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BV quantization of dynamical fuzzy spectral triples

Gaunt, James; Nguyen, Hans; Schenkel, Alexander

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James Gaunt

Hans Nguyen


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.


Gaunt, J., Nguyen, H., & Schenkel, A. (2022). BV quantization of dynamical fuzzy spectral triples. Journal of Physics A: Mathematical and Theoretical, 55(47), Article 474004.

Journal Article Type Article
Acceptance Date Nov 18, 2022
Online Publication Date Dec 1, 2022
Publication Date Nov 25, 2022
Deposit Date Dec 7, 2022
Publicly Available Date Dec 7, 2022
Journal Journal of Physics A: Mathematical and Theoretical
Electronic ISSN 1751-8121
Peer Reviewed Peer Reviewed
Volume 55
Issue 47
Article Number 474004
Keywords General Physics and Astronomy, Mathematical Physics, Modeling and Simulation, Statistics and Probability, Statistical and Nonlinear Physics
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