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### C-T for conformal higher spin fields from partition function on conically deformed sphere

File | Description | Size | Format | |
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1707.02456.pdf | Accepted version | 490.27 kB | Adobe PDF | View/Open |

10.1007%2FJHEP09(2017)123.pdf | Published version | 647.81 kB | Adobe PDF | View/Open |

Title: | C-T for conformal higher spin fields from partition function on conically deformed sphere |

Authors: | Beccaria, M Tseytlin, AA |

Item Type: | Journal Article |

Abstract: | We consider the one-parameter generalization Sq4 of 4-sphere with a conical singularity due to identification τ = τ +2πq in one isometric angle. We compute the value of the spectral zeta-function at zero ζˆ(q)=ζ(0;q)ζ^(q)=ζ(0;q) that controls the coefficient of the logarithmic UV divergence of the one-loop partition function on Sq4. While the value of the conformal anomaly a-coefficient is proportional to ζˆ(1)ζ^(1), we argue that in general the second c ∼ CT anomaly coefficient is related to a particular combination of the second and first derivatives of ζˆ(q)ζ^(q) at q = 1. The universality of this relation for CT is supported also by examples in 6 and 2 dimensions. We use it to compute the c-coefficient for conformal higher spins finding that it coincides with the “r = −1” value of the one-parameter Ansatz suggested in arXiv:1309.0785. Like the sums of as and cs coefficients, the regularized sum of ζˆs(q)ζ^s(q) over the whole tower of conformal higher spins s = 1, 2,… is found to vanish, implying UV finiteness on Sq4 and thus also the vanishing of the associated Rényi entropy. Similar conclusions are found to apply to the standard 2-derivative massless higher spin tower. We also present an independent computation of the full set of conformal anomaly coefficients of the 6d Weyl graviton theory defined by a particular combination of the three 6d Weyl invariants that has a (2, 0) supersymmetric extension. |

Issue Date: | 26-Sep-2017 |

Date of Acceptance: | 16-Sep-2017 |

URI: | http://hdl.handle.net/10044/1/52404 |

DOI: | https://dx.doi.org/10.1007/JHEP09(2017)123 |

ISSN: | 1029-8479 |

Publisher: | Springer Verlag (Germany) |

Journal / Book Title: | Journal of High Energy Physics |

Volume: | 2017 |

Issue: | 9 |

Copyright Statement: | Open Access, © The Authors. Article funded by SCOAP3 |

Sponsor/Funder: | Commission of the European Communities Science and Technology Facilities Council (STFC) |

Funder's Grant Number: | 290456 ST/L00044X/1 |

Keywords: | Science & Technology Physical Sciences Physics, Particles & Fields Physics AdS-CFT Correspondence Conformal Field Theory Supergravity Models GEOMETRY SUPERGRAVITY INVARIANCE ENTROPY TENSOR SPACE 01 Mathematical Sciences 02 Physical Sciences Nuclear & Particles Physics |

Publication Status: | Published |

Article Number: | 123 |

Appears in Collections: | Physics Theoretical Physics Faculty of Natural Sciences |