Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model

TL;DR

This paper introduces a fuzzy sphere regularisation for the 3d lambda phi^4 model, providing a novel, numerically feasible alternative to lattice methods and exploring its phase structure and connections to string theory.

Contribution

It presents a new fuzzy sphere discretisation approach for the 3d lambda phi^4 model, analyzing its phase diagram and linking strong coupling behavior to string theory models.

Findings

Identified phases: disorder, uniform order, non-uniform order.

Reproduced matrix chain behavior at strong coupling.

Compared phase diagrams with non-commutative torus and 2d fuzzy sphere models.

Abstract

We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice. In contrast to the 2d version, the radius R plays an independent r\^{o}le. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and \lambda. Thus we identify the phases of disorder, uniform order and non-uniform order. We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere. Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c=1-model in string theory. This observation enables a conjecture about the thermodynamic limit.