Conformal field theory, boundary conditions and applications to string theory
C. Schweigert, J. Fuchs, J. Walcher
TL;DR
The work surveys two-dimensional conformal field theory and its boundary formulations for string theory, clarifying the distinction between chiral and full CFT and detailing how surfaces with boundaries model D-branes. It develops the vertex operator algebra framework, conformal blocks, and modular invariance, showing how to assemble full CFTs from chiral data and how factorization constrains correlators. It then applies these insights to string compactifications, notably via simple current modular invariants and the Gepner construction, to produce and analyze D-brane configurations (A- and B-type) and their mirror partners. The approach connects algebraic, geometric, and topological methods to extract physical spectra, RR charges, and gauge content in string vacua, especially in regimes where curvature effects are strong.
Abstract
This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the strong curvature regime by means of CFT on surfaces with boundary.