Related papers: Superpotentials and Higher Order Derivations
We show that for a large subclass of Argyres-Douglas-type theories, the Higgs branch admits multiple hyperkahler quotient realizations as Higgs branches of three dimensional $\mathcal{N}=4$ quiver gauge theories, which are related by a…
This note gives a one-to-one correspondence between the equivalence classes of a certain type of 2-dimensional Calabi-Yau categories, and certain type of quivers, This is an analogue of the result in Stability structures, motivic…
The periplectic Lie superalgebra $\mathfrak{p}(n)$ is one of the most mysterious and least understood simple classical Lie superalgebras with reductive even part. We approach the study of its finite dimensional representation theory in…
Buan, Iyama, Reiten and Smith proved that cluster-tilting objects in triangulated 2-Calabi--Yau categories are closely connected with mutation of quivers with potentials over an algebraically closed field. We prove a more general statement…
We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel…
We present a local computation of deformations of the tangent bundle for a resolved orbifold singularity C^d/G. These correspond to (0,2)-deformations of (2,2)-theories. A McKay-like correspondence is found predicting the dimension of the…
We study the behavior of representation varieties of quivers with relations under the operation of node splitting. We show how splitting a node gives a correspondence between certain closed subvarieties of representation varieties for…
We construct projective moduli spaces for torsion-free sheaves on noncommutative projective planes. These moduli spaces vary smoothly in the parameters describing the noncommutative plane and have good properties analogous to those of…
Dijkgraaf and Vafa have conjectured the correspondences between topological string theories, ${\cal N}=1$ gauge theories and matrix models. By the use of this conjecture, we calculate the quantum deformations of Calabi-Yau threefolds with…
For a 3D N=4 gauge theory, turning on the $\Omega$-background in RxR$^2_{\epsilon}$ deforms the Coulomb branch chiral ring into the quantum Coulomb branch algebra, generated by the 1/2-BPS monopoles together with the complex scalar in the…
A new trigonometric degeneration of the Sklyanin algebra is found and the functional realization of its representations in space of polynomials in one variable is studied. A further contraction gives the standard quantum algebra…
We show that the irreducible components of any moduli space of semistable representations of a special biserial algebra are always isomorphic to products of projective spaces of various dimensions. This is done by showing that irreducible…
This paper presents analogous results of Hua [7][8] on numbers of representations of quivers over finite fields which respect nilpotent relations under certain assumptions. A closed formula which counts isomorphism classes of absolutely…
In recent series of works, by translating properties of multi-centered supersymmetric black holes into the language of quiver representations, we proposed a formula that expresses the Hodge numbers of the moduli space of semi-stable…
The N-extended supersymmetric self-dual Poincar\'e supergravity equations provide a natural local description of supermanifolds possessing hyperk\"ahler structure. These equations admit an economical formulation in chiral superspace. A…
The moduli dependence of $(2,2)$ superstring compactifications based on Calabi--Yau hypersurfaces in weighted projective space has so far only been investigated for Fermat-type polynomial constraints. These correspond to Landau-Ginzburg…
We establish a correspondence between vector-valued modular forms with respect to a symmetric tensor representation and quasimodular forms. This is carried out by first obtaining an explicit isomorphism between the space of vector-valued…
An exact superpotential is derived for the N=1 theories which arise as massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to coincide with the…
We study a new duality which pairs 4d N=1 supersymmetric quiver gauge theories. They are represented by brane tilings and are worldvolume theories of D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies theories which…
Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n. We show that Gaudin subalgebras form a variety isomorphic to the moduli space of stable curves of genus zero…