238 research outputs found
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
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
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
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
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
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
Seiberg-like duality in three dimensions for orthogonal gauge groups
We propose a duality for N=2 d=3 Chern-Simons gauge theories with orthogonal
gauge groups and matter in the vector representation. This duality generalizes
level-rank duality for pure Chern-Simons gauge theories with orthogonal gauge
groups and is reminiscent of Seiberg duality in four dimensions. We perform
extensive checks by comparing partition functions of theories related by
dualities. We also determine the conformal dimensions of fields using
Z-extremization.Comment: 9 pages, late
A remark on worldsheet fermions and double-scaled matrix models
We provide a heuristic explanation for the emergence of worldsheet fermions
in the continuum limit of some matrix models. We also argue that turning on
Ramond-Ramond flux confines the fermionic degrees of freedom of the
Ramond-Neveu-Schwarz formalism.Comment: 7 pages, late
Chiral de Rham complex and the half-twisted sigma-model
On any Calabi-Yau manifold X one can define a certain sheaf of chiral N=2
superconformal field theories, known as the chiral de Rham complex of X. It
depends only on the complex structure of X, and its local structure is
described by a simple free field theory. We show that the cohomology of this
sheaf can be identified with the infinite-volume limit of the half-twisted
sigma-model defined by E. Witten more than a decade ago. We also show that the
correlators of the half-twisted model are independent of the Kahler moduli to
all orders in worldsheet perturbation theory, and that the relation to the
chiral de Rham complex can be violated only by worldsheet instantons.Comment: 15 pages, late
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