Closed and open conformal field theories and their anomalies

Abstract

In this paper, we give a general axiomatization of anomalies in closed and open conformal field theories. In particular, we generalize Segal's notion of modular functor to a setting where the ``set of labels'' is a 2-vector space. In the case of open conformal field theory, the ``set of $D$-branes'' is a 3-vector space. We also define a ``topological group completion'' of the symmetric bimonoidal category of finite-dimensional vector spaces, and propose it as a candidate for labelling conformal field theories whose modular functors are super-vector spaces.

arXiv comment35 pages

References in corpus (12)

• TFT construction of RCFT correlators I: Partition functions
• D-branes, Categories and N=1 Supersymmetry
• Planar Duality in $SU(2)$ WZW Models
• On the structure of open-closed topological field theory in two dimensions
• TFT construction of RCFT correlators II: Unoriented world sheets
• Overview Of K-Theory Applied To Strings
• Enhanced D-Brane Categories from String Field Theory
• Open-string vertex algebras, tensor categories and operads
• Some Comments on Branes, G-flux, and K-theory
• Generalized complexes and string field theory
• Equivariant Topological Sigma Models
• Unitarity, D-brane dynamics and D-brane categories

Cited by in corpus (6)

• A mathematical theory of gapless edges of 2d topological orders. Part I
• Type IIB String Theory, S-Duality, and Generalized Cohomology
• Open-closed field algebras
• A mathematical formalism for the Kondo effect in WZW branes
• On effective F-theory action in type IIA compactifications
• Perturbative deformations of conformal field theories revisited