Uploaded August 2026 | Updated September 2026, 2 weeks ago
Series Title: From Counting to Emergence in AdS/CFT
Speaker: Sanjaye Ramgoolam (Queen Mary University of London)
Abstract: We start with a review from Lecture 1 of the permutation-based parameterization of gauge-invariant polynomials for a single matrix variable. This framework was used to describe Schur polynomial operators in the half-BPS sector of maximally supersymmetric U(N) Yang Mills theory in four dimensions. These give an orthogonal basis for two-point correlators and resolve the non-trivial free-field mixing problem of multi-traces for general N.
We highlight the powerful underlying algebraic structures controlling two-point and extremal three-point functions in the half-BPS sector. We extend these observations to the quarter- and eighth-BPS sectors, which are spanned by multi-matrix gauge-invariant polynomials. The finite N counting and construction of free-field orthogonal bases for these multi-matrix operators is then described. We conclude by observing how the algebraic perspective and associated diagrammatic structures yield a unifying framework for these results and inform further generalisations.
Series Title: From Counting to Emergence in AdS/CFT
Speaker: Sanjaye Ramgoolam (Queen Mary University of London)
Abstract: We start with a review from Lecture 1 of the permutation-based parameterization of gauge-invariant polynomials for a single matrix variable. This framework was used to describe Schur polynomial operators in the half-BPS sector of maximally supersymmetric U(N) Yang Mills theory in four dimensions. These give an orthogonal basis for two-point correlators and resolve the non-trivial free-field mixing problem of multi-traces for general N.
We highlight the powerful underlying algebraic structures controlling two-point and extremal three-point functions in the half-BPS sector. We extend these observations to the quarter- and eighth-BPS sectors, which are spanned by multi-matrix gauge-invariant polynomials. The finite N counting and construction of free-field orthogonal bases for these multi-matrix operators is then described. We conclude by observing how the algebraic perspective and associated diagrammatic structures yield a unifying framework for these results and inform further generalisations.
