15804 2104.05673 10.1007/JHEP05(2021)241 241 241 A calculation of the Weyl anomaly for 6D conformal higher spins Regular Article - Theoretical Physics 1 15 2021 5 26 2021 4 23 2021 5 16 2021 5 26 The Author(s) 2021 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2021 2021 5 5 R. Aros raros@unab.cl F. Bugini fbugini@ucsc.cl D. E. Diaz danilodiaz@unab.cl grid.412848.3 0000 0001 2156 804X Departamento de Ciencias Físicas Universidad Andres Bello Sazié 2212, Piso 7 Santiago Chile grid.412876.e 0000 0001 2199 9982 Departamento de Matemática y Física Aplicadas Universidad Católica de la Santísima Concepción Alonso de Ribera 2850 Concepción Chile grid.412848.3 0000 0001 2156 804X Departamento de Ciencias Físicas Universidad Andres Bello Autopista Concepción-Talcahuano 7100 Talcahuano Chile Abstract In this work we continue the study of the one-loop partition function for higher derivative conformal higher spin (CHS) fields in six dimensions and its holographic counterpart given by massless higher spin Fronsdal fields in seven dimensions. In going beyond the conformal class of the boundary round 6-sphere, we start by considering a Ricci-flat, but not conformally flat, boundary and the corresponding Poincaré-Einstein space-filling metric. Here we are able to match the UV logarithmic divergence of the boundary with the IR logarithmic divergence of the bulk, very much like in the known 4D/5D setting, under the assumptions of factorization of the higher derivative CHS kinetic operator and WKB-exactness of the heat kernel of the dual bulk field. A key technical ingredient in this construction is the determination of the fourth heat kernel coefficient b 6 for Lichnerowicz Laplacians on both 6D and 7D Einstein manifolds. These results allow to obtain, in addition to the already known type-A Weyl anomaly, two of the three independent type-B anomaly coefficients in terms of the third, say c 3 for instance. In order to gain access to c 3, and thus determine the four central charges independently, we further consider a generic non Ricci-flat Einstein boundary. However, in this case we find a mismatch between boundary and bulk computations for spins higher than two. We close by discussing the nature of this discrepancy and perspectives for a possible amendment. Keywords AdS-CFT Correspondence Anomalies in Field and String Theories Conformal Field Theory ArXiv ePrint: 2104.05673