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

초록

We undertake a comprehensive analysis of the supersymmetric partition function of the U(N)k x U(N)-k ABJM theory on a U(1) fibration over a Riemann surface, 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 AdS4-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 AdS4-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 subclass of Seifert manifolds.

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