TY - JOUR

T1 - Conformal blocks of chiral fields in N = 2 SUSY CFT and affine Laumon spaces

AU - Belavin, V.

PY - 2012

Y1 - 2012

N2 - We consider the problem of computing N = 2 superconformal block functions. We argue that the Kazama-Suzuki coset realization of N = 2 superconformal algebra in terms of the affine sl̂(2) algebra provides relations between N = 2 and sl̂(2) conformal blocks. We show that for N = 2 chiral fields the corresponding sl̂(2) construction of the conformal blocks is based on the ordinary highest weight representation. We use an AGT-type correspondence to relate the four-point sl̂(2) conformal block with Nekrasov's instanton partition functions of a four-dimensional N = 2 SU(2) gauge theory in the presence of a surface operator. Since the previous relation proposed by Alday and Tachikawa requires some special modification of the conformal block function, we revisit this problem and find direct correspondence for the four-point conformal block. We thus find an explicit representation for the sl̂(2) four-point conformal block and hence obtain an explicit combinatorial representation for the N = 2 chiral four-point conformal block.

AB - We consider the problem of computing N = 2 superconformal block functions. We argue that the Kazama-Suzuki coset realization of N = 2 superconformal algebra in terms of the affine sl̂(2) algebra provides relations between N = 2 and sl̂(2) conformal blocks. We show that for N = 2 chiral fields the corresponding sl̂(2) construction of the conformal blocks is based on the ordinary highest weight representation. We use an AGT-type correspondence to relate the four-point sl̂(2) conformal block with Nekrasov's instanton partition functions of a four-dimensional N = 2 SU(2) gauge theory in the presence of a surface operator. Since the previous relation proposed by Alday and Tachikawa requires some special modification of the conformal block function, we revisit this problem and find direct correspondence for the four-point conformal block. We thus find an explicit representation for the sl̂(2) four-point conformal block and hence obtain an explicit combinatorial representation for the N = 2 chiral four-point conformal block.

KW - Conformal and W symmetry

KW - Duality in gauge field theories

UR - http://www.scopus.com/inward/record.url?scp=84868266010&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2012)156

DO - 10.1007/JHEP10(2012)156

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AN - SCOPUS:84868266010

SN - 1126-6708

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 156

ER -