On self-dualities for scalar $\phi^4$ theory

TL;DR

This paper explores self-dualities in scalar 4 theory by analyzing saddle point expansions, revealing a sign flip relation between phases and providing new insights into the phase diagram, especially in four dimensions.

Contribution

It introduces a novel saddle point expansion approach that uncovers a sign flip duality between symmetric and broken phases in scalar 4 theory, including new results for four dimensions.

Findings

Broken and symmetric phases are related by a sign flip of the quartic coupling.

Previous phase diagram results are recovered for dimensions less than 4.

New insights into the phase structure at four dimensions are provided.

Abstract

Scalar field theory is studied by constructing interacting saddle point expansions in the symmetric and broken phase, respectively. Focusing on analytically tractable saddle expansions, it is found that broken and symmetric phases are related by sign flip of the quartic coupling. Applications to dimensions $d<4$ recover previous results for the phase diagram, whereas $d=4$ is possibly new.