A supersymmetric matrix model: III. Hidden SUSY in statistical systems

Abstract

The Hamiltonian of a recently proposed supersymmetric matrix model has been shown to become block-diagonal in the large-N, infinite 't Hooft coupling limit. We show that (most of) these blocks can be mapped into seemingly non-supersymmetric $(1+1)$-dimensional statistical systems, thus implying non-trivial (and apparently yet-unknown) relations within their spectra. Furthermore, the ground states of XXZ-chains with an odd number of sites and asymmetry parameter $\Delta =-1/2$, objects of the much-discussed Razumov--Stroganov conjectures, turn out to be just the strong-coupling supersymmetric vacua of our matrix model.

18 pages, note and references added at the end

References in corpus (6)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Three-body local correlation function in the Lieb-Liniger model: bosonization approach
• Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain
• Planar Quantum Mechanics: an Intriguing Supersymmetric Example
• The q-deformed Bose gas: Integrability and thermodynamics
• A supersymmetric matrix model: II. Exploring higher-fermion-number sectors

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• Superfrustration of charge degrees of freedom
• Factorised solutions of Temperley-Lieb $q$KZ equations on a segment
• Loop formulation of supersymmetric Yang-Mills quantum mechanics
• The planar spectrum in U(N)-invariant quantum mechanics by Fock space methods: I. The bosonic case
• The number of gauge singlets in supersymmetric Yang-Mills quantum mechanics
• Solutions of D=2 supersymmetric Yang-Mills quantum mechanics with SU(N) gauge group
• Fock space methods and large N
• Symmetry classes of alternating sign matrices in the nineteen-vertex model
• Solving some gauge systems at infinite N
• On the supersymmetric vacua of the Veneziano-Wosiek model