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Abstract: It has recently been argued by Alday et al that the inclusion of surfaceoperators in 4d N=2 SU2 quiver gauge theories should correspond to insertionsof certain degenerate operators in the dual Liouville theory. So far only theinsertion of a single surface operator has been treated in a semi-classicallimit. In this paper we study and generalise this proposal. Our approachrelies on the use of topological string theory techniques. On the B-model sidewe show that the effects of multiple surface operator insertions in 4d N=2gauge theories can be calculated using the B-model topological recursionmethod, valid beyond the semi-classical limit. On the mirror A-model side wefind by explicit computations that the 5d lift of the SUN gauge theorypartition function in the presence of one or many surface operators is equalto an A-model topological string partition function with the insertion of oneor many toric branes. This is in agreement with an earlier proposal by Gukov.Our A-model results were motivated by and agree with what one obtains bycombining the AGT conjecture with the dual interpretation in terms ofdegenerate operators. The topological string theory approach also opens up newpossibilities in the study of 2d Toda field theories.

Autor: Can Kozcaz, Sara Pasquetti, Niclas Wyllard

Fuente: https://arxiv.org/

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