The sphere partition function of 3d N=4 Chern-Simons-matter theories is conjectured to equal a sum of twisted traces on Verma modules over the quantization of their moduli spaces of vacua, extending prior work and revealing new Abelian dualities.
Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories
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In these lectures I give a pedagogical presentation of some of the recent progress in supersymmetric Chern-Simons-matter theories, coming from the use of localization and matrix model techniques. The goal is to provide a simple derivation of the exact interpolating function for the free energy of ABJM theory on the three-sphere, which implies in particular the N^{3/2} behavior at strong coupling. I explain in detail part of the background needed to understand this derivation, like holographic renormalization, localization of path integrals, and large N techniques in matrix models
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Twisted traces and quantization of moduli stacks of 3d $\mathcal{N}=4$ Chern-Simons-matter theories
The sphere partition function of 3d N=4 Chern-Simons-matter theories is conjectured to equal a sum of twisted traces on Verma modules over the quantization of their moduli spaces of vacua, extending prior work and revealing new Abelian dualities.