TL;DR
This paper uses the Brauer algebra to analyze one-loop BPS operators in N=4 SYM, identifying quarter BPS operators and including non-planar corrections through algebraic methods.
Contribution
It introduces a novel algebraic approach using the Brauer algebra to classify and analyze BPS operators, including non-planar effects, in N=4 SYM.
Findings
Identification of BPS operators labeled by Brauer algebra irreducible representations
Construction of quarter BPS operators with algebraic methods
Inclusion of full non-planar corrections in the analysis
Abstract
We analyse the one-loop dilatation operator with the help of the Brauer algebra. We find some BPS operators in N=4 SYM, which are labelled by irreducible representations of the Brauer algebra. Some of them are quarter BPS operators. The result includes full non-planar corrections. Our construction and proof are based on simple algebraic arguments and are carried out for any number of fields.
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