Brane-worlds and theta-vacua

TL;DR

This paper explains anomaly mismatches in brane-world reductions by spectral asymmetry changes, proposing a scenario where a QCD-like theta-angle relaxes to zero without light axions, with potential cosmological implications.

Contribution

It introduces a novel explanation for anomaly mismatches in odd-to-even dimensional reductions using spectral asymmetry, linking to theta-angle relaxation without axions.

Findings

Spectral asymmetry accounts for anomaly mismatch.

A scenario for theta-angle relaxation without light axions.

Potential cosmological implications for QCD-like theories.

Abstract

Reductions from odd to even dimensionalities ($5\to 4$ or $3\to 2$), for which the effective low-energy theory contains chiral fermions, present us with a mismatch between ultraviolet and infrared anomalies. This applies to both local (gauge) and global currents; here we consider the latter case. We show that the mismatch can be explained by taking into account a change in the spectral asymmetry of the massive modes--an odd-dimensional analog of the phenomenon described by the Atiyah-Patodi-Singer theorem in even dimensionalities. The result has phenomenological implications: we present a scenario in which a QCD-like $\theta$-angle relaxes to zero on a certain (possibly, cosmological) timescale, despite the absence of any light axion-like particle.