BV quantization of dynamical fuzzy spectral triples

Abstract

This paper provides a systematic study of gauge symmetries in the dynamical fuzzy spectral triple models for quantum gravity that have been proposed by Barrett and collaborators. We develop both the classical and the perturbative quantum BV formalism for these models, which in particular leads to an explicit homological construction of the perturbative quantum correlation functions. We show that the relevance of ghost and antifield contributions to such correlation functions depends strongly on the background Dirac operator $D_0$ around which one perturbs, and in particular on the amount of gauge symmetry that it breaks. This will be illustrated by studying quantum perturbations around 1.) the gauge-invariant zero Dirac operator $D_0=0$ in a general $(p,q)$-model, and 2.) a simple example of a non-trivial $D_0$ in the quartic $(0,1)$-model.

arXiv comment22 pages. v2: Final version accepted for publication in Journal of Physics A

References in corpus (19)

• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• Noncommutative Geometry and Gravity
• Classification of Finite Spectral Triples
• Noncommutative D=4 gravity coupled to fermions
• On the perturbation lemma, and deformations
• Matrix geometries and fuzzy spaces as finite spectral triples
• Monte Carlo simulations of random non-commutative geometries
• Bootstrapping Dirac Ensembles
• Spectral estimators for finite non-commutative geometries
• Phase Transition in Random Noncommutative Geometries
• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• Spectral Statistics of Dirac Ensembles
• Finite spectral triples for the fuzzy torus
• From Noncommutative Geometry to Random Matrix Theory
• On multimatrix models motivated by random noncommutative geometry II: A Yang-Mills-Higgs matrix model
• Noncommutative geometry and the BV formalism: application to a matrix model
• The BV formalism: theory and application to a matrix model
• A homological approach to the Gaussian Unitary Ensemble

Cited by in corpus (3)

• Spectral Statistics of Dirac Ensembles
• From Noncommutative Geometry to Random Matrix Theory
• The loop equations for noncommutative geometries on quivers