Higher-loop corrections to the infrared evolution of a gauge theory with fermions

Abstract

We consider a vectorial, asymptotically free gauge theory and analyze the effect of higher-loop corrections to the beta function on the evolution of the theory from the ultraviolet to the infrared. We study the case in which the theory contains N f copies of a fermion transforming according to the fundamental representation and several higher-dimensional representations of the gauge group. We also calculate higher-loop values of the anomalous dimension of the mass, γm ofψψ at the infrared zero of the beta function. We find that for a given theory, the values of γm calculated to three-and four-loop order, and evaluated at the infrared zero computed to the same order, tend to be somewhat smaller than the value calculated to two-loop order. The results are compared with recent lattice simulations.

Comparison of some exact and perturbative results for a supersymmetricSU(Nc)gauge theory

“…Second, we find that when one goes from the two-loop anomalous dimension evaluated at the two-loop IR zero of β, γ IR,2ℓ or the scheme-independent γ IR,SI , to the three-loop result γ IR,3ℓ , the value decreases. Again, this is the same trend that we found for the corresponding non-supersymmetric theory in [18]. Thus, as with the IR zero, this suggests that for both the non-supersymmetric and the supersymmetric theory with corresponding matter field representation content, the lowest-order calculation of the value of γ m at the IR fixed point gives a larger value than the true value.…”

“…Our most detailed analyses here were for the cases R = F and R = Adj, with briefer studies of the S 2 and A 2 cases. It is useful to compare our results with what we found in [18] (see also [19], whose results were in agreement with those in [18]) for a nonsupersymmetric SU(N c ) gauge theory with N f copies of massless fermions in various representations. We believe that our findings for the supersymmetric gauge theory, besides being of interest in their own right, provide further insight into the results that we obtained previously for the non-supersymmetric theory.…”

“…This is the same trend that we found in [18] for a non-supersymmetric SU(N c ) with N f copies of massless fermions in the fundamental representation.…”

“…There, the bound that the full operator dimension ofψ i ψ i be larger than 1 implies that γ m ≤ 2, as we noted in Eq. (4.2) of [18] (equivalent to the bound from Eq. (4.1) of [18]).…”

Fundamental partial compositeness

“…β (1) TC < ∼ 1 3 β (1) TC | gauge . This is intuitively reasonable since matter screens the confining gauge interactions and the resulting naive condition is roughly compatible with earlier estimates [34,35,[39][40][41]. Considering TC-fermions and TC-scalars in 9 We adopt the common notation T a R T a R = C2(R)I and Tr[T a R T b R ] = T (R)δ ab with TR the generators of the R representation.…”