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Index for three dimensional superconformal field theories with general Rcharge assignments
 JHEP
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Lectures on localization and matrix models in Supersymmetric Chern–simons–matter Theories
, 2012
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Exact results in d = 2 supersymmetric gauge theories,” 2012. Talk given at the conference
 Maths of String and Gauge Theory”, 3  5 May
"... We compute exactly the partition function of two dimensional N = (2, 2) gauge theories on S2 and show that it admits two dual descriptions: either as an integral over the Coulomb branch or as a sum over vortex and antivortex excitations on the Higgs branches of the theory. We further demonstrate th ..."
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We compute exactly the partition function of two dimensional N = (2, 2) gauge theories on S2 and show that it admits two dual descriptions: either as an integral over the Coulomb branch or as a sum over vortex and antivortex excitations on the Higgs branches of the theory. We further demonstrate that correlation functions in two dimensional Liouville/Toda CFT compute the S2 partition function for a class of N = (2, 2) gauge theories, thereby uncovering novel modular properties in two dimensional gauge theories. Some of these gauge theories flow in the infrared to CalabiYau sigma models – such as the conifold – and the topology changing flop transition is realized as crossing symmetry in Liouville/Toda CFT. Evidence for Seiberg duality in two dimensions is exhibited by demonstrating that the partition function of conjectured Seiberg dual pairs are the same.
Superconformal Index with Duality Domain Wall
, 2012
"... We study a superconformal index for N = 4 super YangMills on S1×S3 with a half BPS duality domain wall inserted at the great twosphere in S3. The index is obtained by coupling the 3d generalized superconformal index on the duality domain wall with 4d halfindices. We further consider insertions of ..."
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We study a superconformal index for N = 4 super YangMills on S1×S3 with a half BPS duality domain wall inserted at the great twosphere in S3. The index is obtained by coupling the 3d generalized superconformal index on the duality domain wall with 4d halfindices. We further consider insertions of line operators to the configuration and propose integral equations which express that the 3d index on duality domain wall is a duality kernel relating half indices of two line operators related by the duality map. We explicitly check the proposed integral equations for various duality domain walls and line operators in the N = 4 SU(2) theory. We also briefly comment on a generalization to N = 2 A1 Gaiotto theories with a simple example, N = 2 SU(2) SYM with four flavors.