864 research outputs found
Topological Disorder Operators in Three-Dimensional Conformal Field Theory
Many abelian gauge theories in three dimensions flow to interacting conformal
field theories in the infrared. We define a new class of local operators in
these conformal field theories which are not polynomial in the fundamental
fields and create topological disorder. They can be regarded as
higher-dimensional analogues of twist and winding-state operators in free 2d
CFTs. We call them monopole operators for reasons explained in the text. The
importance of monopole operators is that in the Higgs phase, they create
Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in
three-dimensional QED using large N_f expansion. In particular, we show that
monopole operators belong to representations of the conformal group whose
primaries have dimension of order N_f. We also show that monopole operators
transform non-trivially under the flavor symmetry group, with the precise
representation depending on the value of the Chern-Simons coupling.Comment: 24 pages, latex. v2: a reference to prior work has been adde
Nonrenormalization Theorem for Gauge Coupling in 2+1D
We prove that \be-function of the gauge coupling in gauge theory
coupled to any renormalizable system of spinor and scalar fields is zero. This
result holds both when the gauge field action is the Chern-Simons action and
when it is the topologically massive action.Comment: 8 pages, LaTeX file, CALT-68-191
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
Anomalies and Graded Coisotropic Branes
We compute the anomaly of the axial U(1) current in the A-model on a
Calabi-Yau manifold, in the presence of coisotropic branes discovered by
Kapustin and Orlov. Our results relate the anomaly-free condition to a recently
proposed definition of graded coisotropic branes in Calabi-Yau manifolds. More
specifically, we find that a coisotropic brane is anomaly-free if and only if
it is gradable. We also comment on a different grading for coisotropic
submanifolds introduced recently by Oh.Comment: AMS Tex, 11 page
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
D-branes on general N=1 backgrounds: superpotentials and D-terms
We study the dynamics governing space-time filling D-branes on Type II flux
backgrounds preserving four-dimensional N=1 supersymmetry. The four-dimensional
superpotentials and D-terms are derived. The analysis is kept on completely
general grounds thanks to the use of recently proposed generalized
calibrations, which also allow one to show the direct link of the
superpotentials and D-terms with BPS domain walls and cosmic strings
respectively. In particular, our D-brane setting reproduces the tension of
D-term strings found from purely four-dimensional analysis. The holomorphicity
of the superpotentials is also studied and a moment map associated to the
D-terms is proposed. Among different examples, we discuss an application to the
study of D7-branes on SU(3)-structure backgrounds, which reproduces and
generalizes some previous results.Comment: 50 pages; v2: table of contents, some clarifications and references
added; v3: typos corrected and references adde
Supersymmetry enhancement by monopole operators
We describe a method which allows one to study hidden symmetries in a large
class of strongly coupled supersymmetric gauge theories in three dimensions. We
apply this method to the ABJM theory and to the infrared limit of N=4 SQCD with
adjoint and fundamental matter. We show that the U(N) ABJM model with
Chern-Simons level k=1 or k=2 has hidden N=8 supersymmetry. Hidden
supersymmetry is also shown to occur in N=4 d=3 SQCD with one fundamental and
one adjoint hypermultiplet. The latter theory, as well as the U(N) ABJM theory
at k=1, are shown to have a decoupled free sector. This provides evidence that
both models are dual to the infrared limit of N=8 U(N) super-Yang-Mills theory.Comment: 29 pages, late
Supersymmetric D-branes and calibrations on general N=1 backgrounds
We study the conditions to have supersymmetric D-branes on general {\cal N}=1
backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms
of the two pure spinors associated to the SU(3)\times SU(3) structure on
T_M\oplus T^\star_M, and can be split into two parts each involving a different
pure spinor. The first involves the integrable pure spinor and requires the
D-brane to wrap a generalised complex submanifold with respect to the
generalised complex structure associated to it. The second contains the
non-integrable pure spinor and is related to the stability of the brane. The
two conditions can be rephrased as a generalised calibration condition for the
brane. The results preserve the generalised mirror symmetry relating the type
IIA and IIB backgrounds considered, giving further evidence for this duality.Comment: 23 pages. Some improvements and clarifications, typos corrected and
references added. v3: Version published in JHE
Twisted K-theory and finite-dimensional approximation
We provide a finite-dimensional model of the twisted K-group twisted by any
degree three integral cohomology class of a CW complex. One key to the model is
Furuta's generalized vector bundle, and the other is a finite-dimensional
approximation of Fredholm operators.Comment: 26 pages, LaTeX 2e, Xypic; main theorem improve
Localization and traces in open-closed topological Landau-Ginzburg models
We reconsider the issue of localization in open-closed B-twisted
Landau-Ginzburg models with arbitrary Calabi-Yau target. Through careful
analsysis of zero-mode reduction, we show that the closed model allows for a
one-parameter family of localization pictures, which generalize the standard
residue representation. The parameter which indexes these pictures
measures the area of worldsheets with topology, with the residue
representation obtained in the limit of small area. In the boundary sector, we
find a double family of such pictures, depending on parameters and
which measure the area and boundary length of worldsheets with disk
topology. We show that setting and varying interpolates
between the localization picture of the B-model with a noncompact target space
and a certain residue representation proposed recently. This gives a complete
derivation of the boundary residue formula, starting from the explicit
construction of the boundary coupling. We also show that the various
localization pictures are related by a semigroup of homotopy equivalences.Comment: 36 page
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