Perturbatively exact supersymmetric partition functions of ABJM theory on Seifert manifolds and holography

TL;DR

This paper computes the supersymmetric partition function of ABJM theory on Seifert manifolds to all orders in 1/N, matches it with holographic duals including higher derivative corrections, and clarifies the role of U(1)_R holonomy.

Contribution

It provides a perturbatively exact calculation of the ABJM partition function on Seifert manifolds and establishes a detailed holographic correspondence including 4-derivative and 1-loop corrections.

Findings

Exact partition function matches holographic on-shell action.

Clarification of U(1)_R holonomy in the dual geometry.

Insights into logarithmic corrections from M-theory loops.

Abstract

We undertake a comprehensive analysis of the supersymmetric partition function of the $\text{U}(N)_k\times\text{U}(N)_{-k}$ ABJM theory on a Seifert manifold, evaluating it to all orders in the $1/N$-perturbative expansion up to exponentially suppressed corrections. Through holographic duality, our perturbatively exact result is successfully matched with the regularized on-shell action of a dual Euclidean AdS$_4$-Taub-Bolt background incorporating 4-derivative corrections, and also provides valuable insights into the logarithmic corrections that emerge from the 1-loop calculations in M-theory path integrals. In this process, we revisit the Euclidean AdS$_4$-Taub-Bolt background carefully, elucidating the flat connection in the background graviphoton field. This analysis umambiguously determines the U(1)$_R$ holonomy along the Seifert fiber, thereby solidifying the holographic comparison regarding the partition function on a large class of Seifert manifolds.