Abstract
A double-trace deformation is the simplest perturbation of a conformal field theory that has a gravity dual. In this paper we review the existing results for the case in which the deformation is composed from a scalar operator, and extend them to the case of a spinor operator. In particular we check the validity of the c-conjecture along the RG flow induced by the deformation, using both Cardy’s c-function and the recent proposal by Myers and Sinha of a c-function from entanglement entropy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. Witten, Multi-trace operators, boundary conditions and AdS/CFT correspondence, hep-th/0112258 [SPIRES].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [SPIRES].
T. Hartman and L. Rastelli, Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT, JHEP 01 (2008) 019 [hep-th/0602106] [SPIRES].
M. Berkooz, A. Sever and A. Shomer, Double-trace deformations, boundary conditions and spacetime singularities, JHEP 05 (2002) 034 [hep-th/0112264] [SPIRES].
S.S. Gubser and I. Mitra, Double-trace operators and one-loop vacuum energy in AdS/CFT, Phys. Rev. D 67 (2003) 064018 [hep-th/0210093] [SPIRES].
J.L. Cardy, Is There a c Theorem in Four-Dimensions?, Phys. Lett. B 215 (1988) 749 [SPIRES].
S.S. Gubser and I.R. Klebanov, A universal result on central charges in the presence of double-trace deformations, Nucl. Phys. B 656 (2003) 23 [hep-th/0212138] [SPIRES].
T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, ar**v:0907.2694 [SPIRES].
H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, ar**v:0903.2477 [SPIRES].
T. Faulkner, G.T. Horowitz and M.M. Roberts, Holographic quantum criticality from multi-trace deformations, ar**v:1008.1581 [SPIRES].
R.C. Myers and A. Sinha, Seeing a c-theorem with holography, Phys. Rev. D 82 (2010) 046006 [ar**v:1006.1263] [SPIRES].
L. Vecchi, Multitrace deformations, Gamow states and Stability of AdS/CFT, ar**v:1005.4921 [SPIRES].
M. Henneaux, Boundary terms in the AdS/CFT correspondence for spinor fields, hep-th/9902137 [SPIRES].
M. Henningson and K. Sfetsos, Spinors and the AdS/CFT correspondence, Phys. Lett. B 431 (1998) 63 [hep-th/9803251] [SPIRES].
W. Mueck and K.S. Viswanathan, Conformal field theory correlators from classical field theory on anti-de Sitter space. II: Vector and spinor fields, Phys. Rev. D 58 (1998) 106006 [hep-th/9805145] [SPIRES].
A.B. Zamolodchikov, Irreversibility of the Flux of the Renormalization Group in a 2D Field Theory, JETP Lett. 43 (1986) 730 [SPIRES].
A.D. Shapere and Y. Tachikawa, A counterexample to the ’a-theorem’, JHEP 12 (2008) 020 [ar**v:0809.3238] [SPIRES].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [SPIRES].
G.W. Gibbons, S.W. Hawking and M.J. Perry, Path Integrals and the Indefiniteness of the Gravitational Action, Nucl. Phys. B 138 (1978) 141 [SPIRES].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [SPIRES].
S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy, JHEP 08 (2006) 045 [hep-th/0605073] [SPIRES].
R. Camporesi and A. Higuchi, On the Eigen functions of the Dirac operator on spheres and real hyperbolic spaces, J. Geom. Phys. 20 (1996) 1 [gr-qc/9505009] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
Ar**v ePrint : 1007.2047
Rights and permissions
About this article
Cite this article
Allais, A. Double-trace deformations, holography and the c-conjecture. J. High Energ. Phys. 2010, 40 (2010). https://doi.org/10.1007/JHEP11(2010)040
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2010)040