1202.1297 (Thomas A. Ryttov et al.)

Comparison of Some Exact and Perturbative Results for a Supersymmetric
SU($N_c$) Gauge Theory    [PDF]

Thomas A. Ryttov, Robert Shrock

We consider vectorial, asymptotically free ${\cal N}=1$ supersymmetric
SU($N_c$) gauge theories with $N_f$ copies of massless chiral super fields in
various representations and study how perturbative predictions for the lower
boundary of the infrared conformal phase, as a function of $N_f$, compare with
exact results. We make use of two-loop and three-loop calculations of the beta
function and anomalous dimension of the quadratic chiral super field operator
product for this purpose. The specific chiral superfield contents that we
consider are $N_f$ copies of (i) $F+\bar F$, (ii) $Adj$, (iii) $S_2+\bar S_2$,
and (iv) $A_2 + \bar A_2$, where $F$, $Adj$, $S_2$, and $A_2$ denote,
respectively, the fundamental, adjoint, and symmetric and antisymmetric rank-2
tensor representations. We find that perturbative results slightly overestimate
the value of $N_{f,cr}$ relative to the respective exact results for these
representations, i.e., slightly underestimate the interval in $N_f$ for which
the theory has infrared conformal behavior. Our results provide a measure of
how closely perturbative calculations reproduce exact results for these
theories.

View original: http://arxiv.org/abs/1202.1297