Abstract
We derive recursion relations for the anomalous dimensions of double-trace operators occurring in the conformal block expansion of four-point stress tensor correlators in the 6d (2, 0) theory, which encode higher-derivative corrections to supergravity in AdS7 × S4 arising from M-theory. As a warm-up, we derive analogous recursion relations for four-point functions of scalar operators in a toy non-supersymmetric 6d conformal field theory.
Highlights
Solutions directly from the crossing equations, confirming the results of [6] as well as giving an alternative and more direct method for obtaining higher-derivative results
In appendix C we describe a general algorithm for solving the recursion relations for anomalous dimensions, and in appendix D we describe the solutions for spin truncation L = 2
Given that no Lagrangian description is presently known for this model, our strategy is to use superconformal and crossing symmetry of four-point correlators of stress tensor multiplets
Summary
In [7] the authors considered four-point correlators of scalar operators in an abstract nonsupersymmetric CFT in two and four dimensions, and showed that the solutions to the crossing equations whose conformal block expansion is truncated in spin are in one-to-one correspondence with local quartic interactions of a massive scalar field in AdS (modulo integration by parts and equations of motion). The conformal block expansion of F (u, v) is given by the following sum over primary operators:. N,l≥0 where An,l are OPE coefficients and GB∆,l are the bosonic conformal blocks given in terms of hypergeometric functions in appendix A, which implicitly depend on n through the scaling dimensions of the conformal primary operator ∆. After solving the recursion relations, we can deduce the 1/c correction to the OPE coefficients A(n1,l) using the following formula: A(n1,l). This formula was first found in two and four dimensions [7, 16] and was subsequently observed to hold in six dimensions [6]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
