Related papers: Quiver algebras and their representations for arbi…
We compute superpotentials for quiver gauge theories arising from marginal D-Brane decay on collapsed del Pezzo cycles S in a Calabi-Yau X. This is done using the machinery of A-infinity products in the derived category of coherent sheaves…
We prove that multiplicative preprojective algebras, defined by Crawley-Boevey and Shaw, are 2-Calabi-Yau algebras, in the case of quivers containing unoriented cycles. If the quiver is not itself a cycle, we show that the center is…
We prove a special case of a conjecture of Davison which pertains to superpotential descriptions of fundamental group algebras $k[\pi_1(X)]$. We consider the case in which the manifold $X$ is the mapping torus $M_{g, \varphi}$ of a genus…
In this paper we prove that Graded Calabi Yau Algebras of dimension 3 are isomorphic to path algebras of quivers with relations derived from a superpotential. We show that for a given quiver $Q$ and a degree $d$, the set of good…
The BPS bound is formulated in light-cone superspace for the N = 4 superYang-Mills theory. As a consequence of the superalgebra all momenta are shown to be expressed as a quadratic form in the relevant supertransformations, and these forms…
By exploiting new mathematical relations between Pandharipande-Thomas (PT) invariants, closely related to Gopakumar-Vafa (GV) invariants, and rank 0 Donaldson-Thomas (DT) invariants counting D4-D2-D0 BPS bound states, we rigorously compute…
Placing a set of branes at a Calabi-Yau singularity leads to an N=1 quiver gauge theory. We analyze F-term deformations of such gauge theories. A generic deformation can be obtained by making the Calabi-Yau non-commutative. We discuss…
We describe a technique which enables one to quickly compute an infinite number of toric geometries and their dual quiver gauge theories. The central object in this construction is a ``brane tiling,'' which is a collection of D5-branes…
We study quivers with potential (QPs) whose Jacobian algebras are finite dimensional selfinjective. They are an analogue of the `good QPs' studied by Bocklandt whose Jacobian algebras are 3-Calabi-Yau. We show that 2-representation-finite…
We introduce unbounded strongly irreducible operators and transitive operators. These operators are related to a certain class of indecomposable Hilbert representations of quivers on infinite-dimensional Hilbert spaces. We regard the theory…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
In this paper, we construct quantum invariants for knotoid diagrams in $\mathbb{R}^2$. The diagrams are arranged with respect to a given direction in the plane ({\it Morse knotoids}). A Morse knotoid diagram can be decomposed into basic…
A superpotential algebra is square if its quiver admits an embedding into a two-torus such that the image of its underlying graph is a square grid, possibly with diagonal edges in the unit squares; examples are provided by dimer models in…
We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas- invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives a new perspective on recent work of…
F-theory compactifications on appropriate local elliptic Calabi-Yau manifolds engineer six dimensional superconformal field theories and their mass deformations. The partition function $Z_{top}$ of the refined topological string on these…
Topological string theory partition function gives rise to Gromov-Witten invariants, Donaldson-Thomas invariants and 5D BPS indices. Using the remodeling conjecture, which connects Topological Recursion with topological string theory for…
We begin the study of categorifications of Donaldson-Thomas invariants associated with Hilbert schemes of points on the three-dimensional affine space, which we call DT categories. The DT category is defined to be the category of matrix…
We consider the moduli space of the McKay quiver representations associated to the binary polyhedral groups G < SU(2) < SU(3). The derived category of such representations is equivalent to the derived category of coherent sheaves on the…
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…
A new type of algebras that represent a generalization of both quantum groups and braided groups is defined. These algebras are given by a pair of solutions of the Yang--Baxter equation that satisfy some additional conditions. Several…