Enhanced Global Symmetries and The Chiral Phase Transition

TL;DR

This paper explores how near a chiral phase transition, a gauge theory's spectrum may exhibit an enhanced global symmetry leading to parity doubling, which could impact electroweak symmetry breaking and precision measurements.

Contribution

It proposes a connection between parity doubling and an enhanced global symmetry near the chiral phase transition, using an effective Lagrangian framework.

Findings

Parity doubling correlates with an enhanced global symmetry.

Spectrum splits into two sectors with distinct symmetry properties.

Enhanced symmetry can suppress contributions to the S parameter.

Abstract

We examine the possibility that the physical spectrum of a vector-like gauge field theory exhibits an enhanced global symmetry near a chiral phase transition. A transition from the Goldstone phase to the symmetric phase is expected as the number of fermions N_f is increased to some critical value. Various investigations have suggested that a parity-doubled spectrum develops as the critical value is approached. Using an effective Lagrangian as a guide, we note that parity doubling is associated with the appearance of an enhanced global symmetry in the spectrum of the theory. The enhanced symmetry would develop as the spectrum splits into two sectors, with the first exhibiting the usual pattern of a spontaneously broken chiral symmetry, and the second exhibiting an additional, unbroken symmetry and parity doubling. The first sector includes the Goldstone bosons and other states such as massive scalar partners. The second includes a parity-degenerate vector and axial vector along with other possible parity partners. We note that if such a near-critical theory describes symmetry breaking in the electroweak theory, the additional symmetry suppresses the contribution of the parity doubled sector to the S parameter.