Higher Loop Anomalies and their Consistency Conditions in Nonlocal Regularization

TL;DR

This paper develops an algebraic framework within the field-antifield formalism to analyze higher loop BRST anomalies, introducing a local consistency condition and exemplifying it through explicit two-loop anomaly computations in chiral W3 gravity.

Contribution

It introduces a procedure to distinguish genuine local higher loop anomalies from lower loop effects and derives a generalized Wess-Zumino consistency condition within a nonlocal regularization framework.

Findings

Derived a local consistency condition for higher loop anomalies.

Explicitly computed the two-loop anomaly in chiral W3 gravity.

Verified the two-loop consistency condition through explicit calculation.

Abstract

An algebraic program of computation and characterization of higher loop BRST anomalies is presented. We propose a procedure for disentangling a genuine{\it local} higher loop anomaly from the quantum dressings of lower loop anomalies. For such higher loop anomalies we derive a local consistency condition, which is the generalisation of the Wess-Zumino condition for the one-loop anomaly. The development is presented in the framework of the field-antifield formalism, making use of a nonlocal regularization method. The theoretical construction is exemplified by explicitly computing the two-loop anomaly of chiral $W_3$ gravity. We also give, for the first time, an explicit check of the local two--loop consistency condition that is associated with this anomaly.