Graviton scattering and a sum rule for the c anomaly in 4D CFT

Gillioz, Marc; Lu, Xiaochuan; Luty, Markus A.

doi:10.1007/jhep09(2018)025

Title: Graviton scattering and a sum rule for the c anomaly in 4D CFT

Journal Article · Wed Sep 05 00:00:00 EDT 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep09(2018)025· OSTI ID:1505197

Gillioz, Marc ^[1]; Lu, Xiaochuan ^[2]; Luty, Markus A. ^[2]

Ecole Polytechnique Federale Lausanne (Switzlerland). Theoretical Particle Physics Lab.
Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)

4D CFTs have a scale anomaly characterized by the coefficient c, which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor. By studying the CFT contribution to 4-point graviton scattering amplitudes in Minkowski space we derive a sum rule for c in terms of TT O OPE coefficients. The sum rule can be thought of as a version of the optical theorem, and its validity depends on the existence of the massless and forward limits of the $$\langle$$TTTT$$\rangle$$ correlation functions that contribute. The finiteness of these limits is checked explicitly for free scalar, fermion, and vector CFTs. The sum rule gives c as a sum of positive terms, and therefore implies a lower bound on c given any lower bound on TT O OPE coefficients. We compute the coefficients to the sum rule for arbitrary operators of spin 0 and 2, including the energy-momentum tensor.

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Research Organization:: Univ. of California, Davis, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-91ER40674

OSTI ID:: 1505197

Journal Information:: Journal of High Energy Physics (Online), Vol. 2018, Issue 9; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 20 works

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