The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS${}_4$ Black Hole Entropy

Abstract

We study the topologically twisted index of $\mathcal{N}=6$ supersymmetric Chern-Simons matter theory with $U(N{)}_k\times U(N{)}_{-k}$ gauge group in the 't Hooft limit, that is, for $N,k\to \infty$ with $\lambda =N/k$ fixed. In the regime where $\lambda$ is fixed and large we find an analytical expression for the leading order term of the index. The leading term of the index matches precisely the Bekenstein-Hawking entropy of the dual asymptotically AdS${}_4$ magnetically charged black holes embedded in IIA supergrvity on AdS${}_4\times {\mathbb{CP}}^3$, after a standard Legendre transformation. We numerically explore the genus expansion of the topologically twisteed index beyond the leading order, focusing on the genus one contribution, that is, $N^0$. We find qualitative agreement with the topological expansion of the free energy on $S^3$ at genus one. Our logarithmic in $\lambda$ term constitutes a prediction for the one-loop effective action on the IIA supergravity side.

30 pages, 14 figures, 6 tables

References in corpus (7)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Holographic microstate counting for AdS${}_4$ black holes in massive IIA supergravity
• Localization of the action in AdS/CFT
• Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity
• Logarithmic Corrections to Entropy of Magnetically Charged AdS4 Black Holes
• Instanton Corrections of 1/6 BPS Wilson Loops in ABJM Theory

Cited by in corpus (10)

• Microscopic Entropy of Rotating Electrically Charged AdS${}_4$ Black Holes from Field Theory Localization
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• Universal 3d Cardy Block and Black Hole Entropy
• Large $N$ Partition Functions of the ABJM Theory
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• One-loop determinants for black holes in 4d gauged supergravity
• Universal Entropy and Hawking Radiation of Near-Extremal AdS${}_4$ Black Holes
• The large-N partition function for non-parity-invariant Chern-Simons-matter theories
• Subleading corrections to the free energy in a theory with $N^{5/3}$ scaling