I argue that a certain perturbative proximity exists between some supersymmetric and nonsupersymmetric theories (namely, pure Yang-Mills and adjoint QCD with two flavors, adjQCDNf=2). I start with N=2 super-Yang-Mills theory built of two N=1 superfields: vector and chiral. In N=1 language, the latter presents matter in the adjoint representation of SU(N). Then, I convert the matter superfield into a phantom one (in analogy with ghosts), breaking N=2 down to N=1. The global SU(2) acting between two gluinos in the original theory becomes graded. Exact results in thus deformed theory allow one to obtain insights in certain aspects of nonsupersymmetric gluodynamics. In particular, it becomes clear how the splitting of the β function coefficients in pure gluodynamics, β1=(4-13)N and β2=(6-13)N2, occurs. Here, the first terms in the braces (4 and 6, always integers) are geometry related, while the second terms (-13 in both cases) are bona fide quantum effects. In the same sense, adjQCDNf=2 is close to N=2 SYM. Thus, I establish a certain proximity between pure gluodynamics and adjQCDNf=2 with supersymmetric theories. (Of course, in both cases, we loose all features related to flat directions and Higgs/Coulomb branches in N=2.) As a warmup exercise, I use this idea in the two-dimensional CP(1) sigma model with N=(2,2) supersymmetry, through the minimal heterotic N=(0,2)→ bosonic CP(1).
Bibliographical noteFunding Information:
I am grateful to K. Chetyrkin, A. Kataev, A. Losev, C. H. Sheu, and K. Stepanyanz for useful communications. This work is supported in part by U.S. DOE Grant No. de-sc0011842.
© 2020 authors. Published by the American Physical Society.