2 research outputs found

    The twisted gradient flow coupling at one loop

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    We compute the one-loop running of the SU(N)SU(N) 't Hooft coupling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scale l~\tilde{l} given by an adequate combination of the torus size and the rank of the gauge group, and is computed in the continuum using dimensional regularization. We present the strategy to regulate the divergences for a generic twist tensor, and determine the matching to the MS‾\overline{\rm MS} scheme at one-loop order. For the particular case in which the twist tensor is non-trivial in a single plane, we evaluate the matching coefficient numerically and determine the ratio of Λ\Lambda parameters between the two schemes. We analyze the NN dependence of the results and the possible implications for non-commutative gauge theories and volume independence.Comment: 52 pages, 12 figure

    Memory efficient finite volume schemes with twisted boundary conditions

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    In this paper we explore a finite volume renormalization scheme that combines three main ingredients: a coupling based on the gradient flow, the use of twisted boundary conditions and a particular asymmetric geometry, that for SU(N)SU(N) gauge theories consists on a hypercubic box of size l2×(Nl)2l^2 \times (Nl)^2, a choice motivated by the study of volume independence in large NN gauge theories. We argue that this scheme has several advantages that make it particularly suited for precision determinations of the strong coupling, among them translational invariance, an analytic expansion in the coupling and a reduced memory footprint with respect to standard simulations on symmetric lattices, allowing for a more efficient use of current GPU clusters. We test this scheme numerically with a determination of the Λ\Lambda parameter in the SU(3)SU(3) pure gauge theory. We show that the use of an asymmetric geometry has no significant impact in the size of scaling violations, obtaining a value ΛMS‾8t0=0.603(17)\Lambda_{\overline{MS}} \sqrt{8 t_0} =0.603(17) in good agreement with the existing literature. The role of topology freezing, that is relevant for the determination of the coupling in this particular scheme and for large NN applications, is discussed in detail.Comment: 35 pages, 17 figure