RUI: Applications of Supersymmetry to Quantum Mechanics

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Abstract PI:Donald Spector Institution: Hobart and William Smith College PHY 0457048 TITLE RUI: Applications of Supersymmetry to Quantum Mechanics The PI will continue his ongoing investigation of supersymmetric quantum mechanics with a central charge. He will explore the properties necessary for such systems to exhibit target space dualities, extending his previous work by incorporating chiral superfields, new target spacemanifolds, and central charges that depend on fermionic fields. This study of the relations among superalgebras, central charges, and dualities in a streamlined setting will provide insight into the behavior of field theories and string theory. Shape invariance, a powerful technique for understanding exactly soluble systems, has beens shown by the PI to have a BPS (Bogomol?nyi-Prasad-Sommerfield) formulation. Based on this and the established connection between BPS phenomena and topological solitons, the PI will identify specific models in which shape invariance emerges in the presence of a topologically non-trivial background, leading to a geometrical interpretation of shape invariance and the identification of new shape invariant models.. He will extend from one to higher dimensions the use of partial supersymmetry to find asymptotic energy level distributions of quantum Hamiltonians. This should shed light on conjectures in quantum chaos regarding the statistics of energy levels in two-dimensional systems.