Extremal correlators in four-dimensional SCFT

TL;DR

This work addresses whether extremal four-point correlators in 4D SCFTs renormalise with coupling. It combines superconformal Ward identities and harmonic superspace analyticity to show such correlators factorise into products of two-point functions with a constant coefficient, and employs the reduction formula in $N=2$ harmonic superspace to constrain coupling dependence. The main results demonstrate non-renormalisation for extremal ($p_4= ext{sum}_{i=1}^3 p_i$) and certain subextremal cases, valid for any finite $N_c$ and across $N=2$ theories (hypermultiplets) and $N=4$ SYM. This provides a field-theory justification for AdS/CFT expectations and highlights the power of harmonic analyticity in restricting quantum corrections in four-dimensional SCFTs.

Abstract

It is shown that certain extremal correlators in four-dimensional N=2 superconformal field theories (including N=4 super-Yang-Mills as a special case) have a free-field functional form. It is further argued that the coupling constant dependence receives no correction beyond the lowest order. These results hold for any finite value of N_c.