Correlator correspondences for Gaiotto-Rapčák dualities and first order formulation of coset models

[1] L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from

four-dimensional gauge theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219]

[INSPIRE].

[2] N. Wyllard, AN −1 conformal Toda field theory correlation functions from conformal N = 2

SU(N ) quiver gauge theories, JHEP 11 (2009) 002 [arXiv:0907.2189] [INSPIRE].

[3] M.R. Gaberdiel and R. Gopakumar, An AdS3 dual for minimal model CFTs, Phys. Rev. D

83 (2011) 066007 [arXiv:1011.2986] [INSPIRE].

[4] T. Arakawa, T. Creutzig and A.R. Linshaw, W-algebras as coset vertex algebras, Invent.

Math. 218 (2019) 145 [arXiv:1801.03822] [INSPIRE].

[5] V. Fateev, A. Zamolodchikov and A. Zamolodchikov, unpublished.

[6] E. Witten, On string theory and black holes, Phys. Rev. D 44 (1991) 314 [INSPIRE].

[7] Y. Hikida and V. Schomerus, The FZZ-duality conjecture: a proof, JHEP 03 (2009) 095

[arXiv:0805.3931] [INSPIRE].

[8] V. Kazakov, I.K. Kostov and D. Kutasov, A matrix model for the two-dimensional black

hole, Nucl. Phys. B 622 (2002) 141 [hep-th/0101011] [INSPIRE].

[9] T. Creutzig and Y. Hikida, Higher rank FZZ-dualities, JHEP 02 (2021) 140

[arXiv:2010.14681] [INSPIRE].

[10] T. Creutzig, Y. Hikida and P.B. Rønne, Higher spin AdS3 supergravity and its dual CFT,

JHEP 02 (2012) 109 [arXiv:1111.2139] [INSPIRE].

[11] S. Ribault and J. Teschner, H3+ -WZNW correlators from Liouville theory, JHEP 06 (2005)

014 [hep-th/0502048] [INSPIRE].

– 35 –

JHEP12(2021)144

V10 = e(−φ

A Self-archived copy in

Kyoto University Research Information Repository

https://repository.kulib.kyoto-u.ac.jp

[12] S. Ribault, Knizhnik-Zamolodchikov equations and spectral flow in AdS3 string theory, JHEP

09 (2005) 045 [hep-th/0507114] [INSPIRE].

[13] Y. Hikida and V. Schomerus, H3+ WZNW model from Liouville field theory, JHEP 10 (2007)

064 [arXiv:0706.1030] [INSPIRE].

[14] K. Gaw¸edzki and A. Kupiainen, Coset construction from functional integrals, Nucl. Phys. B

320 (1989) 625 [INSPIRE].

[15] D. Karabali, Q.-H. Park, H.J. Schnitzer and Z. Yang, A GKO construction based on a path

integral formulation of gauged Wess-Zumino-Witten actions, Phys. Lett. B 216 (1989) 307

[INSPIRE].

[17] T. Creutzig, Y. Hikida and P.B. Rønne, Correspondences between WZNW models and CFTs

with W-algebra symmetry, JHEP 02 (2016) 048 [arXiv:1509.07516] [INSPIRE].

[18] T. Creutzig, N. Genra, Y. Hikida and T. Liu, Correspondences among CFTs with different

W-algebra symmetry, Nucl. Phys. B 957 (2020) 115104 [arXiv:2002.12587] [INSPIRE].

[19] Y. Hikida and V. Schomerus, Structure constants of the OSP(1|2) WZNW model, JHEP 12

(2007) 100 [arXiv:0711.0338] [INSPIRE].

[20] T. Creutzig, Y. Hikida and P.B. Rønne, Supergroup — extended super Liouville

correspondence, JHEP 06 (2011) 063 [arXiv:1103.5753] [INSPIRE].

[21] A. Gerasimov, A. Marshakov and A. Morozov, Free field representation of parafermions and

related coset models, Nucl. Phys. B 328 (1989) 664 [Theor. Math. Phys. 83 (1990) 466]

[Teor. Mat. Fiz. 83 (1990) 186] [INSPIRE].

[22] M. Kuwahara, N. Ohta and H. Suzuki, Conformal field theories realized by free fields, Nucl.

Phys. B 340 (1990) 448 [INSPIRE].

(1)

[23] M. Wakimoto, Fock representations of the affine Lie algebra A1 , Commun. Math. Phys.

104 (1986) 605 [INSPIRE].

[24] P. Goddard, A. Kent and D.I. Olive, Unitary representations of the Virasoro and

super-Virasoro algebras, Commun. Math. Phys. 103 (1986) 105 [INSPIRE].

[25] T. Kugo and I. Ojima, Local covariant operator formalism of nonabelian gauge theories and

quark confinement problem, Prog. Theor. Phys. Suppl. 66 (1979) 1 [INSPIRE].

[26] A. Litvinov and L. Spodyneiko, On W algebras commuting with a set of screenings, JHEP

11 (2016) 138 [arXiv:1609.06271] [INSPIRE].

[27] T. Creutzig, Y. Hikida and D. Stockall, Correlator correspondences for subregular W-algebras

and principal W-superalgebras, JHEP 10 (2021) 032 [arXiv:2106.15073] [INSPIRE].

(2)

[28] B.L. Feigin and A.M. Semikhatov, Wn

[math/0401164] [INSPIRE].

algebras, Nucl. Phys. B 698 (2004) 409

[29] T. Creutzig, N. Genra and S. Nakatsuka, Duality of subregular W -algebras and principal

W -superalgebras, Adv. Math. 383 (2021) 107685 [arXiv:2005.10713] [INSPIRE].

[30] T. Creutzig, N. Genra, S. Nakatsuka and R. Sato, Correspondences of categories for

subregular W-algebras and principal W-superalgebras, arXiv:2104.00942 [INSPIRE].

– 36 –

JHEP12(2021)144

[16] D. Karabali and H.J. Schnitzer, BRST quantization of the gauged WZW action and coset

conformal field theories, Nucl. Phys. B 329 (1990) 649 [INSPIRE].

A Self-archived copy in

Kyoto University Research Information Repository

https://repository.kulib.kyoto-u.ac.jp

[31] D. Gaiotto and M. Rapčák, Vertex algebras at the corner, JHEP 01 (2019) 160

[arXiv:1703.00982] [INSPIRE].

[32] T. Creutzig and A.R. Linshaw, Trialities of W-algebras, arXiv:2005.10234 [INSPIRE].

[33] Y. Kazama and H. Suzuki, Characterization of N = 2 superconformal models generated by

coset space method, Phys. Lett. B 216 (1989) 112 [INSPIRE].

[34] Y. Kazama and H. Suzuki, New N = 2 superconformal field theories and superstring

compactification, Nucl. Phys. B 321 (1989) 232 [INSPIRE].

[36] K. Ito, N = 2 superconformal CPn model, Nucl. Phys. B 370 (1992) 123 [INSPIRE].

[37] K. Hori and A. Kapustin, Duality of the fermionic 2 − D black hole and N = 2 Liouville

theory as mirror symmetry, JHEP 08 (2001) 045 [hep-th/0104202] [INSPIRE].

[38] T. Creutzig, Y. Hikida and P.B. Rønne, The FZZ duality with boundary, JHEP 09 (2011)

004 [arXiv:1012.4731] [INSPIRE].

[39] H. Ooguri and C. Vafa, Two-dimensional black hole and singularities of CY manifolds, Nucl.

Phys. B 463 (1996) 55 [hep-th/9511164] [INSPIRE].

[40] K. Hori and A. Kapustin, World sheet descriptions of wrapped NS five-branes, JHEP 11

(2002) 038 [hep-th/0203147] [INSPIRE].

[41] T. Creutzig and A.R. Linshaw, Cosets of affine vertex algebras inside larger structures, J.

Algebra 517 (2019) 396 [arXiv:1407.8512] [INSPIRE].

[42] T. Arakawa, T. Creutzig, K. Kawasetsu and A.R. Linshaw, Orbifolds and cosets of minimal

W-algebras, Commun. Math. Phys. 355 (2017) 339 [arXiv:1610.09348] [INSPIRE].

[43] T. Creutzig and A.R. Linshaw, The super W1+∞ algebra with integral central charge, Trans.

Am. Math. Soc. 367 (2015) 5521 [arXiv:1209.6032] [INSPIRE].

[44] N. Genra and A.R. Linshaw, Ito’s conjecture and the coset construction for W k (sl(3|2)),

arXiv:1901.02397 [INSPIRE].

[45] S. Hwang and H. Rhedin, The BRST formulation of G/H WZNW models, Nucl. Phys. B

406 (1993) 165 [hep-th/9305174] [INSPIRE].

[46] A.M. Polyakov, Gauge transformations and diffeomorphisms, Int. J. Mod. Phys. A 5 (1990)

833 [INSPIRE].

[47] M. Bershadsky, Conformal field theories via Hamiltonian reduction, Commun. Math. Phys.

139 (1991) 71 [INSPIRE].

[48] N. Genra, Screening operators for W-algebras, arXiv:1606.00966 [INSPIRE].

[49] N. Genra, Screening operators and parabolic inductions for affine W-algebras,

arXiv:1806.04417.

[50] I.B. Frenkel, H. Garland and G.J. Zuckerman, Semiinfinite cohomology and string theory,

Proc. Nat. Acad. Sci. 83 (1986) 8442 [INSPIRE].

[51] T. Creutzig, B. Feigin and A.R. Linshaw, N = 4 superconformal algebras and diagonal

cosets, arXiv:1910.01228 [INSPIRE].

– 37 –

JHEP12(2021)144

[35] K. Ito, Quantum Hamiltonian reduction and N = 2 coset models, Phys. Lett. B 259 (1991)

73 [INSPIRE].

A Self-archived copy in

Kyoto University Research Information Repository

https://repository.kulib.kyoto-u.ac.jp

[52] J. Polchinski, String theory. Volume 1: an introduction to the bosonic string, Cambridge

Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (2007)

[INSPIRE].

[53] M. Bershadsky and H. Ooguri, Hidden SL(n) symmetry in conformal field theories,

Commun. Math. Phys. 126 (1989) 49 [INSPIRE].

[54] M. Bershtein, B. Feigin and G. Merzon, Plane partitions with a “pit”: generating functions

and representation theory, Selecta Math. (N.S.) 24 (2018) 21.

[55] T. Procházka and M. Rapčák, W-algebra modules, free fields, and Gukov-Witten defects,

JHEP 05 (2019) 159 [arXiv:1808.08837] [INSPIRE].

[57] T. Creutzig, Y. Hikida and P.B. Rønne, N = 1 supersymmetric higher spin holography on

AdS3 , JHEP 02 (2013) 019 [arXiv:1209.5404] [INSPIRE].

[58] T. Procházka and M. Rapčák, Webs of W-algebras, JHEP 11 (2018) 109

[arXiv:1711.06888] [INSPIRE].

[59] V.A. Fateev, The sigma model (dual) representation for a two-parameter family of integrable

quantum field theories, Nucl. Phys. B 473 (1996) 509 [INSPIRE].

[60] T. Creutzig and Y. Hikida, Rectangular W-algebras, extended higher spin gravity and dual

coset CFTs, JHEP 02 (2019) 147 [arXiv:1812.07149] [INSPIRE].

[61] T. Creutzig and Y. Hikida, Rectangular W algebras and superalgebras and their

representations, Phys. Rev. D 100 (2019) 086008 [arXiv:1906.05868] [INSPIRE].

[62] T. Creutzig, Y. Hikida and T. Uetoko, Rectangular W-algebras of types so(M ) and sp(2M )

and dual coset CFTs, JHEP 10 (2019) 023 [arXiv:1906.05872] [INSPIRE].

[63] M.R. Gaberdiel and R. Gopakumar, Large N = 4 holography, JHEP 09 (2013) 036

[arXiv:1305.4181] [INSPIRE].

[64] M.R. Gaberdiel and R. Gopakumar, Higher spins & strings, JHEP 11 (2014) 044

[arXiv:1406.6103] [INSPIRE].

[65] T. Creutzig, Y. Hikida and P.B. Rønne, Extended higher spin holography and Grassmannian

models, JHEP 11 (2013) 038 [arXiv:1306.0466] [INSPIRE].

[66] T. Creutzig, Y. Hikida and P.B. Rønne, Higher spin AdS3 holography with extended

supersymmetry, JHEP 10 (2014) 163 [arXiv:1406.1521] [INSPIRE].

[67] M. Rapčák, Y. Soibelman, Y. Yang and G. Zhao, Cohomological Hall algebras, vertex

algebras and instantons, Commun. Math. Phys. 376 (2019) 1803 [arXiv:1810.10402]

[INSPIRE].

– 38 –

JHEP12(2021)144

[56] T. Creutzig and A.R. Linshaw, Trialities of orthosymplectic W-algebras, arXiv:2102.10224

[INSPIRE].

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