One-Loop Holographic Weyl Anomaly in Six Dimensions

TL;DR

This paper calculates quantum corrections to the holographic Weyl anomaly in six-dimensional supersymmetric theories, revealing vanishing corrections for certain representations and providing explicit formulas for others, with implications for higher-spin multiplets.

Contribution

It introduces a method to compute one-loop holographic Weyl anomaly corrections in 6D supersymmetric theories, including explicit results for specific multiplets and insights into higher-spin extensions.

Findings

Corrections vanish for long representations of t(1,0) theories.

Explicit t(c-a) formulas for short representations with spin 2.

One-loop corrections for t(2,0) M5-brane match opposite free tensor multiplet anomaly.

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 Schr\"odinger 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.