Geometric Monte Carlo and Black Janus Geometries

TL;DR

This paper applies Monte Carlo methods to study black Janus geometries in various dimensions, providing numerical insights into their structure and potential applications in holographic QCD models.

Contribution

It introduces a Monte Carlo numerical approach for analyzing black Janus geometries with arbitrary boundary conditions and geometries, including spherical interfaces.

Findings

Numerical results for 3D and 5D black Janus geometries.

Validation of the method's accuracy and convergence.

Potential application to finite temperature QCD models via AdS/CFT.

Abstract

We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.