Related papers: $A_\infty$ Sabloff Duality via the LSFT Algebra

Given an algebraic Lie algebra $\mathfrak{g}$ over $\mathbb{C}$, we canonically associate to it a Lie algebra $\mathfrak{g}_{\infty}$ defined over $\mathbb{C}_{\infty}$-the reduction of $\mathbb{C}$ mod infinitely large prime, and show that…

We construct shifted symplectic derived enhancements on rigidified moduli spaces of sheaves on Calabi-Yau varieties of dimension at least two. More generally, we prove that any $B\mathbb{G}_m$-action on a non-positively-shifted symplectic…

For a subanalytic Legendrian $\Lambda \subseteq S^{*}M$, we prove that when $\Lambda$ is either swappable or a full Legendrian stop, the microlocalization at infinity $m_\Lambda: \operatorname{Sh}_\Lambda(M) \rightarrow \operatorname{\mu…

A natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of…

We first review aspects of Kac Moody indefinite algebras with particular focus on their hyperbolic subset. Then we present two field theoretical systems where these structures appear as symmetries. The first deals with complete…

Let X be a non-compact Calabi-Yau manifold and f be a holomorphic function on X with compact critical locus. We introduce the notion of f-twisted Sobolev spaces for the pair (X,f) and prove the corresponding Hodge-to-de Rham degeneration…

Let H be a quasi-Hopf algebra, a weak Hopf algebra or a braided Hopf algebra. Let B be an H-bicomodule algebra such that there exists a morphism of H-bicomodule algebras v:H\rightarrow B. Then we can define an object B^{co(H)} which is a…

We show that there is an equivalence of categories between Lie-Rinehart algebras over a commutative algebra $\mathcal O $ and homotopy equivalence classes of negatively graded Lie $\infty $-algebroids over their resolutions (=acyclic Lie…

Given a Hopf algebra H and an algebra A that is an H-module algebra we consider the category of left H-modules and A-bimodules, where morphisms are just right A-linear maps (not necessarily H-equivariant). Given a twist F of H we then…

In this work we present a new approach to constructing Calabi-Yau orbifold models required for compactification in superstring theory. We use the connection of CY orbifolds with the class of exactly solvable N=2 SCFT models to explicitly…

We introduce a family of dualities between certain non-supersymmetric self-dual gauge theories on a large class of $4d$ self-dual asymptotically flat backgrounds, and the large $N$ limit of an independently defined $2d$ chiral defect CFT.…

We sketch a construction of Legendrian Symplectic Field Theory (SFT) for conormal tori of knots and links. Using large $N$ duality and Witten's connection between open Gromov-Witten invariants and Chern-Simons gauge theory, we relate the…

We show that the set of augmentations of the Chekanov-Eliashberg algebra of a Legendrian link underlies the structure of a unital A-infinity category. This differs from the non-unital category constructed in [BC], but is related to it in…

We describe a procedure for classifying N=2 superconformal theories of the type introduced by Davide Gaiotto. Any curve, C, on which the 6D A_{N-1} SCFT is compactified, can be decomposed into 3-punctured spheres, connected by cylinders. We…

Let $H$ be a finite dimensional quasi-Hopf algebra over a field $k$ and ${\mathfrak A}$ a right $H$-comodule algebra in the sense of Hausser and Nill. We first show that on the $k$-vector space ${\mathfrak A}\ot H^*$ we can define an…

We compute the $L_\infty$-theoretic dimensional reduction of the F1/D$p$-brane super $L_\infty$-cocycles with coefficients in rationalized twisted K-theory from the 10d type IIA and type IIB super Lie algebras down to 9d. We show that the…

[GGSM2] showed that height functions give adjoint orbits of semisimple Lie algebras the structure of symplectic Lefschetz fibrations (superpotential of the LG model in the language of mirror symmetry). We describe how to extend the…

In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical Legendrian isotopy invariants: the augmentation category, a unital $A_{\infty}$-category, which lifts the set of…

We consider on one hand the possibility that a supersymmetric ${\cal N}=1$ conformal gauge theory has a strongly coupled locus on the conformal manifold at which a different, dual, conformal gauge theory becomes a good weakly coupled…

We introduce a general notion of depth two for ring homomorphism N --> M, and derive Morita equivalence of the step one and three centralizers, R = C_M(N) and C = End_{N-M}(M \o_N M), via dual bimodules and step two centralizers A =…