A note on the perturbative properties of BPS operators

TL;DR

This paper investigates the perturbative behavior of 1/2 BPS operators in N=2 SCFT, revealing how quantum corrections differentiate protected operators from those acquiring anomalous dimensions, with implications for understanding the Konishi multiplet.

Contribution

It provides an explicit one-loop analysis of two similar quadrilinear operators, showing how quantum effects determine their BPS status and primacy in N=2 SCFT.

Findings

One operator remains protected at one-loop.

The other operator acquires an anomalous dimension.

Quantum corrections can turn a primary into a descendant.

Abstract

We discuss the perturbative behavior of the 1/2 BPS operators in N=2 SCFT on the example of two very similar quadrilinear composite operators made out of hypermultiplets. An explicit one-loop computation shows that one of them is protected while the other acquires an anomalous dimension. Although both operators are superconformal primaries in the free case, the quantum corrections make the latter become a 1/2 BPS descendant of the Konishi multiplet, while the former remains primary. The comparative study of these two operators at higher orders may be helpful in understanding the quantum properties of the Konishi multiplet.