Rotation Symmetry Breaking Condensate in a Scalar Theory

TL;DR

This paper explores a scalar field theory with a nonstandard inverse propagator, revealing that nonconstant configurations can spontaneously break rotational symmetry, leading to layered structures, with implications for understanding symmetry breaking in similar physical systems.

Contribution

It introduces a scalar model with an inverse propagator of the form -p^2 + p^4, demonstrating spontaneous rotation symmetry breaking and analyzing the renormalization group flow of the effective action.

Findings

Nonconstant spin-wave configurations minimize the classical action.

Naive vacuum is unstable towards nonzero momentum mode condensation.

Spontaneous rotation symmetry breaking leads to layered structures.

Abstract

Motivated by an analogy with the conformal factor problem in gravitational theories of the $R+R^2$-type we investigate a $d$-dimensional Euclidean field theory containing a complex scalar field with a quartic self interaction and with a nonstandard inverse propagator of the form $-p^2+p^4$. Nonconstant spin-wave configurations minimize the classical action and spontaneously break the rotation symmetry to a lower-dimensional one. In classical statistical physics this corresponds to a spontaneous formation of layers. Within the effective average action approach we determine the renormalization group flow of the dressed inverse propagator and of a family of generalized effective potentials for nonzero-momentum modes. Already in the leading order of the semiclassical expansion we find strong ``instability induced'' renormalization effects which are due to the fact that the naive vacuum (vanishing field) is unstable towards the condensation of modes with a nonzero momentum. We argue that the (quantum) ground state of our scalar model indeed leads to spontaneous breaking of rotation symmetry.