Related papers: K-Decompositions and 3d Gauge Theories

We construct 3d, N=2 supersymmetric gauge theories by considering a one-parameter `R-flow' of 4d, N=2 theories, where the central charges vary while preserving their phase order. Each BPS state in 4d leads to a BPS particle in 3d, and thus…

In recent work, we related the structure of subvarieties of $n\times n$ complex matrices defined by eigenvalue coincidences to $GL(n-1,\mathbb{C})$-orbits on the flag variety of $\mathfrak{gl}(n,\mathbb{C})$. In the first part of this…

In the first part of this paper we begin the study of polysymplectic manifolds, and of their relationship with PDE's. This notion provides a generalization of symplectic manifolds which is very well suited for the geometric study of PDE's…

We elaborate an unified geometric approach to classical mechanics, Riemann-Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N-connection) structure. There are investigated the conditions when the…

We generalize the familiar notions of overtwistedness and Giroux torsion in 3-dimensional contact manifolds, defining an infinite hierarchy of local filling obstructions called planar torsion, whose integer-valued order $k \ge 0$ can be…

Let U be a real form of a complex semisimple Lie group, and tau, sigma, a pair of commuting involutions on U. This data corresponds to a reflective submanifold of a symmetric space, U/K. We define an associated integrable system, and…

Given an admissible 3-manifold $M$ and a cohomology class $\phi\in H^1(M;\mathbb R)$, we prove that the universal $L^2$-torsion of $M$ detects the fiberedness of $\phi$, except when $M$ is a closed graph manifold that admits no…

The goal of the paper is to give characterization of closed connected manifolds which admit a global multisympletic 3-form of some algebraic type. A generic type of such 3-form is equivalent to a G2-structure. This is the most interesting…

Given a closed, oriented Lagrangian submanifold $L$ in a Liouville domain $\overline{M}$, one can define a Maurer-Cartan element with respect to a certain $L_\infty$-structure on the string homology…

Let $K$ be a field of characteristic zero and let $\mathfrak{sl}_2 (K)$ be the 3-dimensional simple Lie algebra over $K$. In this paper we describe a finite basis for the $\mathbb{Z}_2$-graded identities of the adjoint representation of…

Lagrangian multiforms provide a variational framework for describing integrable hierarchies. This thesis presents two approaches for systematically constructing Lagrangian one-forms, which cover the case of finite-dimensional integrable…

This paper is devoted to deformations of Lagrangian submanifolds contained in the singular locus of a log-symplectic manifold. We prove a normal form result for the log-symplectic structure around such a Lagrangian, which we use to extract…

M-theory geometric engineering on manifolds of special holonomy yields a rich class of novel field theories. In this paper, we construct new 3d $\mathcal{N}=2^{\ast}$ and $\mathcal{N}=4^{\ast}$ gauge theories, realized as mass-deformations…

In this article we address the first part of the programme presented in \cite{Teleman_arXiv_III}, \S 2; we construct the local $K$- theory level of the index formula. Our construction is sufficiently general to encompass the algebra of…

A distinctive duality present in 3d $\mathcal{N}=4$ theories is the 3d mirror symmetry. Under this duality, the Coulomb (Higgs) branch of one theory corresponds to the Higgs (Coulomb) branch of its mirror dual. This paper is divided into…

We further explore the implications of our framework in [arXiv:1301.1977, arXiv:1309.4775], and physically derive, from the principle that the spacetime BPS spectra of string-dual M-theory compactifications ought to be equivalent, (i) a 5d…

We perform a topological-holomorphic twist of $\mathcal{N}=4$ supersymmetric gauge theory on a four-manifold of the form $M_4=\Sigma_1 \times \Sigma_2$ with Riemann surfaces $\Sigma_{1,2}$, and unravel the mathematical implications of its…

We prove that a Kleinian surface groups is determined, up to conjugacy in the isometry group of $\mathbb H^3$, by its simple marked length spectrum. As a first application, we show that a discrete faithful representation of the fundamental…

Given two locally conformal symplectic (LCS) structures on manifolds $M_1$ and $M_2$, we construct a natural $\R^+$-torsor of locally conformal symplectic structures on a certain covering space $M_1 \boxplus M_2$ of $M_1 \times M_2$. As the…

Compactification of M- / string theory on manifolds with $G_2$ structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a…