TY - JOUR
T1 - Moving the CFT into the bulk with TT¯
AU - McGough, Lauren
AU - Mezei, Márk
AU - Verlinde, Herman
N1 - Funding Information:
We thank Vijay Balasubramanian, Clay Cordova, Xi Dong, Raphael Flauger, Tom Hart-man, Bruno Le Floch, Igor Klebanov, Sung-Sik Lee, Hong Liu, and Juan Maldacena for helpful discussions and comments. The research of M.M. was supported in part by the U.S. Department of Energy under grant No. DE-SC0016244. The research of H.V. is supported by NSF grant PHY-1620059.
Publisher Copyright:
© 2018, The Author(s).
PY - 2018/4/1
Y1 - 2018/4/1
N2 - Recent work by Zamolodchikov and others has uncovered a solvable irrelevant deformation of general 2D CFTs, defined by turning on the dimension 4 operator TT¯ ,the product of the left- and right-moving stress tensor. We propose that in the holographic dual, this deformation represents a geometric cutoff that removes the asymptotic region of AdS and places the QFT on a Dirichlet wall at finite radial distance r = rc in the bulk. As a quantitative check of the proposed duality, we compute the signal propagation speed, energy spectrum, and thermodynamic relations on both sides. In all cases, we obtain a precise match. We derive an exact RG flow equation for the metric dependence of the effective action of the TT¯ deformed theory, and find that it coincides with the Hamilton-Jacobi equation that governs the radial evolution of the classical gravity action in AdS.
AB - Recent work by Zamolodchikov and others has uncovered a solvable irrelevant deformation of general 2D CFTs, defined by turning on the dimension 4 operator TT¯ ,the product of the left- and right-moving stress tensor. We propose that in the holographic dual, this deformation represents a geometric cutoff that removes the asymptotic region of AdS and places the QFT on a Dirichlet wall at finite radial distance r = rc in the bulk. As a quantitative check of the proposed duality, we compute the signal propagation speed, energy spectrum, and thermodynamic relations on both sides. In all cases, we obtain a precise match. We derive an exact RG flow equation for the metric dependence of the effective action of the TT¯ deformed theory, and find that it coincides with the Hamilton-Jacobi equation that governs the radial evolution of the classical gravity action in AdS.
KW - AdS-CFT Correspondence
KW - Conformal Field Theory
KW - Renormalization Group
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U2 - 10.1007/JHEP04(2018)010
DO - 10.1007/JHEP04(2018)010
M3 - Article
AN - SCOPUS:85045110089
SN - 1126-6708
VL - 2018
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 4
M1 - 10
ER -