One-Loop Holographic Weyl Anomaly in Six Dimensions

Abstract

We compute $\mathcal{O}(1)$ corrections to the holographic Weyl anomaly for six-dimensional $\mathcal{N}=(1,0)$ and $(2,0)$ theories using the functional Schrödinger method that is conjectured to work for supersymmetric theories on Ricci-flat backgrounds. We show that these corrections vanish for long representations of the $\mathcal{N}=(1,0)$ theory, and we obtain an expression for $\delta (c-a)$ for short representations with maximum spin two. We also confirm that the one-loop corrections to the $\mathcal{N}=(2,0)$ M5-brane theory are equal and opposite to the anomaly for the free tensor multiplet. Finally, we discuss the possibility of extending the results to encompass multiplets with spins greater than two.

28 pages

References in corpus (7)

• Higher spins in AdS_5 at one loop: vacuum energy, boundary conformal anomalies and AdS/CFT
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• Supersymmetric Renyi Entropy and Anomalies in Six-Dimensional (1,0) Superconformal Theories
• $c-a$ from the $N=1$ superconformal index
• Central charges from the $\mathcal{N}=1$ superconformal index
• $C_T$ for higher derivative conformal fields and anomalies of (1,0) superconformal 6d theories
• $C_T$ for conformal higher spin fields from partition function on conically deformed sphere

Cited by in corpus (5)

• Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all
• Holographic (a,c)-charges and Their Universal Relation in d=6 from Massless Higher-order Gravities
• GJMS-like operators on symmetric 2-tensors and their gravitational duals
• A calculation of the Weyl anomaly for 6D Conformal Higher Spins
• One-loop divergences in 7D Einstein and 6D Conformal Gravities