Noncommutative geometry and the BV formalism: Application to a matrix model

JOURNAL OF GEOMETRY AND PHYSICS

卷:120

Article

Iseppi, Roberta A.¹  van Suijlekom, Walter D.² 

[1] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

[2] Radboud Univ Nijmegen, Inst Math Astrophys & Particle Phys, Heyendaalseweg 135, NL-6525 AJ Nijmegen, Netherlands

关键词: Noncommutative geometry;    Batalin-Vilkovisky formalism;    Gauge theory;   

DOI  :  10.1016/j.geomphys.2017.05.009

来源: Elsevier

【 摘 要 】

We analyze a U(2)-matrix model derived from a finite spectral triple. By applying the BV formalism, we find a general solution to the classical master equation. To describe the BV formalism in the context of noncommutative geometry, we define two finite spectral triples: the BV spectral triple and the BV auxiliary spectral triple. These are constructed from the gauge fields, ghost fields and anti-fields that enter the BV construction. We show that their fermionic actions add up precisely to the BV action. This approach allows for a geometric description of the ghost fields and their properties in terms of the BV spectral triple. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free