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Supersymmetric partition functions and the three-dimensional A-twist · Around

2017

Supersymmetric partition functions and the three-dimensional A-twist

Closset, Cyril, Kim, Heeyeon, Willett, Brian

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We study three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories on $\mathcal{M}_{g,p}$, an oriented circle bundle of degree $p$ over a closed Riemann surface, $\Sigma_g$.

We compute the $\mathcal{M}_{g,p}$ supersymmetric partition function and correlation functions of supersymmetric loop operators.
This uncovers interesting relations between observables on manifolds of different topologies.
In particular, the familiar supersymmetric partition function on the round $S^3$ can be understood as the expectation value of a so-called "fibering operator" on $S^2 \times S^1$ with a topological twist.

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