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

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1707.02456.pdfAccepted version490.27 kBAdobe PDFView/Open
10.1007%2FJHEP09(2017)123.pdfPublished version647.81 kBAdobe PDFView/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
Keywords: Science & Technology
Physical Sciences
Physics, Particles & Fields
AdS-CFT Correspondence
Conformal Field Theory
Supergravity Models
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