A Note on Bounds of Scalar Operators in Perturbative SCFTs

TL;DR

This paper investigates bounds on scalar operator dimensions in 4d superconformal field theories using perturbative methods, extending previous work to next-to-next-to-leading order and confirming the conjecture's validity.

Contribution

It computes NNLO corrections to scalar operator bounds in 4d SCFTs, confirming the conjecture's validity at this order in different dominant effect regimes.

Findings

Conjecture holds at NNLO for $ {O}( {4})$ effects.

Null corrections ensure conjecture validity for $ {O}(y^2)$ effects.

Results extend previous NLO verifications to higher-order corrections.

Abstract

Bounds on anomalous dimensions of scalar operators in 4d superconformal field theory are explored through perturbative viewpoint. Following the recent work of Green and Shih, in which a conjecture involved this issue is verified at the NLO, we consider the NNLO corrections to the bounds, which are important in some situations and can be divided into two cases where $\mathcal{O}(\lambda^{4})$ or $\mathcal{O}(y^2)$ effects dominate respectively. In the former case, we find that the conjecture is maintained at NNLO, while in the later case, the statement still holds due to the null corrections arising from $\mathcal{O}(y^{2})$.