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Disordered fermions, extra dimensions, and a solvable Yang-Mills theory

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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… Click to show full 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 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, confines the color and is chirally symmetric in the strong coupling regime. The model can be generalized allowing for Standard Model fermions to be included in the theory. In this case, the emerging theory is an asymptotic safe QCD. We discuss briefly the effective dimensionality of such a theory as well as its gravity dual.

Keywords: mills theory; theory; disordered fermions; model; yang mills

Journal Title: Physical Review D
Year Published: 2019

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