Related papers: Dual Non-Abelian Duality and the Drinfeld Double

Assuming $\mathbf{O}(D,D)$ covariant fields as the `fundamental' variables, Double Field Theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such…

The quantum Yang-Mills theory describing dual ($\tilde g$) and non-dual ($g$) charges and revealing the generalized duality symmetry was developed by analogy with the Zwanziger formalism in QED.

We define the notion of adjustment for strict Lie 2-groups and provide the complete cocycle description for non-Abelian gerbes with connections whose structure 2-group is an adjusted 2-group. Most importantly, we depart from the common…

We show that the Drinfel'd double associated to the standard quantum deformation $sl_\eta(2,R)$ is isomorphic to the (2+1)-dimensional AdS algebra with the initial deformation parameter $\eta$ related to the cosmological constant…

A Drinfel'd algebra gives the systematic construction of generalized parallelizable spaces and this allows us to study an extended T-duality, known as the Poisson-Lie T-duality. Recently, in order to find a generalized U-duality, an…

Based on Mubarakzyanov's classification of four-dimensional real Lie algebras, we classify ten-dimensional Exceptional Drinfeld algebras (EDA). The classification is restricted to EDA's whose maximal isotropic (geometric) subalgebras cannot…

Generalizations of GL(n) abelian Toda and $\widetilde{GL}(n)$ abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by…

We demonstrate the discrete duality symmetry between the Abelian 1-form and 2-form basic gauge fields in the context of a three $(2 + 1)$-dimensional ($3D$) combined system of the field-theoretic model of the free Abelian 1-from and 2-form…

A particular form of non-linear $\sigma$-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-abelian nature of the invariance, with {\it{field dependent structure…

We investigate (non-)Abelian T-duality from the perspective of Poisson-Lie T-plurality. We show that sigma models related by duality/plurality are given not only by Manin triples obtained from decompositions of Drinfel'd double, but also by…

We show that noncommutative electromagnetism and Dirac-Born-Infeld (DBI) theory with scalar fields are SL(2,R) self-dual when noncommutativity is light-like and we are in the slowly varying field approximation. This follows from SL(2,R)…

We exhibit exact conformal field theory descriptions of SO(N) and Sp(N) pairs of Seiberg-dual gauge theories within string theory. The N=1 gauge theories with flavour are realized as low energy limits of the worldvolume theories on D-branes…

We adress ourselves the question of the quantum equivalence of non abelian dualised $\si$-models on the simple example of the T-dualised $SU(2) \si$-model. This theory is classically canonically equivalent to the standard chiral $SU(2)…

The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or…

We attempt to settle the issue as to what is the correct non-abelian generalisation of the Born-Infeld action, via a consideration of the two-loop $\beta$--function for the non-abelian background gauge field in open string theory. An…

This thesis first gives a background and review of the article hep-th/0102038, where we substantiated a conjectured duality between two a priori unrelated gauge theories, N=2 quiver theory and N=2 Seiberg-Witten theory. These gauge theories…

For the St$\ddot u$ckelberg-modified massive Abelian 3-form theory in any arbitrary D-dimension of spacetime, we show that its classical gauge symmetry transformations are generated by the first-class constraints. We establish that the…

We study issues of duality in 3D field theory models over a canonical noncommutative spacetime and obtain the noncommutative extension of the Self-Dual model induced by the Seiberg-Witten map. We apply the dual projection technique to…

We discuss and reinterpret a 4d conformal triality recently discovered in the literature in terms of ordinary Seiberg duality. We observe that a non-abelian global symmetry is explicitly realized by only two out of the three phase. We…

This thesis discusses various aspects of duality in quantum field theory and string theory. In the first part we consider duality in topological quantum field theories, concentrating on the Donaldson and Seiberg-Witten theories as (dual)…