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: In Lecture 1, we reviewed how half-BPS gauge-invariant operators capture, via the operator-state correspondence of AdS/CFT, the dual physics of ordinary gravitons, semi-classical giant gravitons, as well as half-BPS supergravity geometries with AdS_5 times S^5 asymptotics. Limits on the detection of these geometries using asymptotic gravitational observables accessible at sub-Planckian energies lead to physics-motivated mathematical questions about centres of symmetric group algebra.
These centres, of rapidly growing dimension, turn out to be generated non-linearly — through products as well as sums — by surprisingly small sets of conjugacy classes. This has led to efficient eigenvalue-based algorithms, formulated within permutation algebras, for multi-matrix free-field correlators and, in work nearing completion, for one-loop corrections to classical dimensions in the SU(2) sector of N=4 super-Yang-Mills theory. Similar algorithms have been employed in quantum-information tasks involving the detection of projectors and matrix units using quantum phase estimation. We will also discuss potential wider implications of these unexpected simplicities in the structure of symmetric group algebras.
Series Title: From Counting to Emergence in AdS/CFT
Speaker: Sanjaye Ramgoolam (Queen Mary University of London)
Abstract: In Lecture 1, we reviewed how half-BPS gauge-invariant operators capture, via the operator-state correspondence of AdS/CFT, the dual physics of ordinary gravitons, semi-classical giant gravitons, as well as half-BPS supergravity geometries with AdS_5 times S^5 asymptotics. Limits on the detection of these geometries using asymptotic gravitational observables accessible at sub-Planckian energies lead to physics-motivated mathematical questions about centres of symmetric group algebra.
These centres, of rapidly growing dimension, turn out to be generated non-linearly — through products as well as sums — by surprisingly small sets of conjugacy classes. This has led to efficient eigenvalue-based algorithms, formulated within permutation algebras, for multi-matrix free-field correlators and, in work nearing completion, for one-loop corrections to classical dimensions in the SU(2) sector of N=4 super-Yang-Mills theory. Similar algorithms have been employed in quantum-information tasks involving the detection of projectors and matrix units using quantum phase estimation. We will also discuss potential wider implications of these unexpected simplicities in the structure of symmetric group algebras.
