Finite-dimensional algebras, gauge-string duality and thermodynamics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910011782856704 |
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| author | Ramgoolam, Sanjaye |
| author_facet | Ramgoolam, Sanjaye |
| contents | Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue systems using these algebras as state spaces, which provide efficient computational algorithms for the construction of orthogonal bases in the multi-matrix case. Algebraic counting formulae in matrix and tensor systems with $U(N)$ as well as $S_N$ symmetry have led to gauged quantum mechanical models which display a negative branch of specific heat capacity in the micro-canonical ensemble followed by positive specific heat capacity at larger energies measured by a polynomial degree parameter $n$. The negative branch is associated with near-exponential or factorial growth of degeneracies for $ n \gg 1$ in a region of large $N$ stability, while the positive branch occurs when the finite $N$ reduction of degrees of freedom takes over as $n$ becomes sufficiently large compared to $N$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_04845 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite-dimensional algebras, gauge-string duality and thermodynamics Ramgoolam, Sanjaye High Energy Physics - Theory Gauge-invariant polynomial functions of matrix and tensor variables capture combinatorial structures of gauge-string duality, which can be usefully organised using finite-dimensional associative algebras. I review recent work on eigenvalue systems using these algebras as state spaces, which provide efficient computational algorithms for the construction of orthogonal bases in the multi-matrix case. Algebraic counting formulae in matrix and tensor systems with $U(N)$ as well as $S_N$ symmetry have led to gauged quantum mechanical models which display a negative branch of specific heat capacity in the micro-canonical ensemble followed by positive specific heat capacity at larger energies measured by a polynomial degree parameter $n$. The negative branch is associated with near-exponential or factorial growth of degeneracies for $ n \gg 1$ in a region of large $N$ stability, while the positive branch occurs when the finite $N$ reduction of degrees of freedom takes over as $n$ becomes sufficiently large compared to $N$. |
| title | Finite-dimensional algebras, gauge-string duality and thermodynamics |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.04845 |