One-loop supergravity on AdS4 × S7/Zk and comparison with ABJM theory

Liu, James T.; Zhao, Wenli

doi:10.1007/JHEP11(2016)099

Title: One-loop supergravity on AdS₄ × S⁷/Z_k and comparison with ABJM theory

Abstract

The large-N limit of ABJM theory is holographically dual to M-theory on AdS₄ × S⁷/Z_k. The 3-sphere partition function has been obtained via localization, and its leading behavior F_ABJM⁽⁰⁾ ~ k^1/2N^3/2 is exactly reproduced in the dual theory by tree-level supergravity. In this paper, we extend this comparison to the sub-leading O(N⁰) order by computing the one-loop supergravity free energy as a function of k and comparing it with the ABJM result. Curiously, we find that the expressions do not match, with F_SUGRA⁽¹⁾~k⁶, while F_ABJM^⁽¹⁾~ k². Finally, this suggests that the low-energy approximation Z_M-theory = Z_SUGRA breaks down at one-loop order.

Authors:

Liu, James T. ^[1]; Zhao, Wenli ^[1]

Univ. of Michigan, Ann Arbor, MI (United States). Randall Lab. of Physics. Michigan Center for Theoretical Physics

Publication Date:: Fri Nov 18 00:00:00 EST 2016

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

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

OSTI Identifier:: 1368085

Grant/Contract Number:: SC0007859

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 11; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; M-Theory

Citation Formats


                    Liu, James T., and Zhao, Wenli. One-loop supergravity on AdS4 × S7/Zk and comparison with ABJM theory.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP11(2016)099.

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                    Liu, James T., & Zhao, Wenli. One-loop supergravity on AdS4 × S7/Zk and comparison with ABJM theory.  United States.  https://doi.org/10.1007/JHEP11(2016)099

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                    Liu, James T., and Zhao, Wenli. Fri .  
"One-loop supergravity on AdS4 × S7/Zk and comparison with ABJM theory".  United States.  https://doi.org/10.1007/JHEP11(2016)099.  https://www.osti.gov/servlets/purl/1368085.

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@article{osti_1368085,

  title        = {One-loop supergravity on AdS4 × S7/Zk and comparison with ABJM theory},

  author       = {Liu, James T. and Zhao, Wenli},

  abstractNote = {The large-N limit of ABJM theory is holographically dual to M-theory on AdS4 × S7/Zk. The 3-sphere partition function has been obtained via localization, and its leading behavior FABJM(0) ~ k1/2N3/2 is exactly reproduced in the dual theory by tree-level supergravity. In this paper, we extend this comparison to the sub-leading O(N0) order by computing the one-loop supergravity free energy as a function of k and comparing it with the ABJM result. Curiously, we find that the expressions do not match, with FSUGRA(1)~k6, while FABJM(1)~ k2. Finally, this suggests that the low-energy approximation ZM-theory = ZSUGRA breaks down at one-loop order.},

  doi          = {10.1007/JHEP11(2016)099},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 11,

  volume       = 2016,

  place        = {United States},

  year         = {Fri Nov 18 00:00:00 EST 2016},

  month        = {Fri Nov 18 00:00:00 EST 2016}

}

Copy to clipboard

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Title: One-loop supergravity on AdS4 × S7/Zk and comparison with ABJM theory

Abstract

Citation Formats

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The shortened KK spectrum of IIB supergravity on Y p,q journal, February 2014

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Order 1/N2 test of the Maldacena conjecture: cancellation of the one-loop Weyl anomaly journal, December 2000

1/N 2 corrections to the holographic Weyl anomaly journal, January 2014

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Indices for superconformal field theories in 3, 5 and 6 dimensions journal, February 2008

Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT journal, November 2014

The Plancherel measure for p-forms in real hyperbolic spaces journal, December 1994

Anomalous radius shift in AdS 4 / CFT 3 journal, July 2009

c − a from the N = 1 $$ \mathcal{N}=1 $$ superconformal index journal, December 2014

Spectral functions and zeta functions in hyperbolic spaces journal, August 1994

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

Order 1/N2 test of the Maldacena conjecture II: the full bulk one-loop contribution to the boundary Weyl anomaly journal, July 2003

Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant journal, May 2012

Holographic c-theorems in arbitrary dimensions journal, January 2011

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The spectrum of IIB supergravity on AdS5 × S 5 / $ {{\mathbb{Z}}_3} $ and a 1/N 2 test of AdS/CFT journal, June 2013

The holographic Weyl anomaly journal, July 1998

Quantum inequivalence of different field representations journal, July 1980

A note on the chiral anomaly in the AdS/CFT correspondence and 1/N2 correction journal, November 1999

The Boundary Weyl Anomaly in the = 4 SYM/Type IIB Supergravity Correspondence journal, January 2004

Nonperturbative aspects of ABJM theory journal, November 2011

Quantum spinning strings in AdS 4 × ℂℙ 3 : testing the Bethe Ansatz proposal journal, November 2008

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

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Title: One-loop supergravity on AdS₄ × S⁷/Z_k and comparison with ABJM theory

D-brane charges in gravitational duals of 2 + 1 dimensional gauge theories and duality cascades
journal, January 2010

Central Charges from the $N = 1$ Superconformal Index
journal, March 2015

On superconformal characters and partition functions in three dimensions
journal, February 2010

Supergravity one-loop corrections on AdS 7 and AdS 3 , higher spins and AdS/CFT
journal, March 2015

The shortened KK spectrum of IIB supergravity on Y p,q
journal, February 2014

A Note on the Partition Function of ABJM Theory on S3
journal, February 2012

Order 1/N2 test of the Maldacena conjecture: cancellation of the one-loop Weyl anomaly
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1/N 2 corrections to the holographic Weyl anomaly
journal, January 2014

Interpolating between a and F
journal, March 2015

Indices for superconformal field theories in 3, 5 and 6 dimensions
journal, February 2008

Higher spins in AdS5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
journal, November 2014

The Plancherel measure for p-forms in real hyperbolic spaces
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Anomalous radius shift in AdS ₄ / CFT ₃
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c − a from the N = 1 $$ \mathcal{N}=1 $$ superconformal index
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Spectral functions and zeta functions in hyperbolic spaces
journal, August 1994

A one-loop test of quantum supergravity
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Order 1/N2 test of the Maldacena conjecture II: the full bulk one-loop contribution to the boundary Weyl anomaly
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Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
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Holographic c-theorems in arbitrary dimensions
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