On the geometry of quiver gauge theories (stacking exceptional collections)
type: Item
instance of: scholarly article
title: On the geometry of quiver gauge theories (stacking exceptional collections)
zbMATH Open document ID: 1247.14014
author: Christopher P. Herzog
author: Robert L. Karp
published in: Advances in Theoretical and Mathematical Physics
publication date: 2010-10-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/hep-th/0605177
review text: Topological D-branes are represented as objects in the derived category. In this context fractional branes provide ways to determine the low energy gauge theory description D-branes probing a Calabi-Yau singularity. This paper advances the program of using exceptional collections to understand the gauge theory description of a D-brane probing a Calabi-Yau singularity. In many cases they contain only line bundles supported on the exceptional divisor that partially resolves the Calabi-Yau singularity. The exceptional collections were usuful for studying a large class of singularities, such as toric varieties, and also Fano with the help of smooth stacks. In this paper, proved is vanishing of tachyons for these Calabi-Yau singularities, and the authors give a strong exceptional collection for all \(Y^{p,q}\) spaces with \(p-q-2 > 0\). The spaces \(Y^{p,p}\), \(Y^{p,p-1}\) and \(Y^{p,p-2}\) are already shown in the previous paper of the authors [J. High Energy Phys. 2006, No. 02, 061 (2006); \url{arXiv:hep-th/0507175}].
reviewed by: Akira Yoshioka
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J32
Mathematics Subject Classification ID: 14J33
Mathematics Subject Classification ID: 81T30
Mathematics Subject Classification ID: 18E30
Mathematics Subject Classification ID: 32Q25
zbMATH DE Number: 5794637
zbMATH Keywords: fractional brane
zbMATH Keywords: exceptional collection
describes a project that uses: Macaulay2
MaRDI profile type: Publication
arXiv ID: hep-th/0605177
OpenAlex ID: W1783907424
Wikidata QID: Q125976456
DOI: 10.4310/ATMP.2009.V13.N3.A1
description: scientific article