Abstract
Generalizing disorder couplings of the SYK model by means of SU(N) matrices we formulate a lattice model of fermions in d+1 dimensions. Integration of fermions yields an effective theory of Yang-Mills fields in d dimensions, the latter approaching the standard Yang-Mills theory in the case of heavy fermions and the classical limit of vanishing coupling constant of the theory. Quantum mechanically, the theory is solved using large N approximation of the dual effective theory of Hermitian matrices in d dimensions. The theory is asymptotically free and confines the color. In case of massless fermions the emerging theory is an asymptotic safe QCD theory. We discuss also the relationship of this theory to the SYK model.
Highlights
Yang-Mills theories and quantum chromodynamics (QCD) [1,2,3,4] play an important role in our understanding of basic forces of the Universe
While an analytical solution is highly desirable, the high precision lattice simulation of Lüscher and Weisz leaves no doubt that, at low energies, the Yang-Mills theory may be described by an effective string theory [8]
Many years of research in lattice simulations of QCD have proven to be an indispensable tool in understanding the Standard Model at a nonperturbative level
Summary
Yang-Mills theories and quantum chromodynamics (QCD) [1,2,3,4] play an important role in our understanding of basic forces of the Universe. The results of this paper may be summarized as follows: (i) The model with heavy fermions yields an effective theory of local Yang-Mills fields, a theory which approaches the standard Yang-Mills theory in the classical limit of a vanishing coupling constant. (iii) In the large N limit, the theory is dual to a field theory of matrices of order Nt, where Nt is the number of lattice sites along the extra dimension. (viii) the heavy fermion theory shares important properties with the standard Yang-Mills theory, like asymptotic freedom and color confinement, the corresponding beta functions are different functions of the coupling constant. We obtain local theory Yang-Mills fields in the weak coupling limit, whereas in the second we get QCD with a large number of light modes. Appendix C applies our bosonization approach to strong coupling QCD
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