Abstract
We explore an alternative discretization of continuum SU(N c ) Yang-Mills theory on a Euclidean spacetime lattice, originally introduced by Budzcies and Zirnbauer. In this discretization the self-interactions of the gauge field are induced by a path integral over N b auxiliary boson fields, which are coupled linearly to the gauge field. The main progress compared to earlier approaches is that N b can be as small as N c . In the present paper we (i) extend the proof that the continuum limit of the new discretization reproduces Yang-Mills theory in two dimensions from gauge group U(N c ) to SU(N c ), (ii) derive refined bounds on N b for non-integer values, and (iii) perform a perturbative calculation to match the bare parameter of the induced gauge theory to the standard lattice coupling. In follow-up papers we will present numerical evidence in support of the conjecture that the induced gauge theory reproduces Yang-Mills theory also in three and four dimensions, and explore the possibility to integrate out the gauge fields to arrive at a dual formulation of lattice QCD.
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Brandt, B.B., Lohmayer, R. & Wettig, T. Induced QCD I: theory. J. High Energ. Phys. 2016, 87 (2016). https://doi.org/10.1007/JHEP11(2016)087
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DOI: https://doi.org/10.1007/JHEP11(2016)087