# Topologically twisted index in the ’t Hooft limit and the dual ${\mathrm{AdS}}_{4}$ black hole entropy

## Abstract

We study the topologically twisted index of N = 6 supersymmetric Chern-Simons matter theory with U(N)_{k} × U(N) _{–k} gauge group in the ’t Hooft limit, that is, for N, k → ∞ with λ = N/k fixed. In the regime where λ 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} × 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 λ term constitutes a prediction for the one-loop effective action on the IIA supergravity side.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Michigan, Ann Arbor, MI (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)

- OSTI Identifier:
- 1579997

- Alternate Identifier(s):
- OSTI ID: 1656713

- Grant/Contract Number:
- SC0007859

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 12; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Gauge-gravity dualities; Large-N expansion in field theory; Quantum aspects of black holes

### Citation Formats

```
Pando Zayas, Leopoldo A., and Xin, Yu. Topologically twisted index in the ’t Hooft limit and the dual AdS 4 black hole entropy. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.126019.
```

```
Pando Zayas, Leopoldo A., & Xin, Yu. Topologically twisted index in the ’t Hooft limit and the dual AdS 4 black hole entropy. United States. doi:10.1103/PhysRevD.100.126019.
```

```
Pando Zayas, Leopoldo A., and Xin, Yu. Thu .
"Topologically twisted index in the ’t Hooft limit and the dual AdS 4 black hole entropy". United States. doi:10.1103/PhysRevD.100.126019.
```

```
@article{osti_1579997,
```

title = {Topologically twisted index in the ’t Hooft limit and the dual AdS 4 black hole entropy},

author = {Pando Zayas, Leopoldo A. and Xin, Yu},

abstractNote = {We study the topologically twisted index of N = 6 supersymmetric Chern-Simons matter theory with U(N)k × U(N) –k gauge group in the ’t Hooft limit, that is, for N, k → ∞ with λ = N/k fixed. In the regime where λ 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 AdS4 magnetically charged black holes embedded in IIA supergrvity on AdS4 × CP3, 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, N0. We find qualitative agreement with the topological expansion of the free energy on S3 at genus one. Our logarithmic in λ term constitutes a prediction for the one-loop effective action on the IIA supergravity side.},

doi = {10.1103/PhysRevD.100.126019},

journal = {Physical Review D},

number = 12,

volume = 100,

place = {United States},

year = {2019},

month = {12}

}

DOI: 10.1103/PhysRevD.100.126019

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