Conformal anomalies in 6d 4-derivative theories: a heat-kernel analysis

Abstract

We compute the conformal anomalies for some higher-derivative (non-unitary) 6d Weyl invariant theories using the heat-kernel expansion in the background-field method. To this aim we obtain the general expression for the Seeley-DeWitt coefficient $b_6$ for four-derivative differential operators with background curved geometry and gauge fields, which was known only in flat space so far. We consider four-derivative scalars and abelian vectors as well as three-derivative fermions, confirming the result of the literature obtained via indirect methods. We generalise the vector case by including the curvature coupling $FF\mathrm{Weyl}$.

arXiv commentv2: typos corrected, references added

References in corpus (17)

• Heat kernel expansion: user's manual
• Geometric Classification of Conformal Anomalies in Arbitrary Dimensions
• xTras: a field-theory inspired xAct package for Mathematica
• xPerm: fast index canonicalization for tensor computer algebra
• Conformal anomaly of (2,0) tensor multiplet in six dimensions and AdS/CFT correspondence
• Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
• Renormalizable supersymmetric gauge theory in six dimensions
• Stress Tensors from Trace Anomalies in Conformal Field Theories
• Weyl anomaly of conformal higher spins on six-sphere
• The component structure of conformal supergravity invariants in six dimensions
• Conformal anomaly c-coefficients of superconformal 6d theories
• One-loop divergences in 6D, N=(1,0) SYM theory
• $C_T$ for higher derivative conformal fields and anomalies of (1,0) superconformal 6d theories
• One-loop beta-functions in 4-derivative gauge theory in 6 dimensions
• Gauge dependence of the one-loop divergences in $6D$, $\mathcal{N}=(1,0)$ abelian theory
• The renormalization structure of $6D$, $\mathcal{N}=(1,0)$ supersymmetric higher-derivative gauge theory
• Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all

Cited by in corpus (2)

• Six-dimensional one-loop divergences in quantum gravity from the $\mathcal{N}=4$ spinning particle
• Six-dimensional $\mathcal{N}=(2,0)$ Conformal Superspace