Conformal defects in supergravity - backreacted Dirac delta sources

TL;DR

This paper constructs and analyzes gravitational duals of theories with localized scalar sources, revealing that preserving scale invariance constrains the scalar potential and providing insights into defect physics via entanglement entropy.

Contribution

It introduces a numerical method to construct backreacted supergravity solutions with delta function sources, linking the potential to a specific supergravity compactification.

Findings

Scalar potential is uniquely determined by scale invariance.

Numerical solutions at zero and finite temperature are obtained.

Entanglement entropy characterizes defect physics.

Abstract

We construct numerically gravitational duals of theories deformed by localized Dirac delta sources for scalar operators both at zero and at finite temperature. We find that requiring that the backreacted geometry preserves the original scale invariance of the source uniquely determines the potential for the scalar field to be the one found in a certain Kaluza-Klein compactification of $11D$ supergravity. This result is obtained using an efficient perturbative expansion of the backreacted background at zero temperature and is confirmed by a direct numerical computation. Numerical solutions at finite temperatures are obtained and a detailed discussion of the numerical approach to the treatment of the Dirac delta sources is presented. The physics of defect configurations is illustrated with a calculation of entanglement entropy.