Fusion of conformal interfaces

TL;DR

This paper explores the fusion of conformal interfaces in a c=1 conformal field theory, revealing structures similar to black holes in supersymmetric theories and suggesting new algebraic frameworks in string theory.

Contribution

It introduces a novel analogy between conformal interfaces and BPS black holes, uncovering attractor mechanisms and stability properties in the context of conformal field theory.

Findings

Topological interfaces minimize entropy functions.

Interfaces fix bulk radii via attractor mechanisms.

Conserved charges are logarithms of natural numbers.

Abstract

We study the fusion of conformal interfaces in the c=1 conformal field theory. We uncover an elegant structure reminiscent of that of black holes in supersymmetric theories. The role of the BPS black holes is played by topological interfaces, which (a) minimize the entropy function, (b) fix through an attractor mechanism one or both of the bulk radii, and (c) are (marginally) stable under splitting. One significant difference is that the conserved charges are logarithms of natural numbers, rather than vectors in a charge lattice, as for BPS states. Besides potential applications to condensed-matter physics and number theory, these results point to the existence of large solution-generating algebras in string theory.