Built on

D. Gang, N. Kim and L. A. Pando Zayas, Precision Microstate Counting for the Entropy of Wrapped M5-branes , 1905.01559
Original
1905
Earlier work this paper cites.
D. Cassani and L. Papini, The BPS limit of rotating AdS black hole thermodynamics , 1906.10148
Original
1906
Earlier work this paper cites.
P. Orlik and F. Raymond, Actions of the torus on 4-manifolds. i , Transactions of the American Mathematical Society 152
1970
Earlier work this paper cites.
D. Z. Freedman and A. K. Das, Gauge Internal Symmetry in Extended Supergravity , Nucl. Phys. B120
1977
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, Classification of Gravitational Instanton Symmetries , Commun. Math. Phys. 66
1979
Earlier work this paper cites.
L. J. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory , Nucl. Phys. B383
1992
Earlier work this paper cites.
D. R. Brill, J. Louko and P. Peldan, Thermodynamics of (3+1)-dimensional black holes with toroidal or higher genus horizons , Phys. Rev. D56
1997
Earlier work this paper cites.
R. Emparan, C. V. Johnson and R. C. Myers, Surface terms as counterterms in the AdS / CFT correspondence , Phys. Rev. D60
1999
Earlier work this paper cites.
A. Chamblin, R. Emparan, C. V. Johnson and R. C. Myers, Large N phases, gravitational instantons and the nuts and bolts of AdS holography , Phys. Rev. D59
1999
Earlier work this paper cites.
M. M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes , Nucl. Phys. B545
1999
Earlier work this paper cites.
K. Skenderis, Lecture notes on holographic renormalization , Class. Quant. Grav. 19
2002
Earlier work this paper cites.
D. M. J. Calderbank and H. Pedersen, Selfdual Einstein metrics with torus symmetry , J. Diff. Geom. 60
2002
Earlier work this paper cites.
N. A. Nekrasov, Seiberg-Witten prepotential from instanton counting , Adv. Theor. Math. Phys. 7
2003
Earlier work this paper cites.
D. M. J. Calderbank and M. A. Singer, Einstein metrics and complex singularities , Invent. Math. 156
2004
Earlier work this paper cites.
D. Martelli, J. Sparks and S.-T. Yau, The Geometric dual of a-maximisation for Toric Sasaki-Einstein manifolds , Commun. Math. Phys. 268
2006
Earlier work this paper cites.
J. P. Gauntlett and O. Varela, Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions , Phys. Rev. D76
Original
2007
Earlier work this paper cites.
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals , JHEP 10
Original
2008
Earlier work this paper cites.
A. Futaki, H. Ono and G. Wang, Transverse Kahler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds , J. Diff. Geom. 83
2009
Earlier work this paper cites.

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2019

Localization of the action in AdS/CFT

Genolini, Pietro Benetti, Ipiña, Juan Manuel Pérez, Sparks, James

Understand

We derive a simple formula for the action of any supersymmetric solution to minimal gauged supergravity in the AdS$_4$/CFT$_3$ correspondence.

Such solutions are equipped with a supersymmetric Killing vector, and we show that the holographically renormalized action may be expressed entirely in terms of the weights of this vector field at its fixed points, together with certain topological data.
In this sense, the classical gravitational partition function localizes in the bulk.
We illustrate our general formula with a number of explicit examples, in which exact dual field theory computations are also available, which include supersymmetric Taub-NUT and Taub-bolt type spacetimes, as well as black hole solutions.

Built on

D. Gang, N. Kim and L. A. Pando Zayas, Precision Microstate Counting for the Entropy of Wrapped M5-branes , 1905.01559
Original
1905
Earlier work this paper cites.
D. Cassani and L. Papini, The BPS limit of rotating AdS black hole thermodynamics , 1906.10148
Original
1906
Earlier work this paper cites.
P. Orlik and F. Raymond, Actions of the torus on 4-manifolds. i , Transactions of the American Mathematical Society 152
1970
Earlier work this paper cites.
D. Z. Freedman and A. K. Das, Gauge Internal Symmetry in Extended Supergravity , Nucl. Phys. B120
1977
Earlier work this paper cites.
G. W. Gibbons and S. W. Hawking, Classification of Gravitational Instanton Symmetries , Commun. Math. Phys. 66
1979
Earlier work this paper cites.
L. J. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory , Nucl. Phys. B383
1992
Earlier work this paper cites.
D. R. Brill, J. Louko and P. Peldan, Thermodynamics of (3+1)-dimensional black holes with toroidal or higher genus horizons , Phys. Rev. D56
1997
Earlier work this paper cites.
R. Emparan, C. V. Johnson and R. C. Myers, Surface terms as counterterms in the AdS / CFT correspondence , Phys. Rev. D60
1999
Earlier work this paper cites.
A. Chamblin, R. Emparan, C. V. Johnson and R. C. Myers, Large N phases, gravitational instantons and the nuts and bolts of AdS holography , Phys. Rev. D59
1999
Earlier work this paper cites.
M. M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes , Nucl. Phys. B545
1999
Earlier work this paper cites.
K. Skenderis, Lecture notes on holographic renormalization , Class. Quant. Grav. 19
2002
Earlier work this paper cites.
D. M. J. Calderbank and H. Pedersen, Selfdual Einstein metrics with torus symmetry , J. Diff. Geom. 60
2002
Earlier work this paper cites.
N. A. Nekrasov, Seiberg-Witten prepotential from instanton counting , Adv. Theor. Math. Phys. 7
2003
Earlier work this paper cites.
D. M. J. Calderbank and M. A. Singer, Einstein metrics and complex singularities , Invent. Math. 156
2004
Earlier work this paper cites.
D. Martelli, J. Sparks and S.-T. Yau, The Geometric dual of a-maximisation for Toric Sasaki-Einstein manifolds , Commun. Math. Phys. 268
2006
Earlier work this paper cites.
J. P. Gauntlett and O. Varela, Consistent Kaluza-Klein reductions for general supersymmetric AdS solutions , Phys. Rev. D76
Original
2007
Earlier work this paper cites.
O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals , JHEP 10
Original
2008
Earlier work this paper cites.
A. Futaki, H. Ono and G. Wang, Transverse Kahler geometry of Sasaki manifolds and toric Sasaki-Einstein manifolds , J. Diff. Geom. 83
2009
Earlier work this paper cites.