Chiral Modulations in Curved Space II: Conifold Geometries

TL;DR

This paper investigates how curved conifold geometries influence chiral symmetry breaking and inhomogeneous condensate formation in strongly-coupled fermion theories, providing a general effective action and numerical solutions.

Contribution

It extends previous work to include conifold geometries, deriving a general finite temperature effective action for inhomogeneous condensates on these manifolds.

Findings

Condensate exhibits kink-like profile vanishing at the singularity

Curvature effects induce inhomogeneous phases and chiral symmetry restoration

Numerical solutions confirm the theoretical predictions

Abstract

In this paper, we extend our previous analysis concerning the formation of inhomogeneous condensates in strongly-coupled fermion effective field theories on curved spaces and include the case of conifold geometries that represent the simplest tractable case of manifolds with curvature singularities. In the set-up considered here, by keeping the genuine thermodynamical temperature constant, we may single out the role that curvature effects play on the breaking/restoration of chiral symmetry and on the appearance of inhomogeneous phases. The first goal of this paper is to construct a general expression of the finite temperature effective action for inhomogeneous condensates in the case of four-fermion effective field theories on conifold geometries with generic Riemannian smooth base (generalised cones). The other goal is to implement numerically the above formal results and construct self-consistent solutions for the condensate. We explicitly show that the condensate assumes a kink-like profile, vanishing at the singularity that is surrounded by a bubble of restored chiral symmetry phase.