Related papers: A-twisted Landau-Ginzburg models
We define Landau quasi-particles within the Gutzwiller variational theory, and derive their dispersion relation for general multi-band Hubbard models in the limit of large spatial dimensions D. Thereby we reproduce our previous calculations…
In this paper we introduce and study some mathematical structures on top of transitive Lie algebroids in order to formulate gauge theories in terms of generalized connections and their curvature: metrics, Hodge star operator and integration…
Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L$_\infty$ algebra, that governs not only the action of the symmetries but also…
Gauge fixing in the non-perturbative domain of non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity. To compare results from different methods it is necessary to resolve this ambiguity explicitly. Such a resolution is…
P. Clarke describes mirror symmetry as a duality between Landau--Ginzburg models, so that the dual of an LG model is another LG model. We describe examples in which the underlying space is a total space of a vector bundle on the projective…
In this article, following an insight of Kontsevich, we extend the famous Weil conjecture (as well as the strong form of the Tate conjecture) from the realm of algebraic geometry to the broad noncommutative setting of dg categories. As a…
This is a study of the Landau-Ginzburg/Calabi-Yau correspondence, and related matters, using linear sigma models.
We discuss aspects of the algebraic geometry of compact non-commutative Calabi-Yau manifolds. In this setting, it is appropriate to consider local holomorphic algebras which can be glued together into a compact Calabi-Yau algebra. We…
Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy…
We construct Landau-Ginzburg Lagrangians for minimal bosonic ($N=0$) $W$-models perturbed with the least relevant field, inspired by the theory of $N=2$ supersymmetric Landau-Ginzburg Lagrangians. They agree with the Lagrangians for…
We consider Landau-Ginzburg models stemming from groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group $G^\star$, which serves as the appropriate…
We study the fate of discrete gauge groups and discrete charges of gravitational theories under twisted circle compactification. We then apply our results to six-dimensional F-theory vacua with discrete gauge symmetries and relate them to…
FJRW theory is a formulation of physical Landau-Ginzburg models with a rich algebraic structure, rooted in enumerative geometry. As a consequence of a major physical conjecture, called the Landau-Ginzburg/Calabi-Yau correspondence, several…
We uncover an infinite class of novel zero-form non-invertible symmetries in a broad family of four-dimensional models, studied years ago by Gaillard and Zumino (GZ), which includes several extended supergravities as particular subcases.…
Let \(X\) be an irreducible smooth complex projective variety, and let \(G\) be a connected reductive linear algebraic group over \(\mathbb{C}\). In this paper, we first classify integrable transitive algebraic Lie algebroids on $X$. We…
The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to second-order phase transitions, from superconductivity,…
The Ginzburg-Landau functional is a phase transition model which is suitable for clustering or classification type problems. We study the asymptotics of a sequence of Ginzburg-Landau functionals with anisotropic interaction potentials on…
Computer simulations of amphiphilic systems are reviewed. Research areas cover a wide range of length and time scales, and a whole hierarchy of models and methods has been developed to address them all. They range from atomistically…
This article develops a duality principle applicable to a large class of variational problems. Firstly, we apply the results to a Ginzburg-Landau type model. In a second step, we develop another duality principle and related primal dual…
We investigate the fusion of B-type interfaces in two-dimensional supersymmetric Landau-Ginzburg models. In particular, we propose to describe the fusion of an interface in terms of a fusion functor that acts on the category of modules of…