Rigid Surface Operators
By Sergei Gukov, E. Witten. 2008
243 citations recorded by the source corpus.
Surface operators in gauge theory are analogous to Wilson and ’t Hooft line operators except that they are supported on a two-dimensional surface rather than a one-dimensional curve. In a previous paper, we constructed a certain class of half-BPS surface operators in N = 4 super Yang–Mills theory, and determined how they transform under S-duality. Those surface operators depend on a relatively large number of freely adjustable parameters. In the present paper, we consider the opposite case of half-BPS surface operators that are “rigid” in the sense that they do not depend on any parameters at all. We present some simple constructions of rigid half-BPS surface operators and attempt to determine how they transform under duality. This attempt is only partially successful, suggesting that our constructions are not the whole story. The partial match suggests interesting connections with quantization. We discuss some possible refinements and some string theory constructions which might lead to a more complete picture.
Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/055fffe741039200c031f67e8d8f29576ba30fe3
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Citations in the corpus
- 2d index and surface operators (2013, methodology): “Thus, one can introduce a surface operator supported on S by postulating a singularity for gauge fields along S or, alternatively, one may couple 4d gauge theory to a 2d theory T2d with global (flavor) symmetry group G [29, 30].”
- Twisted wild character varieties (2015, background): “This duality is known to be related to Langlands duality in some cases [29, 25], but apparently suffers from “missing orbits” in certain untwisted cases [28].”
- Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories (2012, background): “This surface operator is closely related to those studied by Gukov and Witten [31, 32].”
- Generalized global symmetries (2014, background): “J H E P 0 2 ( 2 0 1 5 ) 1 7 2 surface operators [33, 34] associated to elements of Z(G).”
- Wall-crossing in coupled 2d-4d systems (2011, background): “Deeper developments along this direction have come with the inclusion of surface defects [6, 7, 8].”
- Homological algebra of knots and BPS states (2011, background): “tions, one needs to consider various sectors of the U(r) gauge theory on R×LK labeled by non-trivial flat connections (Wilson lines) around the codimension-2 locus where D3′-branes meet D3-branes, cf. [15, 48]. In this paper we are mostly interested in knots colored by symmetric and antisymmetric rep”
- Defects and quantum Seiberg-Witten geometry (2014, background): “They can be described either as Gukov-Witten monodromy defects [3, 4] or by coupling to a class of 3d N = 4 supersymmetric gauge theories.”
- Reading between the lines of four-dimensional gauge theories (2013, unknown): “3 of [63]).”
- Fivebranes and Knots (2011, background): “An alternative description of the surface operator which makes it clear that it behaves well as long as the quadruple (α, β, γ, η) is regular is presented in section 3 of [109].”
- Coupling a QFT to a TQFT and duality (2014, background): “Examples of such surfaces and the way they can end on lines were considered in [14, 15].”