Factorisation of \( \mathcal{N} = 2 \) theories on the squashed 3-sphere
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Publication:339157
DOI10.1007/JHEP04(2012)120zbMATH Open1348.81430arXiv1111.6905OpenAlexW3123156361MaRDI QIDQ339157
Author name not available (Why is that?)
Publication date: 7 November 2016
Published in: (Search for Journal in Brave)
Abstract: Partition functions of 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 R^2 x S_1 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/b^2, on the dual R^2 x S_1 corresponding to the 1/b ->0 degeneration. The ellipsoid partition appears to provide the hbar -> hbar^L modular invariant non-perturbative completion of the vortex theory.
Full work available at URL: https://arxiv.org/abs/1111.6905
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