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Effective conformal theory and the flat-space limit of AdS

Fitzpatrick, A. Liam and Katz, Emanuel and Poland, David and Simmons-Duffin, David (2011) Effective conformal theory and the flat-space limit of AdS. Journal of High Energy Physics, 2011 (7). Art. No. 023. ISSN 1029-8479.

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We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, O, we consider the anomalous dimensions, γ(n,l), of the double-trace operators of the form O(∂^2)^n(∂)^lO. Purely from the CFT we find that perturbative unitarity places a bound on these dimensions of |γ(n,l)| < 4. Non-renormalizable AdS interactions lead to violations of the bound at large values of n. We also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. We show that the presence of the heavy field “unitarizes” the growth in the anomalous dimensions, and leads to a resonance like behavior in γ(n, l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, we demonstrate that bulk flat-space S-matrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum of anomalous dimensions in d-dimensional CFTs and flatspace S-matrix elements in d + 1 dimensions. We comment on the emergence of flat-space locality from the CFT perspective.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Poland, David0000-0003-3854-2430
Simmons-Duffin, David0000-0002-2937-9515
Additional Information:© 2011 SISSA, Trieste, Italy. Received: May 13, 2011. Accepted: June 5, 2011. Published: July 5, 2011. We would like to thank J. Penedones, J.Maldacena, and A. Cohen for helpful conversations, and J. Polchinski, S. Giddings, and J. Kaplan for comments on the manuscript. We also thank the Aspen Center for Physics for its hospitality during the completion of this work. ALF and EK are supported by DOE grant DE-FG02-01ER-40676 and NSF CAREER grant PHY-0645456, and EK is supported also by an Alfred P. Sloan Fellowship. DP and DSD are supported by the Harvard Center for the Fundamental Laws of Nature and by NSF grant PHY-0556111.
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-01ER-40676
Alfred P. Sloan FoundationUNSPECIFIED
Harvard Center for the Fundamental Laws of NatureUNSPECIFIED
Subject Keywords:AdS-CFT Correspondence, Field Theories in Higher Dimensions, 1/N Expansion
Issue or Number:7
Record Number:CaltechAUTHORS:20170816-092357056
Persistent URL:
Official Citation:Fitzpatrick, A.L., Katz, E., Poland, D. et al. J. High Energ. Phys. (2011) 2011: 23.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80472
Deposited By: Ruth Sustaita
Deposited On:16 Aug 2017 22:51
Last Modified:20 Nov 2020 20:03

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