms of vertex operator superalgebras and representation theory of superalgebras; the two continuous parameters are part of the construction rather than fitted post hoc.

free parameters (1)
  • two continuous parameters of W^{N=2}_infty
    The universal algebra is defined as a 2-parameter family; these parameters label the family and are not determined by fitting to external data within the paper.
axioms (1)
  • standard math Standard axioms of vertex operator superalgebras and their modules
    All constructions, quotients, and duality statements presuppose the usual definition and basic properties of vertex algebras in the super setting.
invented entities (2)
  • Universal N=2 supersymmetric W_infty algebra no independent evidence
    purpose: Classifying object that extends the N=2 superconformal algebra and generates all W(2,3,...,N) type algebras as quotients under mild hypotheses
    Newly constructed object whose existence is the main theorem.
  • N=2 supersymmetric Y-algebras no independent evidence
    purpose: 1-parameter quotients of the universal algebra whose mutual isomorphisms are proved
    Newly named family whose dualities form a central result.

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Reference graph

Works this paper leans on

101 extracted references · 101 canonical work pages

  1. [1]

    Adamovi´ c,Representations of theN= 2superconformal vertex algebra, Int

    D. Adamovi´ c,Representations of theN= 2superconformal vertex algebra, Int. Math. Res. Not. (1999), 61-79

    work page 1999

  2. [2]

    Adamovi´ c, T

    D. Adamovi´ c, T. Arakawa, T. Creutzig, A. R. Linshaw, A. Moreau, P. M. Frajria and P. Papi,W-algebras as conformal extensions of affine VOAs, [arXiv:2508.18889 [math.QA]]

    work page arXiv

  3. [3]

    Adamovic, T

    D. Adamovic, T. Creutzig and N. Genra,Relaxed and logarithmic modules of csl3, Math. Ann.389(2024) no.1, 281-324

    work page 2024

  4. [4]

    Adamovi´ c, B

    D. Adamovi´ c, B. Feigin, and S. Nakatsuka,Center of the affinegln|1 at the critical level and pseudo-differential operators, arXiv:2601.21850

    work page arXiv

  5. [5]

    Adamovi´ c, V

    D. Adamovi´ c, V. G. Kac, P. M¨ oseneder Frajria, P. Papi and O. Perˇ se,Conformal embeddings of affine vertex algebras in minimalW-algebras I: structural results, J. Algebra500(2018), 117-152

    work page 2018

  6. [6]

    Adamovi´ c, P

    D. Adamovi´ c, P. M¨ oseneder Frajria and P. Papi,New Approaches for Studying Conformal Embeddings and Collapsing Levels forW-Algebras, Int. Math. Res. Not. (2023) no.22, 19431-19475

    work page 2023

  7. [7]

    Adamovi´ c, and S

    D. Adamovi´ c, and S. Nakatsuka,Center of affinesl2|1 at the critical level, Int. Math. Res. Not. IMRN 2025, no. 14, Paper No. rnaf212, 18 pp

    work page 2025

  8. [8]

    Altschuler, M

    D. Altschuler, M. Bauer and C. Itzykson,The Branching Rules of Conformal Embeddings, Commun. Math. Phys. 132 (1990), 349-364

    work page 1990

  9. [9]

    Arakawa,Associated varieties of modules over Kac-Moody algebras andC 2-cofiniteness ofW-algebras, Int

    T. Arakawa,Associated varieties of modules over Kac-Moody algebras andC 2-cofiniteness ofW-algebras, Int. Math. Res. Not. (2015) Vol. 2015 11605-11666

    work page 2015

  10. [10]

    Arakawa,Rationality ofW-algebras: principal nilpotent cases, Ann

    T. Arakawa,Rationality ofW-algebras: principal nilpotent cases, Ann. Math. 182 (2015), no. 2, 565-694

    work page 2015

  11. [11]

    Arakawa,Rationality of admissible affine vertex algebras in the category O, Duke Math

    T. Arakawa,Rationality of admissible affine vertex algebras in the category O, Duke Math. J., 165 (2016), 67-93

    work page 2016

  12. [12]

    Chiral algebras of class $\mathcal{S}$ and Moore-Tachikawa symplectic varieties

    T. Arakawa,Chiral algebras of classSand Moore-Tachikawa symplectic varieties, arXiv:1811.01577

    work page Pith review arXiv

  13. [13]

    Arakawa, T

    T. Arakawa, T. Creutzig, and B. Feigin,Urod algebras and translation ofW-algebras, Forum Math. Sigma 10 (2022), Paper No. e33, 31 pp

    work page 2022

  14. [14]

    Arakawa, T

    T. Arakawa, T. Creutzig, K. Kawasetsu,On lisse non-admissible minimal and principalW-algebras, Contemp. Math., 829 American Mathematical Society, Providence, RI, 2025, 1-13

    work page 2025

  15. [15]

    Arakawa, T

    T. Arakawa, T. Creutzig and K. Kawasetsu,Weight representations of affine Kac-Moody algebras and small quantum groups, Adv. Math.477(2025), 110365

    work page 2025

  16. [16]

    Arakawa, T

    T. Arakawa, T. Creutzig, and A. Linshaw,W-algebras as coset vertex algebras, Invent. Math. 218, no. 1 (2019), 145-195. 66

    work page 2019

  17. [17]

    Arakawa and E

    T. Arakawa and E. Frenkel,Quantum Langlands duality of representations ofW-algebras, Compos. Math. 155, no. 12 (2019), 2235-2262

    work page 2019

  18. [18]

    Arakawa, C

    T. Arakawa, C. H. Lam, and H. Yamada,Parafermion vertex operator algebras andW-algebras, Trans. Amer. Math. Soc. 371 (2019), no. 6, 4277-4301

    work page 2019

  19. [19]

    F. Bais, P. Bouwknegt, M. Surridge, and K. Schoutens,Coset construction for extended Virasoro algebras, Nuclear Phys. B, 304(2) (1988), 371-391

    work page 1988

  20. [20]

    Blumenhagen,N= 2-supersymmetricW-algebras, Nuclear Physics B 405.2-3 (1993), 744-776

    R. Blumenhagen,N= 2-supersymmetricW-algebras, Nuclear Physics B 405.2-3 (1993), 744-776

    work page 1993

  21. [21]

    Briot and E

    C. Briot and E. Ragoucy,W-superalgebras as truncations of super-Yangians, J. Phys. A 36 (2003), no. 4, 1057-1081

    work page 2003

  22. [22]

    Candu, and M

    C. Candu, and M. Gaberdiel,Duality inN= 2minimal model holography, J. High Energy Phys. 2013, no. 2, 070, front matter + 26 pp

    work page 2013

  23. [23]

    Creutzig,Fusion categories for affine vertex algebras at admissible levels, Selecta Math

    T. Creutzig,Fusion categories for affine vertex algebras at admissible levels, Selecta Math. (2019) no.25, 1-21

    work page 2019

  24. [24]

    Creutzig,Tensor categories of weight modules of bsl2 at admissible level, J

    T. Creutzig,Tensor categories of weight modules of bsl2 at admissible level, J. Lond. Math. Soc. (2)110(2024), no. 6, Paper No. e70037, 38 pp

    work page 2024

  25. [25]

    Resolving Verlinde’s formula of logarithmic CFT.arXiv:2411.11383 [math.QA]

    T. Creutzig,Resolving Verlinde’s formula of logarithmic CFT, [arXiv:2411.11383 [math.QA]]

    work page arXiv

  26. [26]

    Creutzig, D

    T. Creutzig, D. E. Diaconescu and M. Ma,Affine Laumon Spaces and IteratedW-Algebras, Commun. Math. Phys. 402 (2023) no.3, 2133-2168

    work page 2023

  27. [27]

    Creutzig, J

    T. Creutzig, J. Fasquel, V. Kovalchuk, A. Linshaw, and S. Nakatsuka,Minimal W-algebras ofso N at level minus one. arXiv preprint arXiv:2506.15605

    work page arXiv

  28. [28]

    Creutzig, B

    T. Creutzig, B. Feigin and A. R. Linshaw,N= 4superconformal algebras and diagonal cosets, Int. Math. Res. Not.2021 (2021) no.24, 18768-18811

    work page 2021

  29. [29]

    Creutzig and D

    T. Creutzig and D. Gaiotto,Vertex Algebras forS-duality, Comm. Math. Phys. 379(2020), no.3, 785-845

    work page 2020

  30. [30]

    Creutzig, N

    T. Creutzig, N. Genra, S. Nakatsuka and R. Sato,Correspondences of Categories for SubregularW-Algebras and Principal W-Superalgebras, Commun. Math. Phys.393(2022) no.1, 1-60

    work page 2022

  31. [31]

    Creutzig and Y

    T. Creutzig and Y. Hikida,RectangularW-algebras, extended higher spin gravity and dual coset CFTs, JHEP 147 (2019)

    work page 2019

  32. [32]

    Creutzig, Y

    T. Creutzig, Y. Hikida and P. B. Ronne,Higher spin AdS 3 supergravity and its dual CFT, JHEP02(2012), 109

    work page 2012

  33. [33]

    Creutzig, Y

    T. Creutzig, Y. Z. Huang and J. Yang,Braided tensor categories of admissible modules for affine Lie algebras, Commun. Math. Phys.362(2018) no.3, 827-854

    work page 2018

  34. [34]

    Creutzig, S

    T. Creutzig, S. Kanade and A. R. Linshaw,Simple current extensions beyond semi-simplicity, Commun. Contemp. Math. 22 (2020) no.01, 1950001

    work page 2020

  35. [35]

    Creutzig, S

    T. Creutzig, S. Kanade, A. R. Linshaw and D. Ridout,Schur–Weyl Duality for Heisenberg Cosets, Transform. Groups 24 (2019) no.2, 301-354

    work page 2019

  36. [36]

    Creutzig, S

    T. Creutzig, S. Kanade and R. McRae,Tensor categories for vertex operator superalgebra extensions, Mem. Amer. Math. Soc. 295 (2024), no. 1472, vi+181 pp

    work page 2024

  37. [37]

    Creutzig, S

    T. Creutzig, S. Kanade and R. McRae,Gluing vertex algebras, Adv. Math. 396 (2022), 108174

    work page 2022

  38. [38]

    Creutzig, V

    T. Creutzig, V. Kovalchuk and A. Linshaw,New universal vertex algebras as glueings of the basic ones, arXiv:2512.19508

    work page arXiv

  39. [39]

    Creutzig and A

    T. Creutzig and A. Linshaw,Cosets of affine vertex algebras inside larger structures, Journal of Algebra, 517, 396-438, 2019

    work page 2019

  40. [40]

    Creutzig and A

    T. Creutzig and A. Linshaw,Trialities ofW-algebras, Camb. J. Math. vol. 10, no. 1 (2022), 69-194

    work page 2022

  41. [41]

    Creutzig and A

    T. Creutzig and A. Linshaw,Trialities of orthosymplecticW-algebras, Adv. Math. 409 (2022), 108678, 79pp

    work page 2022

  42. [42]

    Creutzig and A

    T. Creutzig and A. R. Linshaw,The superW 1+∞ algebra with integral central charge, Trans. Am. Math. Soc.367(2015) no.8, 5521-5551

    work page 2015

  43. [43]

    Creutzig, A

    T. Creutzig, A. R. Linshaw, S. Nakatsuka and R. Sato,Duality via convolution ofW-algebras, Selecta Math.31(2025) no.3, 56

    work page 2025

  44. [44]

    Creutzig, T

    T. Creutzig, T. Liu, D. Ridout and S. Wood,Unitary and non-unitaryN= 2minimal models, JHEP06(2019), 024

    work page 2019

  45. [45]

    Ribbon categories of weight modules for affine𝔰𝔩 2 at admissible levels.arXiv:2411.11386 [math.QA]

    T. Creutzig, R. McRae and J. Yang,Ribbon categories of weight modules for affinesl 2 at admissible levels, [arXiv:2411.11386 [math.QA]]

    work page arXiv

  46. [46]

    Creutzig and S

    T. Creutzig and S. Nakatsuka,Cosets from equivariant W-algebras, Represent. Theory27(2023) no.21, 766-777

    work page 2023

  47. [47]

    Creutzig and D

    T. Creutzig and D. Ridout,Modular Data and Verlinde Formulae for Fractional Level WZW Models II, Nucl. Phys. B 875(2013), 423-458

    work page 2013

  48. [48]

    Creutzig, D

    T. Creutzig, D. Ridout and M. Rupert,A Kazhdan–Lusztig Correspondence forL − 3 2 (sl3), Commun. Math. Phys.400 (2023) no.1, 639-682

    work page 2023

  49. [49]

    De Sole and V

    A. De Sole and V. Kac,Freely generated vertex algebras and non-linear Le conformal algebras, Comm. Math. Phys. 254 (2005), no. 3, 659-694

    work page 2005

  50. [50]

    De Sole and V

    A. De Sole and V. Kac,Finite vs affineW-algebras, Jpn. J. Math. vol. 1, no. 1 (2006), 137-261

    work page 2006

  51. [51]

    A. A. Davydov et al.,The Witt group of non-degenerate braided fusion categories, J. Reine Angew. Math.677(2013), 135–177

    work page 2013

  52. [52]

    Fasquel, C

    J. Fasquel, C. Raymond and D. Ridout,Modularity of Admissible-Levelsl 3 Minimal Models with Denominator 2, Com- mun. Math. Phys.406(2025) no.11, 279

    work page 2025

  53. [53]

    Fateev and S

    V. Fateev and S. Lykyanov,The models of two-dimensional conformal quantum field theory withZ n symmetry, Internat. J. Modern Phys. A, 3(2) (1988), 507-520

    work page 1988

  54. [54]

    Feigin and E

    B. Feigin and E. Frenkel,Duality inW-algebras, Int. Math. Res. Notices 1991 (1991), no. 6, 75-82

    work page 1991

  55. [55]

    Feigin and E

    B. Feigin and E. Frenkel,Quantization of the Drinfeld-Sokolov reduction, Phys. Lett. B 246 (1990), 75–81

    work page 1990

  56. [56]

    B. L. Feigin, A. M. Semikhatov and I. Y. Tipunin,Equivalence between chain categories of representations of affine sl(2) and N=2 superconformal algebras, J. Math. Phys.39(1998), 3865-3905 67

    work page 1998

  57. [57]

    Frenkel, V

    E. Frenkel, V. Kac, and M. Wakimoto,Characters and fusion rules forW-algebras via quantized Drinfeld-Sokolov reduc- tion, Comm. Math. Phys. 147 (1992), 295–328

    work page 1992

  58. [58]

    Gaiotto and M

    D. Gaiotto and M. Rapˇ c´ ak,Vertex Algebras at the Corner, J. High Energy Phys. 2019, no. 1, 160, front matter+85 pp

    work page 2019

  59. [59]

    Gaiotto, M

    D. Gaiotto, M. Rapˇ c´ ak, and T. Zhou,Deformed Double Current Algebras, Matrix ExtendedW ∞ Algebras, Coproducts, and Intertwiners from the M2-M5 Intersection, Comm. Math. Phys. 406 (2025), no. 12, Paper No. 311, 139 pp

    work page 2025

  60. [60]

    Gannon,Exotic quantum subgroups and extensions of affine Lie algebra VOAs – part I, [arXiv:2301.07287 [math.QA]]

    T. Gannon,Exotic quantum subgroups and extensions of affine Lie algebra VOAs – part I, [arXiv:2301.07287 [math.QA]]

    work page arXiv

  61. [61]

    Genra and T

    N. Genra and T. Juillard,Reduction by stages for finiteW-algebras, Math. Z. 308 (2024), Paper no. 15

    work page 2024

  62. [62]

    Reduction by stages for affine W-algebras.arXiv:2501.04501 [math.RT]

    N. Genra and T. Juillard, Reduction by stages for affine W-algebras, [arXiv:2501.04501 [math.RT]]

    work page arXiv

  63. [63]

    Genra and A

    N. Genra and A. Linshaw,Ito’s conjecture and the coset realization ofW k(sl(3|2)), arXiv:1901.02397, 14 pages, to appear in RIMS Kokyuroku Bessatsu

    work page arXiv 1901

  64. [64]

    Genra, A

    N. Genra, A. Song, and U. Suh,Principal SUSY and nonSUSY W-algebras and their Zhu algebras, Comm. Math. Phys. 406 (2025), no. 12, Paper No. 306

    work page 2025

  65. [65]

    Goddard, A

    P. Goddard, A. Kent, D. Olive,Virasoro algebras and coset space models, Phys. Lett B 152 (1985) 88-93

    work page 1985

  66. [66]

    Heluani and V

    R. Heluani and V. Kac,Supersymmetric vertex algebras, Comm. Math. Phys. vol. 271 no. 1 (2007), 103-178

    work page 2007

  67. [67]

    Y. Z. Huang, A. Kirillov and J. Lepowsky,Braided tensor categories and extensions of vertex operator algebras, Commun. Math. Phys.337(2015) no.3, 1143-1159

    work page 2015

  68. [68]

    Ito,Quantum Hamiltonian reduction andN= 2coset models, Phys.Lett

    K. Ito,Quantum Hamiltonian reduction andN= 2coset models, Phys.Lett. B 259 (1991) 73–78

    work page 1991

  69. [69]

    Ito,N= 2superconformalCP(n)model, Nucl

    K. Ito,N= 2superconformalCP(n)model, Nucl. Phys. B 370 (1992) 123

    work page 1992

  70. [70]

    Kawasetsu and D

    K. Kawasetsu and D. Ridout,Relaxed highest-weight modules II: Classifications for affine vertex algebras, Commun. Contemp. Math.24(2022) no.05, 2150037

    work page 2022

  71. [71]

    Kawasetsu, D

    K. Kawasetsu, D. Ridout and S. Wood,Admissible-levelsl 3 minimal models, Lett. Math. Phys.112(2022) no.5, 96

    work page 2022

  72. [72]

    V. Kac, S. Roan, and M. Wakimoto,Quantum reduction for affine superalgebras, Comm. Math. Phys. 241 (2003), no. 2-3, 307–342

    work page 2003

  73. [73]

    Kac and M

    V. Kac and M. Wakimoto,Classification of modular invariant representations of affine algebras, InInfinite-dimensional Lie algebras and groups (Luminy-Marseille, 1988), volume 7 of Adv. Ser. Math. Phys. pages 138–177. World Sci. Publ., Teaneck, NJ, 1989

    work page 1988

  74. [74]

    Kac and M

    V. Kac and M. Wakimoto.Quantum reduction and representation theory of superconformal algebras, Advances in Math- ematics 185, no. 2 (2004): 400-458

    work page 2004

  75. [75]

    Kac and M

    V. Kac and M. Wakimoto,On free field realization of quantum affine W-algebras, Comm. Math. Phys. 395 (2022), no. 2, 571–600

    work page 2022

  76. [76]

    Li,Vertex algebras and vertex Poisson algebras, Commun

    H. Li,Vertex algebras and vertex Poisson algebras, Commun. Contemp. Math. 6 (01), 61-110, 2004

    work page 2004

  77. [77]

    Lin,Mirror extensions of rational vertex operator algebras, Trans

    X. Lin,Mirror extensions of rational vertex operator algebras, Trans. Am. Math. Soc.369(2017) no.6, 3821-3840

    work page 2017

  78. [78]

    Linshaw,Invariant theory and the Heisenberg vertex algebra, Int

    A. Linshaw,Invariant theory and the Heisenberg vertex algebra, Int. Math. Res. Not. IMRN (2012), no. 17, 4014-4050

    work page 2012

  79. [79]

    Linshaw,Invariant subalgebras of affine vertex algebras, Adv

    A. Linshaw,Invariant subalgebras of affine vertex algebras, Adv. Math. 234, pp. 61-84, 2013

    work page 2013

  80. [80]

    Linshaw,The structure of the Kac-Wang-Yan algebra, Comm

    A. Linshaw,The structure of the Kac-Wang-Yan algebra, Comm. Math. Phys. 345, No. 2, (2016), 545-585

    work page 2016

Showing first 80 references.