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Factorisation of \( \mathcal{N} = 2 \) theories on the squashed 3-sphere

  • Sara Pasquetti
Article

Abstract

Partition functions of \( \mathcal{N} = 2 \) theories on the squashed 3-sphere have been recently shown to localise to matrix integrals. By explicitly evaluating the matrix integral we show that abelian partition functions can be expressed as a sum of products of two blocks. We identify the first block with the partition function of the vortex theory, with equivariant parameter \( \hbar = 2\pi i{b^2} \), defined on \( {\mathbb{R}^2} \times {S_1} \) R corresponding to the b→0 degeneration of the ellipsoid. The second block gives the partition function of the vortex theory, with equivariant parameter \( {\hbar^L} = {{{2\pi i}} \left/ {{{b^2}}} \right.} \), on the dual \( {\mathbb{R}^2} \times {S_1} \) corresponding to the 1/b→0 degeneration. The ellipsoid partition appears to provide the \( \hbar \to {\hbar^L} \) modular invariant non-perturbative completion of the vortex theory.

Keywords

Supersymmetry and Duality Chern-Simons Theories Topological Strings String Duality 

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Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  1. 1.School of PhysicsQueen Mary University of LondonLondonU.K
  2. 2.Pure Mathematics section, Huxley BuildingImperial CollegeLondonU.K

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