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 deri...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-09-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2018)025 |
| _version_ | 1818349832779071488 |
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| author | Marc Gillioz Xiaochuan Lu Markus A. Luty |
| author_facet | Marc Gillioz Xiaochuan Lu Markus A. Luty |
| author_sort | Marc Gillioz |
| collection | DOAJ |
| description | 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 $$ \mathcal{O} $$ 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 〈TTTT〉 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 $$ \mathcal{O} $$ OPE coefficients. We compute the coefficients to the sum rule for arbitrary operators of spin 0 and 2, including the energy-momentum tensor. |
| first_indexed | 2024-12-13T18:12:13Z |
| format | Article |
| id | doaj.art-cdf43b17fd4a49e2b8a657ee377dfe2b |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T18:12:13Z |
| publishDate | 2018-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-cdf43b17fd4a49e2b8a657ee377dfe2b2022-12-21T23:35:56ZengSpringerOpenJournal of High Energy Physics1029-84792018-09-012018915110.1007/JHEP09(2018)025Graviton scattering and a sum rule for the c anomaly in 4D CFTMarc Gillioz0Xiaochuan Lu1Markus A. Luty2Theoretical Particle Physics Laboratory, Institute of Physics, EPFLCenter for Quantum Mathematics and Physics (QMAP), University of CaliforniaCenter for Quantum Mathematics and Physics (QMAP), University of CaliforniaAbstract 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 $$ \mathcal{O} $$ 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 〈TTTT〉 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 $$ \mathcal{O} $$ OPE coefficients. We compute the coefficients to the sum rule for arbitrary operators of spin 0 and 2, including the energy-momentum tensor.http://link.springer.com/article/10.1007/JHEP09(2018)025Anomalies in Field and String TheoriesConformal Field Theory |
| spellingShingle | Marc Gillioz Xiaochuan Lu Markus A. Luty Graviton scattering and a sum rule for the c anomaly in 4D CFT Journal of High Energy Physics Anomalies in Field and String Theories Conformal Field Theory |
| title | Graviton scattering and a sum rule for the c anomaly in 4D CFT |
| title_full | Graviton scattering and a sum rule for the c anomaly in 4D CFT |
| title_fullStr | Graviton scattering and a sum rule for the c anomaly in 4D CFT |
| title_full_unstemmed | Graviton scattering and a sum rule for the c anomaly in 4D CFT |
| title_short | Graviton scattering and a sum rule for the c anomaly in 4D CFT |
| title_sort | graviton scattering and a sum rule for the c anomaly in 4d cft |
| topic | Anomalies in Field and String Theories Conformal Field Theory |
| url | http://link.springer.com/article/10.1007/JHEP09(2018)025 |
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