Loop and surface operators in $ \mathcal{N} = 2 $ gauge theory and Liouville modular geometry

By L. Alday, D. Gaiotto, Sergei Gukov, Yuji Tachikawa, H. Verlinde. 2009

224 citations recorded by the source corpus.

Recently, a duality between Liouville theory and four dimensional $ \mathcal{N} = 2 $ gauge theory has been uncovered by some of the authors. We consider the role of extended objects in gauge theory, surface operators and line operators, under this correspondence. We map such objects to specific operators in Liouville theory. We employ this connection to compute the expectation value of general supersymmetric ’t Hooft-Wilson line operators in a variety of $ \mathcal{N} = 2 $ gauge theories.

Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7c55cc0fee4a9abb7767492cdacf9655073d7ced

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Citations in the corpus

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.”
Exact results in D = 2 supersymmetric gauge theories (2012, unknown): “ultiplet elds, leaving the more complete correspondence for other theories to a separate publication [24]. This correspondence can be enriched by adding defects both in gauge theory and in Toda as in [14,40,43](see also [44]) and it would be interesting to establish a detailed dictionary between gau”
Gauge theory loop operators and Liouville theory (2009, methodology): “Note. We have coordinated the submission to the arXiv of our work and the related work by Fernando Alday, Davide Gaiotto, Sergei Gukov, Yuji Tachikawa and Herman Verlinde [ 31 ].”
On the Defect Group of a 6D SCFT (2015, methodology): “A notable example of this type are the 4D N = 2 theories of class S [7–10] obtained by compactifications of the 6D (2, 0) theories on Riemann surfaces [11–15].”
A& B model approaches to surface operators and Toda thoeries (2010, methodology): “in the 2dToda theory [4]. Surface operators provide a particularly interesting class of observables in the T (n,g)(Ar) theories. A proposal for how to describe them in the dual 2dCFT was presented in [1] (other observables such as Wson and ’t Hooft loops have also been studied [1, 7]). Recently argu”
Affine SL(2) Conformal Blocks from 4d Gauge Theories (2010, background): “This construction led to the classification of the loop operators in four dimensions in terms of the loops on C2 [8] and the evaluation of their expectation values [6,9].”
S-duality and 2d topological QFT (2009, background): “ rich class of 4d superconformal ﬁeld theories arise by compactifying the 6d (2,0) theory on a punctured Riemann surface Σ [1], and this has inspired a precise dictionary between 4d and 2d quantities [5, 6, 7, 8, 9]. In this paper we have added a new entry to this dictionary. Previous work has focus”
2d index and surface operators (2013, background): “for our purposes. Compared to N= 4, the surface operators in N= 2 theories remain somewhat unexplored. For the theories of class S, they are related to degenerate vertex operators of Liouville theory [32]. One can construct a subset of possible 1The references cited are but a few examples. They are ”
Vortex Counting and Lagrangian 3-Manifolds (2010, methodology): “Indeed, the results of [13] can be used to reformulate as CFT conformal blocks many of the vortex/BPS partition functions previously described, and we will give examples in the case of U (1) and SU (2) 4d theories.”
Instanton counting with a surface operator and the chain-saw quiver (2011, background): “From this point of view, the introduction of a surface operator corresponds to an insertion of a degenerate field on the Riemann surface, without changing the two-dimensional theory [71, 13].”