Boundary Entropy Can Increase Under Bulk RG Flow

TL;DR

This paper shows that the boundary entropy in a quantum system can increase during bulk RG flow, challenging previous assumptions, with implications for string theory and condensed matter physics.

Contribution

It demonstrates that boundary entropy can increase under bulk RG flow using conformal perturbation theory, providing explicit examples and discussing broader applications.

Findings

Boundary entropy can increase during bulk RG flow.

Explicit calculations in minimal models support this behavior.

Implications for D-branes and impurity problems are discussed.

Abstract

The boundary entropy log(g) of a critical one-dimensional quantum system (or two-dimensional conformal field theory) is known to decrease under renormalization group (RG) flow of the boundary theory. We study instead the behavior of the boundary entropy as the bulk theory flows between two nearby critical points. We use conformal perturbation theory to calculate the change in g due to a slightly relevant bulk perturbation and find that it has no preferred sign. The boundary entropy log(g) can therefore increase during appropriate bulk flows. This is demonstrated explicitly in flows between minimal models. We discuss the applications of this result to D-branes in string theory and to impurity problems in condensed matter.