Closed and open conformal field theories and their anomalies

Details Closed and open conformal field theories and their anomalies Closed and open conformal field theories and their anomalies

2004-01-10

arxiv.org/abs/hep-th/0401061v1

Commun.Math.Phys. 254 (2005) 221-253

Physics

High Energy Physics

High Energy Physics - Theory

35 pages

Scientific paper

10.1007/s00220-004-1202-8

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.

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