5d partition functions with a twist

DOI10.1007/JHEP11(2018)058zbMATH Open1404.81223arXiv1808.06744WikidataQ128990676 ScholiaQ128990676MaRDI QIDQ1635155

Author name not available (Why is that?)

Publication date: 18 December 2018

Published in: (Search for Journal in Brave)

Abstract: We derive the partition function of 5d

c a l N = 1

gauge theories on the manifold

S_{b}^{3} i m e s S i g m a_{f r a k g}

with a partial topological twist along the Riemann surface,

S i g m a_{f r a k g}

. This setup is a higher dimensional uplift of the two-dimensional A-twist, and the result can be expressed as a sum over solutions of Bethe-Ansatz-type equations, with the computation receiving nontrivial non-perturbative contributions. We study this partition function in the large

N

limit, where it is related to holographic RG flows between asymptotically locally AdS

_{6}

and AdS

_{4}

spacetimes, reproducing known holographic relations between the corresponding free energies on

S^{5}

and

S^{3}

and predicting new ones. We also consider cases where the 5d theory admits a UV completion as a 6d SCFT, such as the maximally supersymmetric

c a l N = 2

Yang-Mills theory, in which case the partition function computes the 4d index of general class

c a l S

theories, which we verify in certain simplifying limits. Finally, we comment on the generalization to

{c a l M}_{3} i m e s S i g m a_{f r a k g}

with more general three-manifolds

{c a l M}_{3}

and focus in particular on

{c a l M}_{3} = S i g m a_{f r a k g^{'}} i m e s S^{1}

, in which case the partition function relates to the entropy of black holes in AdS

_{6}

.

Full work available at URL: https://arxiv.org/abs/1808.06744

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