Phase structures in fuzzy geometries

TL;DR

This paper investigates the phase structures of quantum field theories on fuzzy geometries, revealing novel phases and symmetry-breaking phenomena stabilized by topological features through analytical and simulation methods.

Contribution

It introduces new phase phenomena in fuzzy geometries, including stripe phases and topologically stabilized symmetry-breaking, expanding understanding of QFTs in noncommutative spaces.

Findings

Discovery of novel stripe phases

Spontaneous symmetry breaking avoiding Mermin-Wagner theorem

Stability of phases due to topological obstructions

Abstract

We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of BTZ blackholes. Analysis is done analytically and through simulations. Several features like novel stripe phases as well as spontaneous symmetry breaking avoiding Colemen, Mermin, Wagner theorem are brought out. Also we establish that these phases are stable due to topological obstructions.