A& B model approaches to surface operators and Toda thoeries

By C. Kozçaz, Sara Pasquetti, N. Wyllard. 2010

164 citations recorded by the source corpus.

It has recently been argued [1] that the inclusion of surface operators in 4d$ \mathcal{N} = 2 $ 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$ \mathcal{N} = 2 $ 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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ce762b1940dbe8556647be224def3b9c9133dbb0

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Citations in the corpus

Non-Lagrangian theories from brane junctions (2013, methodology): “he TN toric diagram, we arrive at the conclusion that there are a total of 3 NX−1 i=1 i−2 NX−2 i=1 i = (N +4)(N −1) 2 (4.69) independent moduli. The result (4.69) fully agrees with equation (3.36) in [69]. When N is equal to 3, this gives us 7 parameters corresponding to QF,QB,Q1,...,Q5 from subsect”
Quantum geometry of refined topological strings (2011, background): “The Abranes can be given a purely gauge-theoretic formulation as surface operators, studied recently in [30, 31, 32, 33], for example.”
Instanton counting with a surface operator and the chain-saw quiver (2011, background): “The latter viewpoint was more suited to the comparison to the topological string approach in the case of the simple surface operator, as was exemplified in many papers [72, 39, 73, 40, 41].”
Affine SL(2) Conformal Blocks from 4d Gauge Theories (2010, background): “One finds that the degenerate fields of the two-dimensional theory give a surface operator in X4 [6, 7].”