On self-dualities for scalar ${\varphi }^4$ theory

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.

Comments: 4 pages + 5 pages supplemental material; v2: fixed typos, added reference; v3: more typos, added comparison to d=4 Lattice Monte Carlo data