1,082 research outputs found
On the classification of fusion rings
The fusion rules and modular matrix of a rational conformal field theory obey
a list of properties. We use these properties to classify rational conformal
field theories with not more than six primary fields and small values of the
fusion coefficients. We give a catalogue of fusion rings which can arise for
these field theories. It is shown that all such fusion rules can be realized by
current algebras. Our results support the conjecture that all rational
conformal field theories are related to current algebras.Comment: 10 pages, CALT-68-196
Tests of Seiberg-like Duality in Three Dimensions
We use localization techniques to study several duality proposals for
supersymmetric gauge theories in three dimensions reminiscent of Seiberg
duality. We compare the partition functions of dual theories deformed by real
mass terms and FI parameters. We find that Seiberg-like duality for N=3
Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level
of partition functions and is closely related to level-rank duality in pure
Chern-Simons theory. We also clarify the relationship between the
Giveon-Kutasov duality and a duality in theories of fractional M2 branes and
propose a generalization of the latter. Our analysis also confirms previously
known results concerning decoupled free sectors in N=4 gauge theories realized
by monopole operators.Comment: 36 pages, 5 figure
D-branes in Topological Minimal Models: the Landau-Ginzburg Approach
We study D-branes in topologically twisted N=2 minimal models using the
Landau-Ginzburg realization. In the cases of A and D-type minimal models we
provide what we believe is an exhaustive list of topological branes and compute
the corresponding boundary OPE algebras as well as all disk correlators. We
also construct examples of topological branes in E-type minimal models. We
compare our results with the boundary state formalism, where possible, and find
agreement.Comment: 29 pages, late
On perturbations of the isometric semigroup of shifts on the semiaxis
We study perturbations of the semigroup of shifts
on with the property that belongs to a certain Schatten-von Neumann class \gS_p with .
We show that, for the unitary component in the Wold-Kolmogorov decomposition of
the cogenerator of the semigroup , {\it any singular}
spectral type may be achieved by \gS_1 perturbations. We provide an explicit
construction for a perturbation with a given spectral type based on the theory
of model spaces of the Hardy space . Also we show that we may obtain {\it
any} prescribed spectral type for the unitary component of the perturbed
semigroup by a perturbation from the class \gS_p with
The Landau-Ginzburg to Calabi-Yau Dictionary for D-Branes
Based on work by Orlov, we give a precise recipe for mapping between B-type
D-branes in a Landau-Ginzburg orbifold model (or Gepner model) and the
corresponding large-radius Calabi-Yau manifold. The D-branes in Landau-Ginzburg
theories correspond to matrix factorizations and the D-branes on the Calabi-Yau
manifolds are objects in the derived category. We give several examples
including branes on quotient singularities associated to weighted projective
spaces. We are able to confirm several conjectures and statements in the
literature.Comment: 24 pages, refs added + minor correctio
Expectation values of chiral primary operators in holographic interface CFT
We consider the expectation values of chiral primary operators in the
presence of the interface in the 4 dimensional N=4 super Yang-Mills theory.
This interface is derived from D3-D5 system in type IIB string theory. These
expectation values are computed classically in the gauge theory side. On the
other hand, this interface is a holographic dual to type IIB string theory on
AdS_5 x S^5 spacetime with a probe D5-brane. The expectation values are
computed by GKPW prescription in the gravity side. We find non-trivial
agreement of these two results: the gauge theory side and the gravity side.Comment: 17pages, no figur
AGT on the S-duality Wall
Three-dimensional gauge theory T[G] arises on a domain wall between
four-dimensional N=4 SYM theories with the gauge groups G and its S-dual G^L.
We argue that the N=2^* mass deformation of the bulk theory induces a
mass-deformation of the theory T[G] on the wall. The partition functions of the
theory T[SU(2)] and its mass-deformation on the three-sphere are shown to
coincide with the transformation coefficient of Liouville one-point conformal
block on torus under the S-duality.Comment: 14 pages, 3 figures. v2: Revised the analysis in sections 3.3 and 4.
Notes and references added. Version to appear in JHE
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