9,010 research outputs found
Discrete Torsion, AdS/CFT and duality
We analyse D-branes on orbifolds with discrete torsion, extending earlier
results. We analyze certain Abelian orbifolds of the type C^3/ \Gamma, where
\Gamma is given by Z_m x Z_n, for the most general choice of discrete torsion
parameter. By comparing with the AdS/CFT correspondence, we can consider
different geometries which give rise to the same physics. This identifies new
mirror pairs and suggests new dualities at large N. As a by-product we also get
a more geometric picture of discrete torsion.Comment: JHEP format, 6 figure
Resolution of Stringy Singularities by Non-commutative Algebras
In this paper we propose a unified approach to (topological) string theory on
certain singular spaces in their large volume limit. The approach exploits the
non-commutative structure of D-branes, so the space is described by an
algebraic geometry of non-commutative rings. The paper is devoted to the study
of examples of these algebras. In our study there is an auxiliary commutative
algebraic geometry of the center of the (local) algebras which plays an
important role as the target space geometry where closed strings propagate. The
singularities that are resolved will be the singularities of this auxiliary
geometry. The singularities are resolved by the non-commutative algebra if the
local non-commutative rings are regular. This definition guarantees that
D-branes have a well defined K-theory class. Homological functors also play an
important role. They describe the intersection theory of D-branes and lead to a
formal definition of local quivers at singularities, which can be computed
explicitly for many types of singularities. These results can be interpreted in
terms of the derived category of coherent sheaves over the non-commutative
rings, giving a non-commutative version of recent work by M. Douglas. We also
describe global features like the Betti numbers of compact singular Calabi-Yau
threefolds via global holomorphic sections of cyclic homology classes.Comment: 36 pages, Latex, 5 figures. v2:Reference adde
SL(2,Z) Action on Three-Dimensional CFTs and Holography
We show that there is a natural action of SL(2,Z) on the two-point functions
of the energy momentum tensor and of higher-spin conserved currents in
three-dimensional CFTs. The dynamics behind the S-operation of SL(2,Z) is that
of an irrelevant current-current deformation and we point out its similarity to
the dynamics of a wide class of three-dimensional CFTs. The holographic
interpretation of our results raises the possibility that many
three-dimensional CFTs have duals on AdS4 with SL(2,Z) duality properties at
the linearized level.Comment: 18 pages, v2 references adde
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