2,833 research outputs found
Topological boundary conditions in abelian Chern-Simons theory
We study topological boundary conditions in abelian Chern-Simons theory and
line operators confined to such boundaries. From a mathematical point of view,
their relationships are described by a certain 2-category associated to an even
integer-valued symmetric bilinear form (the matrix of Chern-Simons couplings).
We argue that boundary conditions correspond to Lagrangian subgroups in the
finite abelian group classifying bulk line operators (the discriminant group).
We describe properties of boundary line operators; in particular we compute the
boundary associator. We also study codimension one defects (surface operators)
in abelian Chern-Simons theories. As an application, we obtain a classification
of such theories up to isomorphism, in general agreement with the work of Belov
and Moore.Comment: 43 pages, late
On higher rank coisotropic A-branes
This article is devoted to a world sheet analysis of A-type D-branes in
N=(2,2) supersymmetric non-linear sigma models. In addition to the familiar
Lagrangian submanifolds with flat connection we reproduce the rank one A-branes
of Kapustin and Orlov, which are supported on coisotropic submanifolds. The
main focus is however on gauge fields of higher rank and on tachyon profiles on
brane-antibrane pairs. This will lead to the notion of a complex of coisotropic
A-branes. A particular role is played by the noncommutative geometry on the
brane world volume. It ensures that brane-antibrane pairs localize again on
coisotropic submanifolds.Comment: 24 pages; v2: three references adde
The algebra of Wilson-'t Hooft operators
We study the Operator Product Expansion of Wilson-'t Hooft operators in a
twisted N=4 super-Yang-Mills theory with gauge group G. The Montonen-Olive
duality puts strong constraints on the OPE and in the case G=SU(2) completely
determines it. From the mathematical point of view, the Montonen-Olive duality
predicts the L^2 Dolbeault cohomology of certain equivariant vector bundles on
Schubert cells in the affine Grassmannian. We verify some of these predictions.
We also make some general observations about higher categories and defects in
Topological Field Theories.Comment: 55 pages, late
Is there life beyond Quantum Mechanics?
We formulate physically-motivated axioms for a physical theory which for
systems with a finite number of degrees of freedom uniquely lead to Quantum
Mechanics as the only nontrivial consistent theory. Complex numbers and the
existence of the Planck constant common to all systems arise naturally in this
approach. The axioms are divided into two groups covering kinematics and basic
measurement theory respectively. We show that even if the second group of
axioms is dropped, there are no deformations of Quantum Mechanics which
preserve the kinematic axioms. Thus any theory going beyond Quantum Mechanics
must represent a radical departure from the usual a priori assumptions about
the laws of Nature.Comment: 23 pages, latex. v3: commentaries on the axioms expanded, a
non-technical summary added, references added, typos fixed. v4: version
accepted for publication in Journal of Mathematical Physic (under a different
title). Axiomatics is simplified and the number of axioms reduced, some
proofs clarified, typos fixe
A-branes and Noncommutative Geometry
We argue that for a certain class of symplectic manifolds the category of
A-branes (which includes the Fukaya category as a full subcategory) is
equivalent to a noncommutative deformation of the category of B-branes (which
is equivalent to the derived category of coherent sheaves) on the same
manifold. This equivalence is different from Mirror Symmetry and arises from
the Seiberg-Witten transform which relates gauge theories on commutative and
noncommutative spaces. More generally, we argue that for certain generalized
complex manifolds the category of generalized complex branes is equivalent to a
noncommutative deformation of the derived category of coherent sheaves on the
same manifold. We perform a simple test of our proposal in the case when the
manifold in question is a symplectic torus.Comment: 15 pages, late
Holomorphic reduction of N=2 gauge theories, Wilson-'t Hooft operators, and S-duality
We study twisted N=2 superconformal gauge theory on a product of two Riemann
surfaces Sigma and C. The twisted theory is topological along C and holomorphic
along Sigma and does not depend on the gauge coupling or theta-angle. Upon
Kaluza-Klein reduction along Sigma, it becomes equivalent to a topological
B-model on C whose target is the moduli space MV of nonabelian vortex equations
on Sigma. The N=2 S-duality conjecture implies that the duality group acts by
autoequivalences on the derived category of MV. This statement can be regarded
as an N=2 counterpart of the geometric Langlands duality. We show that the
twisted theory admits Wilson-'t Hooft loop operators labelled by both electric
and magnetic weights. Correlators of these loop operators depend
holomorphically on coordinates and are independent of the gauge coupling. Thus
the twisted theory provides a convenient framework for studying the Operator
Product Expansion of general Wilson-'t Hooft loop operators.Comment: 50 pages, latex. v2: an erroneous statement about an analog of the
Hitchin fibration has been fixe
Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
We propose that Symmetry Protected Topological Phases with a finite symmetry
group G are classified by cobordism groups of the classifying space of G. This
provides an explanation for the recent discovery of bosonic SPT phases which do
not fit into the group cohomology classification. We discuss the connection of
the cobordism classification of SPT phases to gauge and gravitational anomalies
in various dimensions.Comment: 17 pages, latex. v2: typos fixed, a footnote on terminology added.
v3: substantially reworked version which takes into account the possibility
of a nontrivial thermal Hall respons
Noncritical Superstrings in a Ramond-Ramond Background
We use the recently found matrix description of noncritical superstring
theory of Type 0A to compute tachyon scattering amplitudes in a background with
a RR flux. We find that after the string coupling is multiplicatively
renormalized, the amplitudes in any genus become polynomial in the RR flux. We
propose that in the limit where both the string coupling and the RR flux go to
infinity, the theory has a weakly-coupled description in terms of another
superstring theory with a vanishingly small RR flux. This duality exchanges the
inverse string coupling and the 0-brane charge. The dual superstring theory
must have a peculiar property that its only field-theoretic degree of freedom
is a massless RR scalar.Comment: 12 pages, late
D_n Quivers From Branes
D-branes can end on orbifold planes if the action of the orbifold group
includes (-1)^{F_L}. We consider configurations of D-branes ending on such
orbifolds and study the low-energy theory on their worldvolume. We apply our
results to gauge theories with eight supercharges in three and four dimensions.
We explain how mirror symmetry for N=4 d=3 gauge theories with gauge group
Sp(k) and matter in the antisymmetric tensor and fundamental representations
follows from S-duality of IIB string theory. We argue that some of these
theories have hidden Fayet-Iliopoulos deformations, not visible classically. We
also study a class of finite N=2 d=4 theories (so-called D_n quiver theories)
and find their exact solution. The integrable model corresponding to the exact
solution is a Hitchin system on an orbifold Riemann surface. We also give a
simple derivation of the S-duality group of these theories based on their
relationship to SO(2n) instantons on R^2\times T^2.Comment: 20 pages, LaTeX. v3: exposition improved (version published in JHEP
Bosonic Topological Insulators and Paramagnets: a view from cobordisms
We classify Bosonic Topological Insulators and Paramagnets in D<=4 spatial
dimensions using the cobordism approach. For D<4 we confirm that the only such
phase which does not fit into the group cohomology classification is the 3D
Bosonic Topological Insulator protected by time-reversal symmetry whose surface
admits an all-fermion topologically ordered state. For D=4 there is a unique
"beyond group cohomology" phase. It is protected by gravitational anomalies of
the boundary theory and is stable without any additional symmetry.Comment: 18 pages, latex. v2: an error in the last section has been corrected,
affecting the classification in D=4. Other results unchange
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