Abstract
Consequences of gauging exact {mathbb{Z}}_k^C center symmetries in several simple SU(N) gauge theories, where k is a divisor of N, are investigated. Models discussed include: the SU(N) gauge theory with Nf copies of Weyl fermions in self-adjoint single-column antisymmetric representation, the well-discussed adjoint QCD, QCD-like theories in which the quarks are in a two-index representation of SU(N), and a chiral SU(N) theory with fermions in the symmetric as well as in anti-antisymmetric representations but without fundamentals. Mixed 't Hooft anomalies between the 1-form {mathbb{Z}}_k^C symmetry and some 0- form (standard) discrete symmetry provide us with useful information about the infrared dynamics of the system. In some cases they give decisive indication to select only few possiblities for the infrared phase of the theory.
Highlights
The concept of gauging a discrete symmetry might sound a bit peculiar from the point of view of conventional idea of gauging a global flavor symmetry, i.e., that of taking the transformation parameters as functions of spacetime and turning it to a local gauge symmetry
Models discussed include: the SU(N ) gauge theory with Nf copies of Weyl fermions in self-adjoint single-column antisymmetric representation, the well-discussed adjoint QCD, QCD-like theories in which the quarks are in a two-index representation of SU(N ), and a chiral SU(N ) theory with fermions in the symmetric as well as in anti-antisymmetric representations but without fundamentals
Mixed ’t Hooft anomalies between the 1-form ZCk symmetry and some 0form discrete symmetry provide us with useful information about the infrared dynamics of the system
Summary
As the gauging of a discrete center symmetry and the calculation of anomalies under such gauging are the basic tools of this paper and will be used repeatedly below, let us briefly review the procedure here. We recall that in order to gauge a ZCk discrete center symmetry in an SU(N ) gauge theory (k being a divisor of N ), one introduces a pair of U(1) 2-form and 1-form ZCk gauge fields (Bc(2), Bc(1)) satisfying the constraint [4] This constraint satisfies the invariance under the U(1) 1-form gauge transformation, Bc(2) → Bc(2) + dλc, Bc(1) → Bc(1) + kλc, where λc is the 1-form gauge function, satisfying the quantized flux. In order to study the anomaly of Uψ(1) symmetry (or of a discrete subgroup of it), ψ → eiαψ, we introduce an external Uψ(1) gauge field Aψ, and couple it to the fermion as ψγμ.
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