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SPECIAL ISSUE — Recent Nonperturbative Developments in QCD-like Theories; Editors: Ari Hietanen, Yannick Meurice and Rajamani NarayananNo Access

Volume independence for Yang–Mills fields on the twisted torus

    https://doi.org/10.1142/S0217751X14450018Cited by:17 (Source: Crossref)

    We review some recent results related to the notion of volume independence in SU(N) Yang–Mills theories. The topic is discussed in the context of gauge theories living on a d-dimensional torus with twisted boundary conditions. After a brief introduction reviewing the formalism for introducing gauge fields on a torus, we discuss how volume independence arises in perturbation theory. We show how, for appropriately chosen twist tensors, perturbative results to all orders in the 't Hooft coupling depend on a specific combination of the rank of the gauge group (N) and the periods of the torus (l), given by lN2/d, for d even. We discuss the well-known relation to noncommutative field theories and address certain threats to volume independence associated to the occurrence of tachyonic instabilities at one-loop order. We end by presenting some numerical results in 2+1 dimensions that extend these ideas to the nonperturbative domain.

    Dedicated to the memory of our friend and colleague, Pierre van Baal

    PACS: 11.15.Pg, 11.15.Ha, 11.10.Nx
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