Branes: from free fields to general backgrounds
J. Fuchs, C. Schweigert

TL;DR
This paper explores the mathematical structure of boundary conditions in conformal field theories, linking automorphisms and algebraic classifications to D-brane configurations in string theory.
Contribution
It introduces a framework connecting boundary conditions, fusion rule automorphisms, and algebraic classifications for D-branes in arbitrary conformal field theories.
Findings
Boundary conditions classified by irreducible representations of a generalized fusion algebra.
Automorphisms of fusion rules correspond to D-brane configurations.
Moduli of D-branes linked to algebraic representations and flat connections.
Abstract
Motivated by recent developments in string theory, we study the structure of boundary conditions in arbitrary conformal field theories. A boundary condition is specified by two types of data: first, a consistent collection of reflection coefficients for bulk fields on the disk; and second, a choice of an automorphism of the fusion rules that preserves conformal weights. Non-trivial automorphisms correspond to D-brane configurations for arbitrary conformal field theories. The choice of the fusion rule automorphism amounts to fixing the dimension and certain global topological features of the D-brane world volume and the background gauge field on it. We present evidence that for fixed choice of the boundary conditions are classified as the irreducible representations of some commutative associative algebra, a generalization of the fusion rule algebra.…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
