39,640 research outputs found
Novel 3d bosonic dualities from bosonization and holography
We use 3d bosonization dualities to derive new non-supersymmetric dualities
between bosonic quiver theories in dimensions. It is shown that such
dualities are a natural non-Abelian generalization of the bosonic
particle-vortex duality. A special case of such dualities is applicable to
Chern-Simons theories living on interfaces in dimensional
Yang-Mills theory across which the theta angle jumps. We also analyze such
interfaces in a holographic construction which provides further evidence for
novel dualities between quiver gauge theories and gauge theories with adjoint
scalars. These conjectured dualities pass some stringent consistency tests.Comment: 33+11 pages, 6 figures. v2: fixed minor typo
The Bond-Algebraic Approach to Dualities
An algebraic theory of dualities is developed based on the notion of bond
algebras. It deals with classical and quantum dualities in a unified fashion
explaining the precise connection between quantum dualities and the low
temperature (strong-coupling)/high temperature (weak-coupling) dualities of
classical statistical mechanics (or (Euclidean) path integrals). Its range of
applications includes discrete lattice, continuum field, and gauge theories.
Dualities are revealed to be local, structure-preserving mappings between
model-specific bond algebras that can be implemented as unitary
transformations, or partial isometries if gauge symmetries are involved. This
characterization permits to search systematically for dualities and
self-dualities in quantum models of arbitrary system size, dimensionality and
complexity, and any classical model admitting a transfer matrix representation.
Dualities like exact dimensional reduction, emergent, and gauge-reducing
dualities that solve gauge constraints can be easily understood in terms of
mappings of bond algebras. As a new example, we show that the (\mathbb{Z}_2)
Higgs model is dual to the extended toric code model {\it in any number of
dimensions}. Non-local dual variables and Jordan-Wigner dictionaries are
derived from the local mappings of bond algebras. Our bond-algebraic approach
goes beyond the standard approach to classical dualities, and could help
resolve the long standing problem of obtaining duality transformations for
lattice non-Abelian models. As an illustration, we present new dualities in any
spatial dimension for the quantum Heisenberg model. Finally, we discuss various
applications including location of phase boundaries, spectral behavior and,
notably, we show how bond-algebraic dualities help constrain and realize
fermionization in an arbitrary number of spatial dimensions.Comment: 131 pages, 22 figures. Submitted to Advances in Physics. Second
version including a new section on the eight-vertex model and the correction
of several typo
3d dualities from 4d dualities
Many examples of low-energy dualities have been found in supersymmetric gauge
theories with four supercharges, both in four and in three space-time
dimensions. In these dualities, two theories that are different at high
energies have the same low-energy limit. In this paper we clarify the relation
between the dualities in four and in three dimensions. We show that every four
dimensional duality gives rise to a three dimensional duality between theories
that are similar, but not identical, to the dimensional reductions of the four
dimensional dual gauge theories to three dimensions. From these specific three
dimensional dualities one can flow to many other low-energy dualities,
including known three dimensional dualities and many new ones. We discuss in
detail the case of three dimensional SU(N_c) supersymmetric QCD theories,
showing how to derive new duals for these theories from the four dimensional
duality.Comment: 84 pages, 3 figures, harvmac. v2: added an appendix on the reduction
of the 4d index to the 3d partition function, added references, minor
corrections and change
On the Worldsheet Derivation of Large N Dualities for the Superstring
Large N topological string dualities have led to a class of proposed
open/closed dualities for superstrings. In the topological string context, the
worldsheet derivation of these dualities has already been given. In this paper
we take the first step in deriving the full ten-dimensional superstring
dualities by showing how the dualities arise on the superstring worldsheet at
the level of F terms. As part of this derivation, we show for F-term
computations that the hybrid formalism for the superstring is equivalent to a
topological string in ten-dimensional spacetime. Using the description, we then show that the D brane boundary state for the
ten-dimensional open superstring naturally emerges on the worldsheet of the
closed superstring dual.Comment: 21 pages harvma
Unified approach to Quantum and Classical Dualities
We show how classical and quantum dualities, as well as duality relations
that appear only in a sector of certain theories ("emergent dualities"), can be
unveiled, and systematically established. Our method relies on the use of
morphisms of the "bond algebra" of a quantum Hamiltonian. Dualities are
characterized as unitary mappings implementing such morphisms, whose even
powers become symmetries of the quantum problem. Dual variables -which were
guessed in the past- can be derived in our formalism. We obtain new
self-dualities for four-dimensional Abelian gauge field theories.Comment: 4+3 pages, 3 figure
Duality in Integrable Systems and Gauge Theories
We discuss various dualities, relating integrable systems and show that these
dualities are explained in the framework of Hamiltonian and Poisson reductions.
The dualities we study shed some light on the known integrable systems as well
as allow to construct new ones, double elliptic among them. We also discuss
applications to the (supersymmetric) gauge theories in various dimensions.Comment: harvmac 45 pp.; v4. minor corrections, to appear in JHE
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