Related papers: Duality for Landau-Ginzburg models
There are numerous generalizations of the celebrated Priestley duality for bounded distributive lattices to the non-distributive setting. The resulting dualities rely on an earlier foundational work of such authors as Nachbin,…
Gauging and duality transformations, two of the most useful tools in many-body physics, are shown to be equivalent up to constant depth quantum circuits in the case of one-dimensional quantum lattice models. This is demonstrated by making…
We investigate a class of (2,2) supersymmetric string vacua which may be represented as Landau--Ginzburg theories with a quasihomogeneous potential which has an isolated singularity at the origin. There are at least three thousand distinct…
Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial $W$ and a related group of symmetries $G$ of $W$. It is known…
Recently, V.Ginzburg introduced and studied in depth the notion of a principal nilpotent pair in a semisimple Lie algebra \g. Our aim is to contribute to the general theory of nilpotent pairs. Roughly speaking, a nilpotent pair (e_1,e_2)…
We study orbifolds of (0,2) models and their relation to (0,2) mirror symmetry. In the Landau-Ginzburg phase of a (0,2) model the superpotential features a whole bunch of discrete symmetries, which by quotient action lead to a variety of…
We prove that a large class of Poincar\'e duality pairs admit rational models (in the sense of Sullivan) of a particularly nice form associated to some Poincar\'e duality CDGA. These models have applications in particular to the…
We give an explicit formula for the duality, previously conjectured by Horja and Borisov, of two systems of GKZ hypergeometric PDEs. We prove that in the appropriate limit this duality can be identified with the inverse of the Euler…
Duality refers to two equivalent descriptions of the same theory from different points of view. Recently there has been tremendous progress in formulating and understanding possible dualities of quantum many body theories in $2+1$-spacetime…
We show how the duality invariant approach to M-theory formulated by Berman and Perry relates to the double field theory proposed by Hull and Zwiebach. In doing so we provide suggestions as to how Ramond fields can be incorporated into the…
We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras…
We present a formal algebraic language to deal with quantum deformations of Lie-Rinehart algebras - or Lie algebroids, in a geometrical setting. In particular, extending the ice-breaking ideas introduced by Xu in [Ping Xu, "Quantum…
We provide a new proof of the super duality equivalence between infinite-rank parabolic BGG categories of general linear Lie (super) algebras conjectured by Cheng and Wang and first proved by Cheng and Lam. We do this by establishing a new…
Consider a Grassmannian $\mathrm{Gr}(2, V)$ for an even-dimensional vector space $V$. Its derived category of coherent sheaves has a Lefschetz exceptional collection with respect to the Pl\"ucker embedding. We consider a variety $X_1$ of…
Recently Seiberg has conjectured a duality symmetry connecting different theories of the supersymmetric QCD type. We provide support for this conjecture by analyzing a flat direction of the theory along which the two dual theories go over…
We consider the Grassmannian X of (n-k)-dimensional subspaces of an n-dimensional complex vector space. We describe a `mirror dual' Landau-Ginzburg model for X consisting of the complement of a particular anti-canonical divisor in a…
A master equation expressing the classical integrability of two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. In particular, a closer connection between integrability and T-duality…
We present the new explicit geometrical knowledge of the Landau-Ginzburg orbifolds, when a typical type of superpotential is considered. Relying on toric geometry, we show the one-to-one correspondence between some of the $(a,c)$ states…
We introduce and study a notion of duality for two classes of optimization problems commonly occurring in probability theory. That is, on an abstract measurable space $(\Omega,\mathcal{F})$, we consider pairs $(E,\mathcal{G})$ where $E$ is…
Given an effective Cartier divisor D with simple normal crossing support on a smooth and proper scheme X over a perfect field of positive characteristic p, there is a natural notion of de Rham-Witt sheaves on X with zeros along D. We show…