Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 2011 | Submitted
Book Section - Chapter Open

Surface operators in 3d Topological Field Theory and 2d Rational Conformal Field Theory

Abstract

We study surface operators in 3d Topological Field Theory and their relations with 2d Rational Conformal Field Theory. We show that a surface operator gives rise to a consistent gluing of chiral and anti-chiral sectors in the 2d RCFT. The algebraic properties of the resulting 2d RCFT, such as the classification of symmetry-preserving boundary conditions, are expressed in terms of properties of the surface operator. We show that to every surface operator one may attach a Morita-equivalence class of symmetric Frobenius algebras in the ribbon category of bulk line operators. This provides a simple interpretation of the results of Fuchs, Runkel and Schweigert on the construction of 2d RCFTs from Frobenius algebras. We also show that every topological boundary condition in a 3d TFT gives rise to a commutative Frobenius algebra in the category of bulk line operators. We illustrate these general considerations by studying in detail surface operators in abelian Chern-Simons theory.

Additional Information

© 2011 American Mathematical Society.

Attached Files

Submitted - Kapustin_2010.pdf

Files

Kapustin_2010.pdf
Files (2.1 MB)
Name Size Download all
md5:81009c1c0ff72d7d60f32c78158c0c8e
2.1 MB Preview Download

Additional details

Created:
August 22, 2023
Modified:
January 13, 2024