Related papers: $\mathcal{N}=2$ Double graded supersymmetric quant…
We investigate supersymmetry in one-dimensional quantum mechanics with point interactions. We clarify a class of point interactions compatible with supersymmetry and present N=2 supersymmetric models on a circle with two point interactions…
We introduce a new kind of non-relativistic ${\cal N}{=}\,8$ supersymmetric mechanics, associated with worldline realizations of the supergroup $SU(2|2)$ treated as a deformation of flat ${\cal N}{=}\,8$, $d{=}1$ supersymmetry. Various…
Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the $\mathcal{N}=1$ Super-Yang-Mills (SYM) theory with gauge…
We revisit the novel symmetries in $\mathcal{N}$ = 2 supersymmetric (SUSY) quantum mechanical (QM) models by considering specific examples of coupled systems. Further, we extend our analysis to a general case and list out all the novel…
In the previous paper arXiv:2003.06470 we introduced the notion of ${\mathbb Z}_2\times{\mathbb Z}_2$-graded classical mechanics and presented a general framework to construct, in the Lagrangian setting, the worldline sigma models invariant…
Irreducible representations (irreps) of $\mathbb{Z}_2^2$-graded supersymmetry algebra of ${\cal N}=2$ are obtained by the method of induced representation and they are used to derive $\mathbb{Z}_2^2$-graded supersymmetric classical actions.…
We realize off-shell, local and gauge invariant $N=8$ supergravity in $D=4$, to cubic order in fields, as the double copy of $N=4$ super Yang-Mills theory (SYM). Employing the homotopy algebra approach, we show that, thanks to a redundant…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
We present massive N=2 supergravity with SO(2)-gauging in nine-dimensions by direct construction. A full lagrangian and transformation rules are fixed, respectively up to quartic and quadratic fermion terms. Corresponding to the generalized…
A $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalisation of the quantum superplane is proposed and studied. We construct a bicovariant calculus on what we shall refer to as the \emph{double-graded quantum superplane}. The commutation…
A classical (or quantum) superintegrable system on an n-dimensional Riemannian manifold is an integrable Hamiltonian system with potential that admits 2n-1 functionally independent constants of the motion that are polynomial in the momenta,…
We study quantum systems with even numbers N of levels that are completely state-controlled by unitary transformations generated by Lie algebras isomorphic to sp(N) of dimension N(N+1)/2. These Lie algebras are smaller than the respective…
We show that in many cases nontrivial and complicated supersymmetric quantum mechanical (SQM) models can be obtained from the simple model describing free dynamics in flat complex space by two operations: (i) Hamiltonian reduction and (ii)…
In Physics and in Mathematics $\mathbb{Z}_2^n$-gradings, $n \geq 2$, do appear quite frequently. The corresponding sign rules are determined by the `scalar product' of the involved $\mathbb{Z}_2^n$-degrees. The present paper is the first of…
We discuss an N=2 quantum mechanics with or without a central charge. A representation is constructed with the number of bosonic degrees of freedom less that one half of the fermionic degrees of freedom. We suggest a systematic method of…
The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical)…
Links between supersymmetric classical and quantum mechanics are explored. Diagrammatic representations for \hbar-expansions of norms of ground states are provided. The WKB spectra of supersymmetric non harmonic oscillators are found.
We formulate N-fold supersymmetry in quantum mechanical systems with reflection operators. As in the cases of other systems, they possess the two significant characters of N-fold supersymmetry, namely, almost isospectrality and weak…
We construct an $\mathcal{N}=2$ supersymmetric gauged quantum mechanics, by starting from the 3d Chern-Simons-matter theory holographically dual to massive Type IIA string theory on AdS$_4 \times S^6$, and Kaluza-Klein reducing on $S^2$…
We consider specific examples of $\mathcal{N}$ = 2 supersymmetric quantum mechanical models and list out all the novel symmetries. In each case, we show the existence of two sets of discrete symmetries that correspond to the Hodge duality…