Exact results for boundaries and domain walls in 2d supersymmetric theories

Abstract

We apply supersymmetric localization to N=(2,2) gauged linear sigma models on a hemisphere, with boundary conditions, i.e., D-branes, preserving B-type supersymmetries. We explain how to compute the hemisphere partition function for each object in the derived category of equivariant coherent sheaves, and argue that it depends only on its K theory class. The hemisphere partition function computes exactly the central charge of the D-brane, completing the well-known formula obtained by an anomaly inflow argument. We also formulate supersymmetric domain walls as D-branes in the product of two theories. In particular 4d line operators bound to a surface operator, corresponding via the AGT relation to certain defects in Toda CFT's, are constructed as domain walls. Moreover we exhibit domain walls that realize the sl(2) affine Hecke algebra.

75 pages; version 2: minor corrections, added some comments and references; version 3: tex error fixed

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• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
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• Small Instantons, Little Strings and Free Fermions
• Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary
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• Exact Partition Functions on RP2 and Orientifolds
• 2d SCFTs from M2-branes
• 2d Partition Function in Omega-background and Vortex/Instanton Correspondence
• Semichiral Fields on S^2 and Generalized Kähler Geometry
• Les Houches lectures on non-perturbative Seiberg-Witten geometry