Conformal anomalies for (maximal) 6d conformal supergravity

authored by: Lorenzo Casarin, Christian Kennedy, Gabriele Tartaglino-Mazzucchelli
Abstract: We compute the conformal anomalies for 6d (2,0) conformal supergravity by direct calculation in component fields. The main novel results consist of the type-B anomaly coefficients for the gravitino and the 3-form, as well as their explicit quadratic action on some specific backgrounds. We also comment on the graviton contribution, whose Lagrangian is essentially given by the Q-curvature. We confirm the expectation that, when coupling (2,0) conformal supergravity to 26 copies of the (2,0) tensor multiplet, the resulting theory is free of conformal anomalies. We also consider the conformal anomalies for its (1,0) truncation and confirm their relation with the chiral anomaly polynomial recently derived. For calculating the anomalies, we work with an Einstein on-shell background and make a factorised Ansatz for the operators governing the quadratic fluctuations. This reduces the calculation to evaluating heat-kernel coefficients of standard 2-derivative operators. We fix and check our Ansatz against the explicit evaluation of the component-field supergravity action in some cases.
Organisation(s): Institute of Theoretical Physics
Faculty of Mathematics and Physics
External Organisation(s): Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
University of Queensland
Type: Article
Journal: Journal of high energy physics
Volume: 2024
ISSN: 1029-8479
Publication date: 30.10.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Nuclear and High Energy Physics
Electronic version(s): https://doi.org/10.1007/JHEP10(2024)227 (Access: Open)

BibTeX

@article{862d18020cad473ca2355f71fb0544f2,
title = "Conformal anomalies for (maximal) 6d conformal supergravity",
abstract = "We compute the conformal anomalies for 6d (2,0) conformal supergravity by direct calculation in component fields. The main novel results consist of the type-B anomaly coefficients for the gravitino and the 3-form, as well as their explicit quadratic action on some specific backgrounds. We also comment on the graviton contribution, whose Lagrangian is essentially given by the Q-curvature. We confirm the expectation that, when coupling (2,0) conformal supergravity to 26 copies of the (2,0) tensor multiplet, the resulting theory is free of conformal anomalies. We also consider the conformal anomalies for its (1,0) truncation and confirm their relation with the chiral anomaly polynomial recently derived. For calculating the anomalies, we work with an Einstein on-shell background and make a factorised Ansatz for the operators governing the quadratic fluctuations. This reduces the calculation to evaluating heat-kernel coefficients of standard 2-derivative operators. We fix and check our Ansatz against the explicit evaluation of the component-field supergravity action in some cases.",
keywords = "Anomalies in Field and String Theories, Field Theories in Higher Dimensions, Scale and Conformal Symmetries, Supergravity Models",
author = "Lorenzo Casarin and Christian Kennedy and Gabriele Tartaglino-Mazzucchelli",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",
year = "2024",
month = oct,
day = "30",
doi = "10.1007/JHEP10(2024)227",
language = "English",
volume = "2024",
journal = "Journal of high energy physics",
issn = "1029-8479",
publisher = "Springer Verlag",
number = "10",
}