2020/09/26 by Mikhail Shifman, Shifman, Mikhail
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2009.12654
openalex publication_date 2020/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
I argue that a certain perturbative proximity exists between some supersymmetric and non-supersymmetric theories (namely, pure Yang-Mills and adjoint QCD with two flavors, adjQCDNf=2). I start with \mathcal N=2 super-Yang-Mills theory built of two \mathcal N=1 superfields: vector and chiral. In \mathcal N=1 language the latter presents matter in the adjoint representation of SU(N). Then I convert the matter superfield into a "\em phantom" one (in analogy with ghosts), breaking \mathcal N=2 down to \mathcal N=1. The global SU(2) acting between two gluinos in the original theory becomes graded. Exact results in thus deformed theory allows one to obtain insights in certain aspects of non-supersymmetric gluodynamics. In particular, it becomes clear how the splitting of the β function coefficients in pure gluodynamics, β1 =(4 -\frac 13 )N and β2= (6-\frac 13)N2, occurs. Here the first terms in the braces (4 and 6, always integers) are geometry-related while the second terms (-\frac 13 in both cases) are \it bona fide quantum effects. In the same sense adjQCDNf=2 is close to \mathcal 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 \mathcal N=2.) As a warmup exercise I use this idea in 2D CP(1) sigma model with \mathcal N=(2,2) supersymmetry, through the minimal heterotic \mathcal N=(0,2) → bosonic CP(1).