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On the Symmetries of Classical String Theory

Constantin Bachas

TL;DR

The paper investigates how conformal defects and interfaces in two-dimensional conformal field theories generate extended, spectrum-generating symmetries of classical string theory. It develops the framework of loop operators in 2d sigma models, analyzes their RG flows to infrared fixed points via generalized Dirac-Born-Infeld dynamics, and shows that topological defects commute with the diagonal Virasoro algebra, enabling defect-induced spectrum shifts without breaking conformal symmetry. By folding and unfolding, conformal interfaces are shown to map D-branes across different closed-string backgrounds, with fusion rules and angle compositions encoding automorphisms, T-dualities, and more general symmetry operations; in particular, discrete moduli of topological interfaces form multiplicative fusion algebras. The explicit $c=1$ example with D1/D2-branes on a two-torus demonstrates concrete boundary states, entropy of interfaces, and conditions for topological (automorphism) cases, supporting the view that defect algebras provide a rich extension of classical string symmetries and may relate to doubled-geometry and attractor-type phenomena in gravitational analogies.

Abstract

I discuss some aspects of conformal defects and conformal interfaces in two spacetime dimensions. Special emphasis is placed on their role as spectrum-generating symmetries of classical string theory.

On the Symmetries of Classical String Theory

TL;DR

The paper investigates how conformal defects and interfaces in two-dimensional conformal field theories generate extended, spectrum-generating symmetries of classical string theory. It develops the framework of loop operators in 2d sigma models, analyzes their RG flows to infrared fixed points via generalized Dirac-Born-Infeld dynamics, and shows that topological defects commute with the diagonal Virasoro algebra, enabling defect-induced spectrum shifts without breaking conformal symmetry. By folding and unfolding, conformal interfaces are shown to map D-branes across different closed-string backgrounds, with fusion rules and angle compositions encoding automorphisms, T-dualities, and more general symmetry operations; in particular, discrete moduli of topological interfaces form multiplicative fusion algebras. The explicit example with D1/D2-branes on a two-torus demonstrates concrete boundary states, entropy of interfaces, and conditions for topological (automorphism) cases, supporting the view that defect algebras provide a rich extension of classical string symmetries and may relate to doubled-geometry and attractor-type phenomena in gravitational analogies.

Abstract

I discuss some aspects of conformal defects and conformal interfaces in two spacetime dimensions. Special emphasis is placed on their role as spectrum-generating symmetries of classical string theory.

Paper Structure

This paper contains 3 sections, 14 equations, 1 figure.

Table of Contents

  1. Loop operators in 2d CFT
  2. Interfaces as spectrum-generating symmetries
  3. The $c=1$ CFT and a black hole analogy

Figures (1)

  • Figure 1: An interface brought from infinity to the boundary of a a cylindrical worldsheet maps the D-branes of one bulk CFT to those of the other. Conformal interfaces between two theories with the same central charge act thus as spectrum-generating symmetries of classical string theory. In many worked-out examples these include and extend the perturbative dualities, and other classical symmetries, of the open- and closed-string action.