Induced QCD I: theory

Abstract

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.

Diagrammatic representation of scalar QCD and sign problem at nonzero chemical potential

“…The case of N f > 3 is particularly interesting when one wants to go beyond strong coupling. Recent approaches which lend themselves easily to the formulation outlined in this paper are detailed in [14][15][16]. The main goal in these references is to rewrite the gauge plaquette action in such a way as to make only single links appear in the new action, at the expense of introducing auxiliary bosonic field variables.…”

“…The main goal in these references is to rewrite the gauge plaquette action in such a way as to make only single links appear in the new action, at the expense of introducing auxiliary bosonic field variables. The auxiliary fields are either scalar fields [15] or matrix valued fields [16]. In particular, the additional scalar fields naturally increase the number of flavors to N f > 3.…”

New dual representation for staggered lattice QCD

“…The decoupling Eq. (29), also extends to the case where strong coupling dimers combine on a given site with links carrying a non-zero gauge flux. In this case the tensor T ρ can be decomposed as:…”

“…Proceeding in a similar fashion as in Eqs. (28), (29), (31) and with reference to Fig. 9 (a), one gets…”

“…More recently, other approaches that are not limited to small µ B have been proposed, such as the Complex Langevin approach [20,21], the Lefschetz thimble approach [22][23][24], or the density of states method [25]. To name also some approaches that are in the spirit of a dual representation: the 3-dimensional effective theory [26,27] (a joint strong coupling and hopping parameter expansion that can be mapped to SU(3) spin model), decoupling the gauge links using Hubbard-Stratonovich transformations [28], "Induced QCD" based on an alternative discretization of Yang Mills Theory [29,30]. All these approaches have their shortcomings, and a method that allows to simulate lattice QCD at finite density has not yet been established.…”