Epsilon-expansion in quantum field theory in curved spacetime

TL;DR

This paper explores epsilon-expansion techniques in curved spacetime for various quantum field theories, analyzing fixed points, effective actions, and curvature-induced phase transitions, with potential implications for understanding quantum fields in gravitational backgrounds.

Contribution

It introduces epsilon-expansion methods in curved spacetime, investigates fixed points in specific theories, and derives effective actions and phase transition phenomena in this context.

Findings

Epsilon-expansion may be compatible with asymptotic freedom in special supersymmetric solutions.

Effective Lagrangian and potential are derived in 4-epsilon dimensions.

Curvature induces phase transitions from symmetric to broken phases.

Abstract

We discuss epsilon-expansion in curved spacetime for asymptotically free and asymptotically non-free theories. The esistence of stable and unstable fixed points is investigated for $f \phi^4$ and SU(2) gauge theory. It is shown that epsilon-expansion maybe compatible with asymptotic freedom on special solutions of the RG equations in a special case (supersymmetric theory). Using epsilon-expansion RG technique the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL-model are found in 4-epsilon- dimensional curved space (in linear curvature approximation). The curvature- induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.