BV quantization of dynamical fuzzy spectral triples

James Gaunt, Hans Nguyen, Alexander Schenkel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
36 Downloads (Pure)

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 (a) the gauge-invariant zero Dirac operator D 0 = 0 in a general ( p , q ) -model, and (b) a simple example of a non-trivial D 0 in the quartic ( 0 , 1 ) -model.

Original languageEnglish
Article number474004
JournalJournal of Physics A: Mathematical and Theoretical
Volume55
Issue number47
DOIs
Publication statusPublished - 25 Nov 2022

Keywords

  • BV quantization
  • Dirac operator
  • noncommutative geometry
  • spectral triple

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy

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