# Cluster decomposition, T-duality, and gerby CFTs

@article{Hellerman2006ClusterDT, title={Cluster decomposition, T-duality, and gerby CFTs}, author={Simeon Hellerman and Andr{\'e} Henriques and Tony Pantev and Eric Sharpe and Matthew Ando}, journal={Advances in Theoretical and Mathematical Physics}, year={2006}, volume={11}, pages={751-818} }

In this paper we study CFT’s associated to gerbes. These theories suffer from a lack of cluster decomposition, but this problem can be resolved: the CFT’s are the same as CFT’s for disconnected targets. Such theories also lack cluster decomposition, but in that form, the lack is manifestly not very problematic. In particular, we shall see that this matching of CFT’s, this duality between noneffective-gaugings and sigma models on disconnected targets, is a worldsheet duality related to T-duality…

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## References

SHOWING 1-10 OF 46 REFERENCES

### T-Duality: Topology Change from H-Flux

- Mathematics
- 2004

T-duality acts on circle bundles by exchanging the first Chern class with the fiberwise integral of the H-flux, as we motivate using E8 and also using S-duality. We present known and new examples…

### GLSMs for gerbes (and other toric stacks)

- Physics
- 2006

In this paper, we will discuss gauged linear sigma model descriptions of toric stacks. Toric stacks have a simple description in terms of (symplectic, GIT) C × quotients of homogeneous coordinates,…

### Algebraic orbifold quantum products

- Mathematics
- 2001

The purpose of this note is to give an overview of our work on defining algebraic counterparts for W. Chen and Y. Ruan's Gromov-Witten Theory of orbifolds. This work will be described in detail in a…

### Discrete Torsion

- Mathematics
- 2000

In this article we explain discrete torsion. Put simply, discrete torsion is the choice of orbifold group action on the B ﬁeld. We derive the classiﬁcation H 2 (Γ , U (1)), we derive the twisted…

### Twisted K-theory

- Mathematics
- 2004

Twisted complex K-theory can be defined for a space X equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C ∗ -algebras. Up to equivalence, the twisting…

### Equivariant K-theory

- Mathematics
- 1968

Topological K-theory [2] has many variants which have been developed and exploited for geometric purposes. There are real or quaternionic versions, “Real” K-theory in the sense of [1], equivariant…

### Localized Tachyons and RG Flows

- Mathematics
- 2001

We study condensation of closed string tachyons living on defects, such as orbifold fixed planes and Neveu-Schwarz fivebranes. We argue that the high energy density of localized states decreases in…