Leading multi-stress tensors and conformal bootstrap
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Springer
Received: October 15, 2019 Accepted: November 26, 2019 Published: January 14, 2020
Robin Karlsson, Manuela Kulaxizi, Andrei Parnachev and Petar Tadi´ c School of Mathematics, Trinity College Dublin, Dublin 2, Ireland
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: Near lightcone correlators are dominated by operators with the lowest twist. We consider the contributions of such leading lowest twist multi-stress tensor operators to a heavy-heavy-light-light correlator in a CFT of any even dimensionality with a large central charge. An infinite number of such operators contribute, but their sum is described by a simple ansatz. We show that the coefficients in this ansatz can be determined recursively, thereby providing an operational procedure to compute them. This is achieved by bootstrapping the corresponding near lightcone correlator: conformal data for any minimaltwist determines that for the higher minimal-twist and so on. To illustrate this procedure in four spacetime dimensions we determine the contributions of double- and triple-stress tensors. We compute the OPE coefficients; whenever results are available in the literature, we observe complete agreement. We also compute the contributions of double-stress tensors in six spacetime dimensions and determine the corresponding OPE coefficients. In all cases the results are consistent with the exponentiation of the near lightcone correlator. This is similar to the situation in two spacetime dimensions for the Virasoro vacuum block. Keywords: AdS-CFT Correspondence, Conformal Field Theory ArXiv ePrint: 1909.05775
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP01(2020)076
JHEP01(2020)076
Leading multi-stress tensors and conformal bootstrap
Contents 1 Introduction and summary 1.1 Introduction 1.2 Summary of the results 1.3 Outline
1 1 4 5
2 Review of heavy-heavy-light-light correlator in the lightcone limit
5 8 10 11 12 13 14
4 Minimal-twist double-stress tensors in six dimensions 4.1 Exponentiation of minimal-twist multi-stress tensors in six dimensions 4.2 OPE coefficients of minimal-twist double-stress tensors
16 18 18
5 Discussion
19
1 1.1
Introduction and summary Introduction
The two-point function of the stress tensor in Conformal Field Theories is proportional to a single parameter, the central charge CT . It generally serves as a measure of the number of degrees of freedom in the theory. In two spacetime dimensions this statement can be made precise: one can define a c-function which monotonically decreases along Renormalization Group flows and reduces to the central charge at conformal fixed points [1]. In four spacetime dimensions the situation is a bit more subtle and it is the a-coefficient in the conformal anomaly which necessarily satisfies aIR ≤ aU V [2]. Nevertheless, in any unitary conformal field theory a and CT can only differ by a number of O(1) (see [3] for the original argument and [4–10] for more recent field theoretic proof
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