Chiral anomalies in higher-derivative supersymmetric 6D gauge theories

TL;DR

This paper identifies an internal chiral anomaly in higher-derivative six-dimensional supersymmetric gauge theories that breaks gauge invariance. Using Schwinger splitting and background-field techniques, it shows the gauge-current divergence contains a term proportional to $\epsilon_{\mu\nu\alpha\beta\gamma\delta} \mathrm{Tr}\{T^A F_{\mu\nu} F_{\alpha\beta} F_{\gamma\delta}\}$ with coefficient $\frac{1}{3\cdot 128 \pi^3}$, independent of the HD regulator $M$. The author proposes anomaly cancellation by introducing an adjoint hypermultiplet, which contributes a finite amount to the anomaly and cancels the pure SYM piece, but notes potential quadratic divergences and nonperturbative challenges that complicate a fully consistent 6D HD SUSY theory. The work highlights anomaly cancellation as a critical constraint for consistency and underscores the ongoing difficulty in formulating a nonperturbatively well-defined six-dimensional higher-derivative supersymmetric gauge theory.

Abstract

We show that the recently constructed higher-derivative 6D SYM theory involves an internal chiral anomaly breaking gauge invariance. The anomaly is cancelled when adding to the theory an adjoint matter hypermultiplet.

Figures (1)

• Figure 1: ${\mathcal{G}}_1(x,x+\epsilon)$