Localization on Hopf surfaces
By Benjamin Assel, D. Cassani, D. Martelli. 2014
176 citations recorded by the source corpus.
A bstractWe discuss localization of the path integral for supersymmetric gauge theories with an R-symmetry on Hermitian four-manifolds. After presenting the localization locus equations for the general case, we focus on backgrounds with S1 × S3 topology, admitting two supercharges of opposite R-charge. These are Hopf surfaces, with two complex structure moduli p, q. We compute the localized partition function on such Hopf surfaces, allowing for a very large class of Hermitian metrics, and prove that this is proportional to the supersymmetric index with fugacities p, q. Using zeta function regularisation, we determine the exact proportionality factor, finding that it depends only on p, q, and on the anomaly coefficients a, c of the field theory. This may be interpreted as a supersymmetric Casimir energy, and provides the leading order contribution to the partition function in a large N expansion.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/51d1ade398600083e649dbe780008af140ea99e8
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In Astronomy and Astrophysics
- Z. Komargodski
- L. Pietro
- Cyril Closset
- D. Cassani
- D. Martelli
- Brian Willett
- Benjamin Assel
- Hee-Cheol Kim
In Nuclear and High Energy Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Cardy formulae for SUSY theories in d = 4 and d = 6 (2014, methodology): “Note however that if one restricts to the Römelsberger index rather than the partition function, then the results of [41] are consistent with (4.”
- The Casimir energy in curved space and its supersymmetric counterpart (2015, methodology): “The Casimir energy, Esusy, is thus naturally defined from the large β limit of the partition function [20]”
- Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, methodology): “he physics. However both the result for Fand its Legendre transform do depend on n. For n= 1 we are led to the black hole entropy, while for n= 0 Fis proportional to the supersymmetric Casimir energy [18,19] and yields a vanishing entropy. The fact that the BPS AdS 5 black hole entropy can be rewrit”
- N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “In the physical gauge, the S3 × S1 partition function has a well-known expression as an elliptic hypergeometric integral [2, 12]:”