Related papers: Equivariant Topological T-Duality
The initial motivation of this work was to give a topological interpretation of two-periodic twisted de-Rham cohomology which is generalizable to arbitrary coefficients. To this end we develop a sheaf theory in the context of locally…
We review the recently constructed `double field theory' which introduces in addition to the conventional coordinates associated to momentum modes coordinates associated to winding modes. Thereby, T-duality becomes a global symmetry of the…
We study the relationship between the twisted Orbifold K-theories ${^{\alpha}}K_{orb}(\textsl{X})$ and ${^{\alpha'}}K_{orb}(\textsl{Y})$ for two different twists $\alpha\in Z^3(G;S^1)$ and $\alpha'\in Z^3(G';S^1)$ of the Orbifolds…
We derive a partial electric-magnetic (PEM) duality transformation of the twisted quantum double (TQD) model TQD$(G,\alpha)$---discrete Dijkgraaf-Witten model---with a finite gauge group $G$, which has an Abelian normal subgroup $N$, and a…
We introduce the concept of duality between quantum field theories in the Batalin-Vilkovisky formalism, which is interpreted either as a BV morphism, the result of dual BV pushforwards or a combination of both. When a BV morphism affects…
We consider the notion of a connection on a principal bundle $P(M,G)$ from the point of view of the action of the tangential group $TG$. This leads to a new definition of a connection and allows to interpret gauge transformations as effect…
We consider the moduli space of flat G-bundles over the twodimensional torus, where G is a real, compact, simple Lie group which is not simply connected. We show that the connected components that describe topologically non-trivial bundles…
The structure of quantum principal bundles is studied, from the viewpoint of Tannaka-Krein duality theory. It is shown that if the structure quantum group is compact, principal G-bundles over a quantum space M are in a natural…
This paper is a generalization of a previous paper by the author to connected unipotent linear algebraic groups. The notion of an $ \alpha $-pair answers when an open $ G $-stable, affine, sub-variety $ D(H) $ is a trivial bundle over $ G…
We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…
Toric Duality arises as an ambiguity in computing the quiver gauge theory living on a D3-brane which probes a toric singularity. It is reviewed how, in simple cases Toric Duality is Seiberg Duality. The set of all Seiberg Dualities on a…
An equivariant Thom isomorphism theorem in operator K-theory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a…
In the paper [1] we showed that in double space, where all initial coordinates $x^\mu$ are doubled $x^\mu \to y_\mu$, the T-duality transformations can be performed by exchanging places of some coordinates $x^a$ and corresponding dual…
We study several duality isomorphisms between equivariant bivariant K-theory groups, generalising Kasparov's first and second Poincare duality isomorphisms. We use the first duality to define an equivariant generalisation of Lefschetz…
We consider a TFT on the product of a manifold with an interval, together with a topological and a non-topological boundary condition imposed at the two respective ends. The resulting (in general higher gauge) field theory is…
Equivariant $K$-theory is a generalized equivariant cohomology theory which is a hybrid of the $K$-theory of a topological space and the representation theory of the group acting on it. In this article, we review the basics of equivariant…
We consider two operations on an edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge and taking the partial dual with respect to the edge. These two operations give rise to an action of S_3^{|E(G)|},…
Let X be a smooth elliptic fibration over a smooth base B. Under mild assumptions, we establish a Fourier-Mukai equivalence between the derived categories of two objects, each of which is an O^* gerbe over a genus one fibration which is a…
Starting with a $\mathbb{C}^*$-valued cocycle on the global quotient orbifold $X // G$, we apply transgression techniques for 2-gerbes, as developed by Lupercio and Uribe, to construct a gerbe on the orbifold loop space $\mathcal{L}(X//G)$.…
The notion of a semitransitive binary action of a group $G$ on a topological space is introduced. A duality theorem is proved, establishing a bijective correspondence between semitransitive distributive binary $G$-spaces and topological…