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One-dimensional QCD in thimble regularization

F. Di Renzo and G. Eruzzi
Phys. Rev. D 97, 014503 – Published 12 January 2018

Abstract

QCD in 0+1 dimensions is numerically solved via thimble regularization. In the context of this toy model, a general formalism is presented for SU(N) theories. The sign problem that the theory displays is a genuine one, stemming from a (quark) chemical potential. Three stationary points are present in the original (real) domain of integration, so that contributions from all the thimbles associated to them are to be taken into account: we show how semiclassical computations can provide hints on the regions of parameter space where this is absolutely crucial. Known analytical results for the chiral condensate and the Polyakov loop are correctly reproduced: this is in particular trivial at high values of the number of flavors Nf. In this regime we notice that the single thimble dominance scenario takes place (the dominant thimble is the one associated to the identity). At low values of Nf computations can be more difficult. It is important to stress that this is not at all a consequence of the original sign problem (not even via the residual phase). The latter is always under control, while accidental, delicate cancelations of contributions coming from different thimbles can be in place in (restricted) regions of the parameter space.

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  • Received 2 October 2017

DOI:https://doi.org/10.1103/PhysRevD.97.014503

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Particles & Fields

Authors & Affiliations

F. Di Renzo and G. Eruzzi*

  • Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma and INFN, Gruppo Collegato di Parma I-43100 Parma, Italy

  • *Present address: Maps spa, I-43122 Parma, Italy.

Article Text

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Issue

Vol. 97, Iss. 1 — 1 January 2018

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