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

Abstract

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.

Authors:
 [1];  [2];  [2]
  1. Ecole Polytechnique Federale Lausanne (Switzlerland). Theoretical Particle Physics Lab.
  2. Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
Publication Date:
Research Org.:
Univ. of California, Davis, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1505197
Grant/Contract Number:  
[FG02-91ER40674]
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
[Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 9]; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Anomalies in Field and String Theories; Conformal Field Theory

Citation Formats

Gillioz, Marc, Lu, Xiaochuan, and Luty, Markus A. Graviton scattering and a sum rule for the c anomaly in 4D CFT. United States: N. p., 2018. Web. doi:10.1007/jhep09(2018)025.
Gillioz, Marc, Lu, Xiaochuan, & Luty, Markus A. Graviton scattering and a sum rule for the c anomaly in 4D CFT. United States. doi:10.1007/jhep09(2018)025.
Gillioz, Marc, Lu, Xiaochuan, and Luty, Markus A. Wed . "Graviton scattering and a sum rule for the c anomaly in 4D CFT". United States. doi:10.1007/jhep09(2018)025. https://www.osti.gov/servlets/purl/1505197.
@article{osti_1505197,
title = {Graviton scattering and a sum rule for the c anomaly in 4D CFT},
author = {Gillioz, Marc and Lu, Xiaochuan and Luty, Markus A.},
abstractNote = {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.},
doi = {10.1007/jhep09(2018)025},
journal = {Journal of High Energy Physics (Online)},
number = [9],
volume = [2018],
place = {United States},
year = {2018},
month = {9}
}

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