Related papers: Quantum Serre theorem as a duality between quantum…
We construct N=1 A-D-E quiver gauge theory with the gauge kinetic term which depends on the adjoint chiral superfields, as a low energy effective theory on D5-branes wrapped on 2-cycles of Calabi-Yau 3-fold in IIB string theory. The…
We study the relationship between Serre duality and the Mukai pairing for smooth and proper dg-algebras. We introduce an alternative definition of the Mukai pairing and prove that it coincides with the Mukai pairings defined by…
We analyze the edge mode structure of Euclidean three dimensional gravity from within the quantum theory as embodied by a Ponzano-Regge-Turaev-Viro discrete state sum with Gibbons-=-Hawking-York boundary conditions. This structure is…
We describe a global approach to the study of duality transformations between antisymmetric fields with transitions and argue that the natural geometrical setting for the approach is that of gerbes, these objects are mathematical…
For X a compact Riemann surface of positive genus, the strange duality conjecture predicts that the space of sections of certain theta bundle on moduli of bundles of rank r and level k is naturally dual to a similar space of sections of…
We study four dimensional $N=2$ supersymmetric gauge theories with matter multiplets. For all such models for which the gauge group is $SU(2)$, we derive the exact metric on the moduli space of quantum vacua and the exact spectrum of the…
We introduce the Legendre bundle, a geometric structure encoding the essential duality of dually flat (Hessian) manifolds, and demonstrate that both exponential families in information geometry and a natural class of quantum field theories…
We introduce a twisted version of $K$-theory with coefficients in a $C^*$-algebra $A$, where the twist is given by a new kind of gerbe, which we call Morita bundle gerbe. We use the description of twisted $K$-theory in the torsion case by…
We establish the Schur-Weyl type duality between double affine Hecke algebras and quantum toroidal superalgebras, generalizing the well known result of Vasserot-Varagnolo [VV96] to the super case.
There are two different ways to deform a quantum curve along the flows of the KP hierarchy. We clarify the relation between the two KP orbits: In the framework of suitable connections attached to the quantum curve they are related by a…
Let V and F be holomorphic bundles over a complex manifold M, and s be a holomorphic section of V. We study the cohomology associated to the Koszul complex induced by s, and prove a generalized Serre duality theorem for them.
In this paper we use recently developed calculus of residue currents together with integral formulas to give a new explicit analytic realization, as well as a new analytic proof of Serre duality on any reduced pure $n$-dimensional…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
The partition functions of refined topological strings(A-models) are computed, which give rise to the circle-compactified five-dimensional supersymmetric linear quiver gauge theories in generic (not necessarily self-dual) Omega backgrounds.…
We introduce a cohomological invariant arising from a class in nonabelian cohomology. This invariant generalizes the Dixmier-Douady class and encodes the obstruction to a C*-algebra bundle being the fixed-point algebra of a gauge action. As…
We suggest to compactify the universal covering of the moduli space of complex structures by non-commutative spaces. The latter are described by certain categories of sheaves with connections which are flat along foliations. In the case of…
Double field theory was developed by theoretical physicists as a way to encompass $T$-duality. In this paper, we express the basic notions of the theory in differential-geometric invariant terms, in the framework of para-Kaehler manifolds.…
Let A_k denote the twisted group algebra of the symmetric group S_k, whose representations correspond to the nonlinear projective representations of S_k. We establish a duality relation between A_k and a Lie superalgebra q(n), sometimes…
A linear section of a double vector bundle is a parallel pair of sections which form a vector bundle morphism; examples include the complete lifts of vector fields to tangent bundles and the horizontal lifts arising from a connection in a…
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…