Lattice QCD on nonorientable manifolds

Simon Mages, Bálint C. Tóth, Szabolcs Borsányi, Zoltán Fodor, Sándor D. Katz, Kálmán K. Szabó

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


A common problem in lattice QCD simulations on the torus is the extremely long autocorrelation time of the topological charge when one approaches the continuum limit. The reason is the suppressed tunneling between topological sectors. The problem can be circumvented by replacing the torus with a different manifold, so that the connectivity of the configuration space is changed. This can be achieved by using open boundary conditions on the fields, as proposed earlier. It has the side effect of breaking translational invariance strongly. Here we propose to use a nonorientable manifold and show how to define and simulate lattice QCD on it. We demonstrate in quenched simulations that this leads to a drastic reduction of the autocorrelation time. A feature of the new proposal is that translational invariance is preserved up to exponentially small corrections. A Dirac fermion on a nonorientable manifold poses a challenge to numerical simulations: the fermion determinant becomes complex. We propose two approaches to circumvent this problem.

Original languageEnglish (US)
Article number094512
JournalPhysical Review D
Issue number9
StatePublished - May 1 2017

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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