A calculation of the Weyl anomaly for 6D Conformal Higher Spins
arXiv:2104.05673 · doi:10.1007/JHEP05(2021)241
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 spacefilling 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 b6 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.
arXiv commentv2: 14 pages, minor corrections
References in corpus (26)
- Gauge Theory Correlators from Non-Critical String Theory
- Diffeomorphisms and Holographic Anomalies
- A universal result on central charges in the presence of double-trace deformations
- A field-theory motivated approach to symbolic computer algebra
- Conformal anomaly of (2,0) tensor multiplet in six dimensions and AdS/CFT correspondence
- Double-trace operators and one-loop vacuum energy in AdS/CFT
- Partition functions and double-trace deformations in AdS/CFT
- On partition function and Weyl anomaly of conformal higher spin fields
- Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
- AdS Description of Induced Higher-Spin Gauge Theory
- Spinning AdS Loop Diagrams: Two Point Functions
- The Heat Kernel on
- Loops in AdS: From the Spectral Representation to Position Space
- On conformal higher spin wave operators
- Weyl anomaly of conformal higher spins on six-sphere
- Polyakov formulas for GJMS operators from AdS/CFT
- Consistent Non-Minimal Couplings of Massive Higher-Spin Particles
- On conformal higher spins in curved background
- for conformal higher spin fields from partition function on conically deformed sphere
- On one loop corrections in higher spin gravity
- Generalised superconformal higher-spin multiplets
- Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all
- Superconformal index of higher derivative multiplets in four dimensions
- On the Weyl anomaly of 4D Conformal Higher Spins: a holographic approach
- The Involutive System of Higher-Spin Equations
- One-Loop Holographic Weyl Anomaly in Six Dimensions