Related papers: Duality and normalization, variations on a theme o…
We study $T^2$ compactification of massive type IIA supergravity in presence of possible Ramond-Ramond (RR) background fluxes. The resulting theory in D=8 is shown to possess full $SL(2,R)\times SL(2,R)$ T-duality symmetry similar to the…
In a recent work [1, 2] Sjoberg remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
We found a lot of new three dimensional N = 4 mirror pairs generalizing previous considerations on three dimensional generalized quiver gauge theories. We recovered almost all previous discovered mirror pairs with these constructions. One…
Turner's Conjecture describes all blocks of symmetric groups and Hecke algebras up to derived equivalence in terms of certain double algebras. With a view towards a proof of this conjecture, we develop a general theory of Turner doubles. In…
We discuss the pseudodual chiral model to illustrate a class of two-dimensional theories which have an infinite number of conservation laws but allow particle production, at variance with naive expectations. We describe the symmetries of…
We consider Maxwell theory on a non-spin manifold. Depending on the choice of statistics for line operators, there are three non-anomalous theories and one anomalous theory with different symmetry fractionalizations. We establish the…
We study duality theorems for the relative logarithmic de Rham-Witt sheaves on semi-stable schemes $X$ over a local ring $\mathbb{F}_q[[t]]$, where $\mathbb{F}_q$ is a finite field. As an application, we obtain a new filtration on the…
Let f:S ->B be a relatively minimal fibred surface. In this note we give a partial affirmative answer to a conjecture of Xiao, proving that the direct image of the relative dualizing sheaf of $f$ is ample when the slope of the fibration is…
A new dynamic SU(3)-structure solution in type-IIA is found by T-dualising a deformation of the Maldacena-Nastase solution along an SU(2) isometry. It is argued that this is dual to a quiver gauge theory with multiple Chern-Simons levels. A…
We analyze the spectrum of the exactly duality and gauge invariant higher-derivative double field theory. While this theory is based on a chiral CFT and does not correspond to a standard string theory, our analysis illuminates a number of…
We provide a geometric-combinatorial model for the category of coherent sheaves on the weighted projective line of type (2,2,n) via a cylindrical surface with n marked points on each of its upper and lower boundaries, equipped with an order…
We give two stochastic diffeologies on the free loop space which allow us to define stochastic equivariant cohomology theories in the Chen-Souriau sense and to establish a link with cyclic cohomology. With the second one, we can establish a…
Hidden symmetries are the backbone of Integrable two-dimensional theories. They provide classical solutions of higher dimensional models as well, they seem to survive partially quantisation and their discrete remnants in M-theory called…
For a primal-dual pair of conic linear problems that are described by convex cones $S\subset X$, $T\subset Y$, bilinear symmetric objective functions $\langle\cdot,\cdot\rangle_X$, $\langle\cdot,\cdot\rangle_Y$ and a linear operator…
We give a new simple proof of boundedness of the family of semistable sheaves with fixed numerical invariants on a fixed smooth projective variety. In characteristic zero our method gives a quick proof of Bogomolov's inequality for…
This note presents a uniform treatment of normality and three of its variants---topological, weak and seminormality---for Noetherian schemes. The key is to define these notions for pairs $(Z, X)$ consisting of a (not necessarily reduced)…
We apply the recent proposal for mirrors of nonabelian (2,2) supersymmetric two-dimensional gauge theories to make predictions for two-dimensional supersymmetric gauge theories with exceptional gauge groups G2, F4, E6, E7, and E8. We…
The aim of this paper is to prove a generalization of a theorem of Rao for families of space curves, which caracterizes the biliaison classes of curves. First we introduce the concept of pseudo-isomorphism of coherent sheaves, which…
Several papers have been written studying unexpected hypersurfaces. We say a finite set of points Z admits unexpected hypersurfaces if a general union of fat linear subspaces imposes less that the expected number of conditions on the ideal…