Topologically twisted index in the ’t Hooft limit and the dual AdS 4 black hole entropy

Pando Zayas, Leopoldo A.; Xin, Yu

doi:10.1103/PhysRevD.100.126019

Title: Topologically twisted index in the ’t Hooft limit and the dual ${AdS}_{4}$ 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 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.

Authors:

;

Publication Date:: 2019-12-19

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.

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

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                    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.  https://doi.org/10.1103/PhysRevD.100.126019.

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@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}

}

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Title: Topologically twisted index in the ’t Hooft limit and the dual AdS 4 black hole entropy

Abstract

Citation Formats

Toward microstate counting beyond large N in localization and the dual one-loop quantum supergravity journal, January 2018

Worldsheet derivation of a large N duality journal, October 2002

String Theory Origin of Dyonic N = 8 Supergravity and Its Chern-Simons Duals journal, August 2015

Exact microstate counting for dyonic black holes in AdS4 journal, August 2017

Instanton corrections of 1/6 BPS Wilson loops in ABJM theory journal, September 2016

Black hole microstates in AdS4 from supersymmetric localization journal, May 2016

Entropy functional and the holographic attractor mechanism journal, May 2018

Large N twisted partition functions in 3d-3d correspondence and holography journal, January 2019

Supersymmetric partition functions and the three-dimensional A-twist journal, March 2017

A universal counting of black hole microstates in AdS4 journal, February 2018

Black hole entropy in massive Type IIA journal, January 2018

Comments on twisted indices in 3d supersymmetric gauge theories journal, August 2016

Logarithmic corrections to rotating extremal black hole entropy in four and five dimensions journal, May 2012

On the quantum entropy function in 4d gauged supergravity journal, July 2018

On the on-shell: the action of AdS4 black holes journal, March 2018

A one-loop test of quantum supergravity journal, November 2013

Consistent warped-space Kaluza–Klein reductions, half-maximal gauged supergravities and constructions journal, March 2001

Microscopic and macroscopic entropy of extremal black holes in string theory journal, April 2014

Microstate counting of AdS 4 hyperbolic black hole entropy via the topologically twisted index journal, August 2017

AdS4 solutions of massive IIA from dyonic ISO(7) supergravity journal, March 2016

Holographic microstate counting for AdS4 black holes in massive IIA supergravity journal, October 2017

Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates journal, February 2012

Supersymmetric AdS4 black holes and attractors journal, January 2010

Exact results in ABJM theory from topological strings journal, June 2010

Summing up all genus free energy of ABJM matrix model journal, August 2011

Embedding AdS black holes in ten and eleven dimensions journal, October 1999

Nonperturbative aspects of ABJM theory journal, November 2011

Multimatrix models and tri-Sasaki Einstein spaces journal, February 2011

𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals journal, October 2008

Logarithmic corrections to entropy of magnetically charged AdS 4 black holes journal, November 2017

Large N matrix models for 3d N $$ \mathcal{N} $$ = 2 theories: twisted index, free energy and black holes journal, August 2016

Localization of the action in AdS/CFT journal, October 2019

The equivariant A-twist and gauged linear sigma models on the two-sphere journal, June 2015

Large N topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces journal, August 2016

One-Loop Test of Quantum Black Holes in anti–de Sitter Space journal, June 2018

BPS black holes from massive IIA on S6 journal, September 2017

From Weak to Strong Coupling in ABJM Theory journal, May 2011

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

Toward microstate counting beyond large N in localization and the dual one-loop quantum supergravity
journal, January 2018

Worldsheet derivation of a large N duality
journal, October 2002

String Theory Origin of Dyonic $N = 8$ Supergravity and Its Chern-Simons Duals
journal, August 2015

Exact microstate counting for dyonic black holes in AdS4
journal, August 2017

Instanton corrections of 1/6 BPS Wilson loops in ABJM theory
journal, September 2016

Black hole microstates in AdS4 from supersymmetric localization
journal, May 2016

Entropy functional and the holographic attractor mechanism
journal, May 2018

Large $N$ twisted partition functions in 3d-3d correspondence and holography
journal, January 2019

Supersymmetric partition functions and the three-dimensional A-twist
journal, March 2017

A universal counting of black hole microstates in AdS4
journal, February 2018

Black hole entropy in massive Type IIA
journal, January 2018

Comments on twisted indices in 3d supersymmetric gauge theories
journal, August 2016

Logarithmic corrections to rotating extremal black hole entropy in four and five dimensions
journal, May 2012

On the quantum entropy function in 4d gauged supergravity
journal, July 2018

On the on-shell: the action of AdS4 black holes
journal, March 2018

A one-loop test of quantum supergravity
journal, November 2013

Consistent warped-space Kaluza–Klein reductions, half-maximal gauged supergravities and constructions
journal, March 2001

Microscopic and macroscopic entropy of extremal black holes in string theory
journal, April 2014

Microstate counting of AdS 4 hyperbolic black hole entropy via the topologically twisted index
journal, August 2017

AdS4 solutions of massive IIA from dyonic ISO(7) supergravity
journal, March 2016

Holographic microstate counting for AdS4 black holes in massive IIA supergravity
journal, October 2017

Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates
journal, February 2012

Supersymmetric AdS4 black holes and attractors
journal, January 2010

Exact results in ABJM theory from topological strings
journal, June 2010

Summing up all genus free energy of ABJM matrix model
journal, August 2011

Embedding AdS black holes in ten and eleven dimensions
journal, October 1999

Nonperturbative aspects of ABJM theory
journal, November 2011

Multimatrix models and tri-Sasaki Einstein spaces
journal, February 2011

𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
journal, October 2008

Logarithmic corrections to entropy of magnetically charged AdS 4 black holes
journal, November 2017

Large N matrix models for 3d N $$ \mathcal{N} $$ = 2 theories: twisted index, free energy and black holes
journal, August 2016

Localization of the action in AdS/CFT
journal, October 2019

The equivariant A-twist and gauged linear sigma models on the two-sphere
journal, June 2015

Large N topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces
journal, August 2016

One-Loop Test of Quantum Black Holes in anti–de Sitter Space
journal, June 2018

BPS black holes from massive IIA on S6
journal, September 2017

From Weak to Strong Coupling in ABJM Theory
journal, May 2011