Self-dual quiver moduli and orientifold Donaldson-Thomas invariants
type: Item
instance of: scholarly article
title: Self-dual quiver moduli and orientifold Donaldson-Thomas invariants
zbMATH Open document ID: 1345.81108
author: Matthew B. Young
published in: Communications in Number Theory and Physics
publication date: 2015-11-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/1408.4888
review text: In string theory, it is of central importance to allow the basic building blocks to be unoriented (one-dimensional manifolds, with or without boundary). For example, the cancellation of ``tadpole-type'' boundaries in the moduli of open strings requires the inclusion of Klein surfaces in the quantization process. Many a hope for eventual contact between string theory and the real world rests on this mechanism for anomaly cancellation. In comparison, triangulated categories with duality, which are the mathematical counterpart of orientifolds, are severely underrepresented in the mathematical literature. This paper contributes to filling this gap in the representation theory of quivers, which is at the heart of many connections between algebra, geometry, and supersymmetric physics. The starting point is a quiver with an involution inverting arrows. Given a choice of duality structure on the fixed nodes, such an involution can be lifted to the abelian category of quiver representations, including the notion of self-dual representations on orthogonal/symplectic vector spaces (Section 2). A compatible stability condition on such a quiver is the choice of a real slope at each vertex that is anti-invariant under the involution. A self-dual representation is semistable with respect to isotropic subobjects if and only if it is semistable as an ordinary representation, and this notion agrees with Mumford's numerical criterion derived from geometric invariant theory for the quotient by the relevant orthogonal/symplectic group (Section 3). The Hall module formalism, introduced by the author in a previous publication, leads to an explicit formula for the number of \({\mathbb F}_q\)-rational points of stacks of semistable self-dual representations. Their generating function is used to give an initial rigorous definition of orientifold Donaldson-Thomas invariants of quiver representations. This is the central result of the paper (Section 4). The behaviour of these invariants under …
reviewed by: Johannes Walcher
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 14D21
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 14N35
zbMATH DE Number: 6505256
zbMATH Keywords: representations of quivers
zbMATH Keywords: categories with duality
zbMATH Keywords: orientifolds
zbMATH Keywords: Donaldson-Thomas theory
describes a project that uses: CoulombHiggs
MaRDI profile type: Publication
arXiv ID: 1408.4888
DOI: 10.4310/CNTP.2015.V9.N3.A1
description: scientific article