Abstract
An important part of a CFT four-point function, the stress tensor sector, comprises the exchanges of the stress tensor and its composites. The OPE coefficients of these multi-stress tensor operators and consequently, the complete stress tensor sector of four- point functions in CFTs with a large central charge, can be determined by computing a heavy-heavy-light-light correlator. We show how one can make substantial progress in this direction by bootstrapping a certain ansatz for the stress tensor sector of the correlator, iteratively computing the OPE coefficients of multi-stress tensor operators with increasing twist. Some parameters are not fixed by the bootstrap — they correspond to the OPE coefficients of multi-stress tensors with spin zero and two. We further show that in holographic CFTs one can use the phase shift computed in the dual gravitational theory to reduce the set of undetermined parameters to the OPE coefficients of multi-stress tensors with spin zero. Finally, we verify some of these results using the Lorentzian OPE inversion formula and comment on its regime of applicability.
Highlights
Introduction and summary1.1 IntroductionConformal field theories (CFTs) are the harmonic oscillators of our times; besides being significantly more amenable to analytic study compared to generic quantum field theories, they provide a non-perturbative definition of gravity in negatively curved spacetimes via the AdS/CFT correspondence [1,2,3]
We further show that in holographic CFTs one can use the phase shift computed in the dual gravitational theory to reduce the set of undetermined parameters to the OPE coefficients of multi-stress tensors with spin zero
We investigate a complementary approach to computing the OPE data of the stress tensor sector using the Lorentzian inversion formula
Summary
Conformal field theories (CFTs) are the harmonic oscillators of our times; besides being significantly more amenable to analytic study compared to generic quantum field theories, they provide a non-perturbative definition of gravity in negatively curved spacetimes via the AdS/CFT correspondence [1,2,3]. We consider the four-point function OH OLOLOH of two pairwise identical scalar operators labeled as “light, L”, and “heavy, H”, depending on whether their conformal dimension scales with the number of degrees of freedom, ∆H ∝ O(CT ), or not, ∆L ∝ O(1) The reason this correlator is well-suited to the exploration of the stress-tensor sector is the presence of an additional parameter, μ, proportional to the ratio of the conformal dimension of the heavy operators with the central charge, μ ∝ ∆H /CT. Matching terms in the correlator obtained from the gravitational calculation to those obtained from the CFT enables us to completely fix the stress tensor sector of the HHLL correlator up to the OPE coefficients of the spin-0 multi-stress tensors which are left undetermined. Non-universality is manifest by the presence of the Gauss-Bonnet coupling in the expressions for the OPE coefficients
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