Related papers: T-duality and the exotic chiral de Rham complex

We study an analogue of the analytic torsion for elliptic complexes that are graded by $\mathbb{Z}_2$, orignally constructed by Mathai and Wu. Motivated by topological T-duality, Bouwknegt an Mathai study the complex of forms on an…

This submission is a PhD dissertation. Kapustin and Witten conjectured that there is a mirror symmetry relation between the hyperk\"ahler structures on certain Higgs bundle moduli spaces. As a consequence, they conjecture an equivalence…

We study the situation when the T-dual of a toric K\"ahler geometry is a generalized K\"ahler geometry involving semi-chiral fields. We explain that this situation is generic for polycylinders, tori and related geometries. Gauging multiple…

The purpose of this paper is to discuss a generalization of the bubble transform to differential forms. The bubble transform was discussed in a previous paper by the authors for scalar valued functions, or zero-forms, and represents a new…

We study a class of four-dimensional N=1 superconformal field theories obtained from the six-dimensional (1,0) theory, on M5-branes on C^2/Z_k orbifold singularity, compactified on a Riemann surface. This produces various quiver gauge…

Supermembrane compactified on a $M_9\times T^2$ target space is globally described by the inequivalent classes of torus bundles over torus. These torus bundles have monodromy in $SL(2,Z)$ when they correspond to the nontrivial central…

We reexamine the results on the global properties of T-duality for principal circle bundles in the context of a dimensionally reduced Gysin sequence. We will then construct a Gysin sequence for principal torus bundles and examine the…

We derive a formula for the global gravitational anomaly of the self-dual field theory on an arbitrary compact oriented Riemannian manifold. Along the way, we uncover interesting links between the theory of determinant line bundles of Dirac…

We introduce pseudoconformal structures on 4--dimensional manifolds and study their properties. Such structures are arising from two different complex operators which agree in a 2--dimensional subbundle of the tangent bundle; this subbundle…

In this article, we extend the van Hamel-Lichtenbaum duality theorem to (not necessarily smooth) proper and geometrically integral varieties defined over a $p$-adic field $k$. More precisely, we prove that for such variety $X$ there exists…

We apply the $C^*$-algebraic formalism of topological T-duality due to Mathai and Rosenberg to a broad class of topological spaces that include the torus bundles appearing in string theory compactifications with duality twists, such as…

Inspired by a recently proposed Duality and Conformal invariant modification of Maxwell theory (ModMax), we construct a one-parameter family of two-dimensional dynamical system in classical mechanics that share many features with the ModMax…

In this paper, we shed new light onto $T\bar{T}$-deformations by engineering them on 2D surface defects, supporting chiral and antichiral CFT's, in a 4D Chern-Simons bulk. This approach is motivated by various connections between…

For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. Such foliations are generalizations of holomorphic principal torus bundles. If there exists a…

This is the third of a series of papers on a new equivariant cohomology that takes values in a vertex algebra, and contains and generalizes the classical equivariant cohomology of a manifold with a Lie group action a la H. Cartan. In this…

Yang-Baxter (YB) deformations of type IIB string theory have been well studied from the viewpoint of classical integrability. Most of the works, however, are focused upon the local structure of the deformed geometries and the global…

We present a superfield formulation of the chiral de Rham complex (CDR) of Malikov-Schechtman-Vaintrob in the setting of a general smooth manifold, and use it to endow CDR with superconformal structures of geometric origin. Given a…

In this paper, we define `simplicial GKM orbifold complexes' and study some of their topological properties. We introduce the concept of filtration of regular graphs and `simplicial graph complexes', which have close relations with…

We apply some methods of homology and K-theory to special classes of branes wrapping homologically nontrivial cycles. We treat the classification of four-geometries in terms of compact stabilizers (by analogy with Thurston's classification…

In this thesis the recently developed duality covariant approach to string and M-theory is investigated. In this formalism the U-duality symmetry of M-theory or T-duality symmetry of Type II string theory becomes manifest upon extending…