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Comments on ABJM free energy on $S^{3}$ at large $N$ and perturbative expansions in M-theory and string theory

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arxiv 2306.02862 v3 pith:5IRZ62AM submitted 2023-06-05 hep-th

Matteo Beccaria , Arkady A. Tseytlin This is my paper · ORCID
classification hep-th
keywords expansionlargem-theorystringtheorytimescoefficientsexpansions
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We compare large $N$ expansion of the localization result for the free energy $F$ in the 3d $\mathcal{N}=6$ superconformal $U(N)_k \times U(N)_{-k}$ Chern-Simons-matter theory to its AdS/CFT counterpart, i.e. to the perturbative expansion of M-theory partition function on AdS$_{4}\times S^{7}/\mathbb{Z}_{k}$ and to the weak string coupling expansion of type IIA effective action on AdS$_{4}\times {\rm CP}^3$. We show that the general form of the perturbative expansions of $F$ on the two sides of the AdS/CFT duality is indeed the same. Moreover, the transcendentality properties of the coefficients in the large $N$, large $k$ expansion of $F$ match those in the corresponding M-theory or string theory expansions. To shed light on the structure of the 1-loop M-theory partition function on AdS$_{4}\times S^{7}/\mathbb{Z}_{k}$ we use the expression for the 1-loop 4-graviton scattering amplitude in the 11d supergravity. We also use the known information about the transcendental coefficients of the leading curvature invariants in the low-energy effective action of type II string theory. Matching of the remaining rational factors in the coefficients requires a precise information about currently unknown RR field strength terms in the corresponding superinvariants.

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Cited by 5 Pith papers

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    hep-th 2025-02 conditional novelty 6.0 of 10

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