Representation stacks, D-branes and noncommutative geometry

2010/09/27 by Lieven Le Bruyn, Bruyn, Lieven Le · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #hep-th #math.QA #math.RA

paper · pdf · doi:10.48550/arxiv.1009.5203

arxiv created 2010/09/27 · arxiv updated 2010/09/28

Abstract

In this note we prove that the spec(C)-points of the representation Artin-stack [rep_n R/PGL_n] of n-dimensional representations of an affine algebra R correspond to algebra morphisms R-->A where A is an Azumaya algebra of degree n over C. We connect this to the study of D-branes and Azumaya noncommutative geometry, developed by Chien-Hao Liu and Shing-Tung Yau in a series of papers from arXiv:0709.1515 to arXiv:1003.1178

Citations

• Azumaya-type noncommutative spaces and morphisms therefrom: Polchinski's D-branes in string theory from Grothendieck's viewpoint
• D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck

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