Factorization of log-corrections in \(\mathrm{AdS}_4/\mathrm{CFT}_3\) from supergravity localization. (English) Zbl 1521.81392
Summary: We use the Atiyah-Singer index theorem to derive the general form of the one-loop corrections to observables in asymptotically anti-de Sitter (\(\mathrm{AdS}_4\)) supersymmetric backgrounds of abelian gauged supergravity. Using the method of supergravity localization combined with the factorization of the supergravity action on fixed points (NUTs) and fixed two-manifolds (Bolts) we show that an analogous factorization takes place for the one-loop determinants of supergravity fields. This allows us to propose a general fixed-point formula for the logarithmic corrections to a large class of supersymmetric partition functions in the large \(N\) expansion of a given 3d dual theory. The corrections are uniquely fixed by some simple topological data pertaining to a particular background in the form of its regularized Euler characteristic \(\chi\), together with a single dynamical coefficient that counts the underlying degrees of freedom of the theory.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
| 83E50 | Supergravity |
| 83C57 | Black holes |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 83E30 | String and superstring theories in gravitational theory |
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