Related papers: T-duality of current algebras and their quantizati…
We systematically apply the formalism of duality walls to study the action of duality transformations on boundary conditions and local and nonlocal operators in two, three, and four-dimensional free field theories. In particular, we…
Previously, we introduced a duality transformation for Euler $G$--Frobenius algebras. Using this transformation, we prove that the simple $A,D,E$ singularities and Pham singularities of coprime powers are mirror self--dual where the mirror…
We use the mapping cone for the relative deRham cohomology of a manifold with boundary in order to show that the Chern-Gauss-Bonnet Theorem for oriented Riemannian vector bundles over such manifolds is a manifestation of Lefschetz Duality…
Two field 2-forms on the space-time manifold, in a relationship of duality, are presented and included in the extended phase-space structure used to describe relativistic particles having both electric and magnetic charges. By exterior…
Self-duality plays a very important role in many applications in field theories possessing topological solitons. In general, the self-duality equations are first order partial differential equations such that their solutions satisfy the…
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 develop a new approach to T-duality based on Courant algebroid relations which subsumes the usual T-duality as well as its various generalisations. Starting from a relational description for the reduction of exact Courant algebroids over…
We find the T-duality transformation rules for 2-dimensional (2,1) supersymmetric sigma-models in (2,1) superspace. Our results clarify certain aspects of the (2,1) sigma model geometry relevant to the discussion of T-duality. The…
We revisit the duality between heterotic string theory compactified on K3 x T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet sector. We derive an explicit map between the field variables of the respective…
The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to…
Drinfel'd double of Lie bialgebroids plays an important role in T-duality of string theories. In the presence of $H$ and $R$ fluxes, Lie bialgebroids should be extended to proto Lie bialgebroids. For both cases, the pair is given by two…
We show that dualising transfer maps in Hochschild cohomology of symmetric algebras commutes with Tate duality. This extends a well-known result in group cohomology.
This thesis investigates the quantum properties of T-duality invariant formalisms of String Theory. We introduce and review duality invariant formalisms of String Theory including the Doubled Formalism. We calculate the background field…
This is the first part of two papers. In this part, we prove the blowup formulae for virtual Hodge polynomials of Gieseker moduli spaces of rank-2 stable sheaves and Uhlenbeck compactification spaces over algebraic surfaces. In particular,…
We compute the factorization homology of a polynomial algebra over a compact and closed manifold with trivialized tangent bundle up to weak equivalence in a new way. This calculation is based on the model of a graph complex and an explicit…
In this paper, we compute the homology coalgebra and cohomology algebra over a field of all generalized moment-angle complexes and give a duality theorem on complementary moment-angle complexes.
In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that they can…
T-Duality is a poorly understood symmetry of the space-time fields of string theory that interchanges long and short distances. It is best understood in the context of toroidal compactification where, loosely speaking, radii of the torus…
In this paper we study the heterotic type IIA duality when fluxes are turned on. We show that many of the known fluxes are dual to each other and claim that certain fluxes on the heterotic side require that the type IIA picture is lifted to…
We discuss the holonomic dual of tautological systems, with a view towards applications to linear free divisors and to homogeneous spaces. As a technical tool, we consider a Chevalley--Eilenberg type complex, generalizing Euler--Koszul…