216,564 research outputs found
Unitary Realizations of U-duality Groups as Conformal and Quasiconformal Groups and Extremal Black Holes of Supergravity Theories
We review the current status of the construction of unitary representations
of U-duality groups of supergravity theories in five, four and three
dimensions. We focus mainly on the maximal supergravity theories and on the N=2
Maxwell-Einstein supergravity (MESGT) theories defined by Jordan algebras of
degree three in five dimensions and their descendants in four and three
dimensions. Entropies of the extremal black hole solutions of these theories in
five and four dimensions are given by certain invariants of their U-duality
groups. The five dimensional U-duality groups admit extensions to spectrum
generating generalized conformal groups which are isomorphic to the U-duality
groups of corresponding four dimensional theories. Similarly, the U-duality
groups of four dimensional theories admit extensions to spectrum generating
quasiconformal groups that are isomorphic to the corresponding U-duality groups
in three dimensions. We outline the oscillator construction of the unitary
representations of generalized conformal groups that admit positive energy
representations, which include the U-duality groups of N=2 MESGT's in four
dimensions. We conclude with a review of the minimal unitary realizations of
U-duality groups that are obtained by quantizations of their quasiconformal
actions.Comment: 24 pages; latex fil
Duality in Supersymmetric SU(N) Gauge Theory with a Symmetric Tensor
Duality in supersymmetric SU(N) gauge theory with a symmetric tensor is
studied using the technique of deconfining and Seiberg's duality. By
construction the gauge group of the dual theory necessarily becomes a product
group. In order to check the duality, several nontrivial consistency conditions
are examined. In particular we find that by deforming along a flat direction,
the duality flows to the Seiberg's duality of SO(N) gauge theory.Comment: LaTeX file, 10 page. a reference adde
F-Theory, T-Duality on K3 Surfaces and N=2 Supersymmetric Gauge Theories in Four Dimensions
We construct T-duality on K3 surfaces. The T-duality exchanges a 4-brane R-R
charge and a 0-brane R-R charge. We study the action of the T-duality on the
moduli space of 0-branes located at points of K3 and 4-branes wrapping it. We
apply the construction to F-theory compactified on a Calabi-Yau 4-fold and
study the duality of N=2 SU(N_c) gauge theories in four dimensions. We discuss
the generalization to the N=1 duality scenario.Comment: 13 pages, late
Heterotic-Type II String Duality and the H-Monopole Problem
Since T-duality has been proved only perturbatively and most of the heterotic
states map into solitonic, non-perturbative, type II states, the 6-dimensional
string-string duality between the heterotic string and the type II string is
not sufficient to prove the S-duality of the former, in terms of the known
T-duality of the latter. We nevertheless show in detail that perturbative
T-duality, together with the heterotic-type II duality, does imply the
existence of heterotic H-monopoles, with the correct multiplicity and multiplet
structure. This construction is valid at a generic point in the moduli space of
heterotic toroidal compactifications.Comment: 12 pages, plain Late
Non-compact Mirror Bundles and (0,2) Liouville Theories
We study (0,2) deformations of N=2 Liouville field theory and its mirror
duality. A gauged linear sigma model construction of the ultraviolet theory
connects (0,2) deformations of Liouville field theory and (0,2) deformations of
N=2 SL(2,R)/U(1) coset model as a mirror duality. Our duality proposal from the
gauged linear sigma model completely agrees with the exact CFT analysis. In the
context of heterotic string compactifications, the deformation corresponds to
the introduction of a non-trivial gauge bundle. This non-compact
Landau-Ginzburg construction yields a novel way to study the gauge bundle
moduli for non-compact Calabi-Yau manifolds.Comment: 34 page
A groupoid approach to noncommutative T-duality
Topological T-duality is a transformation taking a gerbe on a principal torus
bundle to a gerbe on a principal dual-torus bundle. We give a new geometric
construction of T-dualization, which allows the duality to be extended in
following two directions. First, bundles of groups other than tori, even
bundles of some nonabelian groups, can be dualized. Second, bundles whose duals
are families of noncommutative groups (in the sense of noncommutative geometry)
can be treated, though in this case the base space of the bundles is best
viewed as a topological stack.
Some methods developed for the construction may be of independent interest.
These are a Pontryagin type duality that interchanges commutative principal
bundles with gerbes, a nonabelian Takai type duality for groupoids, and the
computation of certain equivariant Brauer groups.Comment: Same theorems, typos correcte
Axial Vector Duality in Affine NA Toda Models
A general and systematic construction of Non Abelian affine Toda models and
its symmetries is proposed in terms of its underlying Lie algebraic structure.
It is also shown that such class of two dimensional integrable models naturally
leads to the construction of a pair of actions related by T-duality
transformationsComment: 9 pages, to appear in JHEP Proc. of the Workshop on Integrable
Theories, Solitons and Duality, IFT-Unesp, Sao Paulo, Brasil, one reference
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