Minimal bosonization of double-graded quantum mechanics

The superalgebra of [Formula: see text]-graded supersymmetric quantum mechanics is shown to be realizable in terms of a single bosonic degree of freedom. Such an approach is directly inspired by a description of the corresponding [Formula: see text]-graded superalgebra in the framework of a Calogero–Vasiliev algebra or, more generally, of a generalized deformed oscillator algebra. In the case of the [Formula: see text]-graded superalgebra, the central element [Formula: see text] has the property of distinguishing between degenerate eigenstates of the Hamiltonian.

SUSY coherent states and enhanced canonical quantizations for Pauli model

In this paper, we study coherent states for a quantum Pauli model through supersymmetric quantum mechanics (SUSYQM) method. From the point of view of canonical quantization, the construction of these coherent states is based on the very important differential operators in SUSYQM call factorization operators. The connection between classical and quantum theory is given by using the geometric properties of these states.

Local G2-manifolds, Higgs bundles and a colored quantum mechanics

M-theory on local G2-manifolds engineers 4d minimally supersymmetric gauge theories. We consider ALE-fibered G2-manifolds and study the 4d physics from the view point of a partially twisted 7d supersymmetric Yang-Mills theory and its Higgs bundle. Euclidean M2-brane instantons descend to non-perturbative effects of the 7d supersymmetric Yang-Mills theory, which are found to be in one to one correspondence with the instantons of a colored supersymmetric quantum mechanics. We compute the contributions of M2-brane instantons to the 4d superpotential in the effective 7d description via localization in the colored quantum mechanics. Further we consider non-split Higgs bundles and analyze their 4d spectrum.

ABCD of ’t Hooft operators

We compute by supersymmetric localization the expectation values of half-BPS ’t Hooft line operators in $$ \mathcal{N} $$ N = 2 U(N ), SO(N ) and USp(N ) gauge theories on S1 × ℝ3 with an Ω-deformation. We evaluate the non-perturbative contributions due to monopole screening by calculating the supersymmetric indices of the corresponding supersymmetric quantum mechanics, which we obtain by realizing the gauge theories and the ’t Hooft operators using branes and orientifolds in type II string theories.