Niclas Wyllard

A& B model approaches to surface operators and Toda thoeries

It has recently been argued [1] that the inclusion of surface operators in 4d

Affine sl(N)conformal blocks from \( \mathcal{N} = 2 \) SU(N) gauge theories

\mathcal{N} = 2

A Note on instanton counting for N=2 gauge theories with classical gauge groups

SU(2) quiver gauge theories should correspond to insertions of certain degenerate operators in the dual Liouville theory. So far only the insertion of a single surface operator has been treated (in a semi-classical limit). In this paper we study and generalise this proposal. Our approach relies on the use of topological string theory techniques. On the B-model side we show that the effects of multiple surface operator insertions in 4d

W-algebras and surface operators in N=2 gauge theories

\mathcal{N} = 2

Lower-dimensional pure-spinor superstrings

gauge theories can be calculated using the B-model topological recursion method, valid beyond the semi-classical limit. On the mirror A-model side we find by explicit computations that the 5d lift of the SU(N) gauge theory partition function in the presence of (one or many) surface operators is equal to an A-model topological string partition function with the insertion of (one or many) toric branes. This is in agreement with an earlier proposal by Gukov [2, 2, 3]. Our A-model results were motivated by and agree with what one obtains by combining the AGT conjecture with the dual interpretation in terms of degenerate operators. The topological string theory approach also opens up new possibilities in the study of 2d Toda field theories.

D-brane boundary states in the pure spinor superstring

Recently Alday and Tachikawa [1] proposed a relation between conformal blocks in a two-dimensional theory with affine sl(2) symmetry and instanton partition functions in four-dimensional conformal

Pure-spinor superstrings in d = 2,4,6

\mathcal{N} = 2

MATRIX MODELS AND

SU(2) quiver gauge theories in the presence of a certain surface operator. In this paper we extend this proposal to a relation between conformal blocks in theories with affine sl(N) symmetry and instanton partition functions in conformal

{\mathcal N} = 2

\mathcal{N} = 2

GAUGE THEORY

SU(N) quiver gauge theories in the presence of a surface operator. We also discuss the extension to non-conformal