248 citations · 3.1k across the 108 of their papers we have counts for
110 papers · 1 filter
Polynomial and Eigenspace Factorisations for the One-loop Dilatation Operator at Finite
Adrian Padellaro, Sanjaye Ramgoolam, Ryo Suzuki
We study gauge-invariant two-matrix polynomials of degree , corresponding to the states in the sector of super Yang-Mills theory with gauge group …
String theory mathematics and matrix data analysis
Sanjaye Ramgoolam
Inspired by matrix techniques in quantum field theory and string theory, we review Permutation Invariant Gaussian Matrix Models (PIGMM), which replace the continuous symmetries of…
Negative heat capacities in spherically symmetric sectors of -matrix quantum mechanics
Denjoe O'Connor, Sanjaye Ramgoolam
We consider the and invariant sectors of the bosonic -matrix harmonic oscillator with gauge symmetry. The micro-canonical degeneracy $\mathcal{Z}( N , d ,…
Oscillators from non-semisimple walled Brauer algebras
Sanjaye Ramgoolam, Michał Studziński
The walled Brauer algebras govern Schur--Weyl duality for unitary groups acting on mixed tensor spaces and pla…
Gauge-string duality, monomial bases and graph determinants
Garreth Kemp, Sanjaye Ramgoolam
Questions at the intersection of the AdS/CFT correspondence and quantum information theory motivate the study of projectors in sequences of subalgebras of finite-dimensional commut…
Critical dimensions and small cycle dominance from all-orders asymptotics of -matrix theory
Yang Lei, Sanjaye Ramgoolam
Supersymmetric sectors of super-Yang-Mills theory motivate the study of the partition function for the counting of gauge-invariant functions of matrices tra…
Finite-dimensional algebras, gauge-string duality and thermodynamics
Sanjaye Ramgoolam
Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimension…
Simple harmonic oscillators from non-semisimple walled Brauer algebras
Sanjaye Ramgoolam, Michał Studziński
Walled Brauer algebras illuminate the combinatorics of mixed tensor representations of , with copies of the fundamental and copies of the anti-fundam…
Gauged permutation invariant tensor quantum mechanics, least common multiples and the inclusion-exclusion principle
Denjoe O'Connor, Sanjaye Ramgoolam
We derive the canonical ensemble partition functions for gauged permutation invariant tensor quantum harmonic oscillator thermodynamics, finding surprisingly simple expressions wit…
Row and column detection complexities of character tables
Adrian Padellaro, Sanjaye Ramgoolam, Rak-Kyeong Seong
Character tables of finite groups and closely related commutative algebras have been investigated recently using new perspectives arising from the AdS/CFT correspondence and low-di…
Eigenvalue systems for integer orthogonal bases of multi-matrix invariants at finite N
Adrian Padellaro, Sanjaye Ramgoolam, Ryo Suzuki
Multi-matrix invariants, and in particular the scalar multi-trace operators of SYM with gauge symmetry, can be described using permutation centraliser algebr…
Counting of surfaces and computational complexity in column sums of symmetric group character tables
Joseph Ben Geloun, Sanjaye Ramgoolam
The character table of the symmetric group , of permutations of objects, is of fundamental interest in theoretical physics, combinatorics as well as computational complexi…
Permutation invariant matrix quantum thermodynamics and negative specific heat capacities in large N systems
Denjoe O'Connor, Sanjaye Ramgoolam
We study the thermodynamic properties of the simplest gauged permutation invariant matrix quantum mechanical system of oscillators, for general matrix size . In the canonical en…
Permutation invariant tensor models and partition algebras
George Barnes, Adrian Padellaro, Sanjaye Ramgoolam
Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Ma…
Gauged permutation invariant matrix quantum mechanics: Partition functions
Denjoe O'Connor, Sanjaye Ramgoolam
The Hilbert spaces of matrix quantum mechanical systems with matrix degrees of freedom have been analysed recently in terms of symmetric group elements …
Gauged permutation invariant matrix quantum mechanics: Path Integrals
Denjoe O'Connor, Sanjaye Ramgoolam
We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of , …
Row-Column duality and combinatorial topological strings
Adrian Padellaro, Rajath Radhakrishnan, Sanjaye Ramgoolam
Integrality properties of partial sums over irreducible representations, along columns of character tables of finite groups, were recently derived using combinatorial topological s…
Matrix and tensor witnesses of hidden symmetry algebras
Sanjaye Ramgoolam, Lewis Sword
Permutation group algebras, and their generalizations called permutation centralizer algebras (PCAs), play a central role as hidden symmetries in the combinatorics of large gau…
SYM, (super)-polynomial rings and emergent quantum mechanical symmetries
Robert de Mello Koch, Sanjaye Ramgoolam
The structure of half-BPS representations of psu leads to the definition of a super-polynomial ring which admits a realisation of psu in terms…
Kronecker coefficients from algebras of bi-partite ribbon graphs
Joseph Ben Geloun, Sanjaye Ramgoolam
Bi-partite ribbon graphs arise in organising the large expansion of correlators in random matrix models and in the enumeration of observables in random tensor models. There is…
Permutation symmetry in large N Matrix Quantum Mechanics and Partition Algebras
George Barnes, Adrian Padellaro, Sanjaye Ramgoolam
We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size . We solve the general 11- parame…
Combinatoric topological string theories and group theory algorithms
Sanjaye Ramgoolam, Eric Sharpe
A number of finite algorithms for constructing representation theoretic data from group multiplications in a finite group G have recently been shown to be related to amplitudes for…
Higher dimensional CFTs as 2D conformally-equivariant topological field theories
Robert de Mello Koch, Sanjaye Ramgoolam
Two and three-point functions of primary fields in four dimensional CFT have a simple space-time dependences factored out from the combinatoric structure which enumerates the field…
Hidden symmetries and Large N factorisation for permutation invariant matrix observables
George Barnes, Adrian Padellaro, Sanjaye Ramgoolam
Permutation invariant polynomial functions of matrices have previously been studied as the observables in matrix models invariant under , the symmetric group of all permutatio…