Related papers: Multiplicative dimensional reduction

We show that there is a natural perverse sheaf on the moduli space of semistable sheaves on a smooth projective Calabi-Yau 3-fold which is locally the perverse sheaf of vanishing cycles for a local Chern-Simons functional. This gives us a…

Bagger-Lambert-Gustavsson theory with infinite dimensional gauge group has been suggested to describe M5-brane as a condensation of multiple M2-branes. Here we perform a topological twisting of the Bagger-Lambert-Gustavsson theory. The…

We construct a mathematical framework for twisted N=2 supersymmetric topological quantum field theory on a 4-manifold. Supersymmetry in flat space is defined and the twist homomorphism is constructed, giving us a supermanifold that is the…

We reformulate the construction of Kontsevich's completion and use Lawson homology to define many new motivic invariants. We show that the dimensions of subspaces generated by algebraic cycles of the cohomology groups of two $K$-equivalent…

We introduce and study a fermionization procedure for the cohomological Hall algebra $\mathcal{H}_{\Pi_Q}$ of representations of a preprojective algebra, that selectively switches the cohomological parity of the BPS Lie algebra from even to…

We propose, motivate and give evidence for a relation between the $\mathcal D$-modules of the quantum cohomology of a smooth complex projective manifold $X$ and a projective bundle $\PP(\oplus L_i)$ over $X$.

In this article, we study quasimaps to moduli spaces of sheaves on a $K3$ surface $S$. We construct a surjective cosection of the obstruction theory of moduli spaces of quasimaps. We then establish reduced wall-crossing formulas which…

For any rigid space over a perfectoid extension of $\mathbb Q_p$ that admits a liftable smooth formal model, we construct an isomorphism between the moduli stacks of Hitchin-small Higgs bundles and Hitchin-small v-vector bundles. This…

We extend the Donaldson-Corlette-Hitchin-Simpson correspondence between Higgs bundles and flat connections on compact K\"ahler manifolds to compact quasi-regular Sasakian manifolds. A particular consequence is the translation of…

We study Hamiltonian field theories on the multisymplectic bundle of a principal G-bundle with Hamiltonian densities invariant under a subgroup $H\subset G$. Using the covariant bracket formulation, we reduce the polysymplectic space and…

We consider BPS states in a large class of d=4, N=2 field theories, obtained by reducing six-dimensional (2,0) superconformal field theories on Riemann surfaces, with defect operators inserted at points of the Riemann surface. Further…

In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,\theta)$, where $G$ is a reductive algebraic group and $\theta$ is an involution of $G$. This generalization involves the notion of a…

We study a class of flat bundles, of finite rank $N$, which arise naturally from the Donaldson-Thomas theory of a Calabi-Yau threefold $X$ via the notion of a variation of BPS structure. We prove that in a large $N$ limit their flat…

This is a continuation of prior work of the author on cosection localization for d-manifolds. We construct reduced virtual fundamental classes for derived manifolds with surjective cosections and cosection localized virtual fundamental…

We propose a relation between the operator of S-duality (of N=4 super Yang-Mills theory in 3+1D) and a topological theory in one dimension lower. We construct the topological theory by compactifying N=4 super Yang-Mills on a circle with an…

These notes give an introduction to Geometric Invariant Theory and symplectic reduction, with lots of pictures and simple examples. We describe their applications to moduli of bundles and varieties, and their infinite dimensional analogues…

For an arbitrary reductive group $G$, we compute the infinitesimal automorphisms of $L$-valued principal $G$-Higgs bundles over a compact K\"ahler manifold $X$, extending known results for $\Omega_X^{1}$-valued $G$-Higgs bundles. Using this…

For any two degrees coprime to the rank, we construct a family of ring isomorphisms parameterized by GSp(2g) between the cohomology of the moduli spaces of stable Higgs bundles which preserve the perverse filtrations. As consequences, we…

In alignment with a programme by Donaldson and Thomas [DT], Thomas [Th] constructed a deformation invariant for smooth projective Calabi-Yau threefolds, which is now called the Donaldson-Thomas invariant, from the moduli space of…

Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried using both, the topological algebra and its central extension, which arise from the twisting of $N=2$ supersymmetry in four…