The virtue of defects in 4D gauge theories and 2D CFTs

By N. Drukker, D. Gaiotto, Joaquim Gomis. 2010

239 citations recorded by the source corpus.

We advance a correspondence between the topological defect operators in Liouville and Toda conformal field theories — which we construct — and loop operators and domain wall operators in four dimensional $ \mathcal{N} = 2 $ supersymmetric gauge theories on S4. Our computation of the correlation functions in Liouville/Toda theory in the presence of topological defect operators, which are supported on curves on the Riemann surface, yields the exact answer for the partition function of four dimensional gauge theories in the presence of various walls and loop operators; results which we can quantitatively substantiate with an independent gauge theory analysis. As an interesting outcome of this work for two dimensional conformal field theories, we prove that topological defect operators and the Verlinde loop operators are different descriptions of the same operators.

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

View Paper: https://www.semanticscholar.org/paper/f594e77e07f36f761b3456d596555d8074b7fdf7

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Citations in the corpus

SUSY gauge theories on squashed three-spheres (2011, background): “In this context, certain 3D supersymmetric gauge theories on S3 play the role of domain walls [18, 19], and their partition functions were shown to correspond to transformation coefficients of conformal blocks under S-duality (or Moore-Seiberg groupoid operation).”
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].”
Correlation functions of Coulomb branch operators (2016, methodology): “These include the computation of Wilson loops [3], ’t Hooft loops [15], domain walls [16,17] and cusp anomalous dimensions at small angles [18] in four dimensional N = 2 QFTs.”
Topological defect lines and renormalization group flows in two dimensions (2018, background): “e assumption that the fusion product of a pair of TDLs involves only the direct sum of nitely many simple lines. This possibility has already been considered in the context of Liouville and Toda CFTs [92,35]. 8.3 From topological to conformal defects The TDLs in CFTs are a special case of conformal ”
Bootstrapping the superconformal index with surface defects (2012, background): “We refer the reader to [16, 74, 75] for a complete discussion of the relevant facts.”
Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories (2012, background): “The study of these untwisted and twisted defects was initiated in [11], and further developed in various papers including [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22].”
Exact Kähler potential from gauge theory and mirror symmetry (2012, methodology): “It would be interesting to construct domain walls preserving the SU(1|1) symmetry used to localize the S(2) partition function, and to compute the partition function in the presence of the domain wall, similarly to what was done for domain walls [24] (see also [25]) on the four-sphere [26].”
Affine SL(2) Conformal Blocks from 4d Gauge Theories (2010, background): “5) (4)The surface operator which corresponds to the insertion of degenerate fields the Liouville/Toda theory [6, 10] has (α1, .”
Framed BPS states (2010, unknown): “Similar junctions exist in the 2d Toda theories on C [56], which are relevant to S4 compactifications of the 4d gauge theory.”
Seiberg-Witten theories on ellipsoids (2012, background): “There one introduces an S-duality domain wall[20, 21] along an S3 inside the S4 which supports a 3D gauge theory on its worldvolume.”
Notes on SUSY gauge theories on three-sphere (2010, background): “Another application has recently been made to the study of domain walls in 4D N = 2 gauge theories [13, 14] in connection with the AGT relation.”
Exact results in D = 2 supersymmetric gauge theories (2012, unknown): “Another direction to study further is a possible connection of our results to the physics of domain walls in three dimensional gauge theories on S3, generalizing the results in [11, 41, 49].”
Chern-Simons theory and S-duality (2011, methodology): “In the special case when M is a mapping cylinder Mφ = C ×φ I, the effective theory TMφ can be thought of as a three-dimensional theory on the duality wall12 within a 4d N = 2 gauge theory [31, 33, 34]).”