Related papers: Non-Commutative T-Duality
We review and extend recent work on the application of the non-commutative geometric framework to an interpretation of the moduli space of vacua of certain deformations of N=4 super Yang-Mills theories. We present a simple worldsheet…
Lee and Pandharipande studied a "double point" algebraic cobordism theory of varieties equipped with vector bundles, and speculated that some features of that story might extend to the case of varieties with principal G-bundles. This note…
We introduce the notion of crystallographic T-duality, inspired by the appearance of $K$-theory with graded equivariant twists in the study of topological crystalline materials. Besides giving a range of new topological T-dualities, it also…
We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and…
Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma Duality…
We exploit a new theory of duality transformations to construct dual representations of models incompatible with traditional duality transformations. Hence we obtain a solution to the long-standing problem of non-Abelian dualities that…
In this paper, we initiate the study of nonassociative strict deformation quantization of C*-algebras with a torus action. We shall also present a definition of nonassociative principal torus bundles, and give a classification of these as…
We study T-duality for open strings on tori $\T^d$. The general boundary conditions for the open strings are constructed, and it is shown that T-duality group, which preserves the mass spectrum of closed strings, preserves also the mass…
We begin by presenting a symmetric version of the circle equivariant T-duality result in a joint work of the second author with Siye Wu, thereby generalising the results there. We then initiate the study of twisted equivariant Courant…
We introduce twisted topological correspondences, which generalize both Katsura's topological correspondences as well as the twisted topological graphs introduced by Li. We show that, up to isomorphism, they are in bijection with certain…
We introduce spherical T-duality, which relates pairs of the form $(P,H)$ consisting of a principal $SU(2)$-bundle $P\rightarrow M$ and a 7-cocycle $H$ on $P$. Intuitively spherical T-duality exchanges $H$ with the second Chern class…
Given a saturated Fell bundle A over an inverse semigroup S which is semi-abelian in the sense that the fibers over the idempotents of S are commutative, we construct a twisted etale groupoid L such that A can be recovered from L in a…
The second author showed how Katsura's construction of the C*-algebra of a topological graph E may be twisted by a Hermitian line bundle L over the edge space E. The correspondence defining the algebra is obtained as the completion of the…
We study the notion of twisted bundles on noncommutative space. Due to the existence of projective operators in the algebra of functions on the noncommutative space, there are twisted bundles with non-constant dimension. The U(1) instanton…
Topological Spherical T-duality was introduced by Bouwknegt, Evslin and Mathai in [BEM15] as an extension of topological T-duality from $S^1$-bundles to $\mathrm{SU}(2)$-bundles endowed with closed 7-forms. This notion was further extended…
In this paper, we develop twisted $K$-theory for stacks, where the twisted class is given by an $S^1$-gerbe over the stack. General properties, including the Mayer-Vietoris property, Bott periodicity, and the product structure $K^i_\alpha…
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…
We investigate the effect of T-duality on noncommutativity. Starting with open strings ending on a D2-brane wrapped on a $T^2$ torus in the presence of a Kalb Ramond field, we consider Buscher transformations on the coordinates and…
We introduce the notions of multiplier C*-category and continuous bundle of C*-categories, as the categorical analogues of the corresponding C*-algebraic notions. Every symmetric tensor C*-category with conjugates is a continuous bundle of…
We introduce the notion of K-theoretic duality for extensions of separable unital nuclear $C^*$-algebras by using K-homology long exact sequence and cyclic six term exact sequence for K-theory groups of extensions. We then prove that the…