Related papers: $\mathcal{N}=2$ supersymmetry and anisotropic scal…
We study a 5d gravity theory with a warped metric and show that two N = 2 supersymmetric quantum-mechanical systems are hidden in the 4d spectrum. The supersymmetry can be regarded as a remnant of higher-dimensional general coordinate…
S-dualities in scale invariant N=2 supersymmetric field theories are derived by embedding those theories in asymptotically free N=2 theories with higher rank gauge groups. S-duality transformations on the coupling of the scale invariant…
We study four dimensional $N=2$ supersymmetric gauge theories with matter multiplets. For all such models for which the gauge group is $SU(2)$, we derive the exact metric on the moduli space of quantum vacua and the exact spectrum of the…
A minimal supersymmetric standard model on noncommutative space-time (NC MSSM) is proposed. The model fulfils the requirements of noncommutative gauge invariance and absence of anomaly. The existence of supersymmetry with a scale of its…
The classical action of a two dimensional N=2 supersymmetric theory, characterized by a general K\"{a}hler potential, is written down on a non(anti)commutative superspace. The action has a power series expansion in terms of the determinant…
{}From the one-loop effective potential for a gas of non-relativistic bosons in two spatial dimensions interacting via a delta-function potential at zero-temperature and finite chemical potential, the anomaly of the energy-momentum tensor…
A brief review of the harmonic superspace approach to the construction of $\mathcal{N}=2$ supersymmetric higher spin theories is given. We define off-shell analytic harmonic gauge potentials of $\mathcal{N}=2$ supersymmetric higher-spin…
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…
We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…
Supersymmetric quantum mechanics (SUSY QM) is a powerful tool for generating new potentials with known spectra departing from an initial solvable one. In these lecture notes we will present some general formulas concerning SUSY QM of first…
In this paper we consider gauged N=2 supergravities which arise in the low-energy limit of type II string theories and study examples which exhibit spontaneous partial supersymmetry breaking. For the quantum STU model we derive the scalar…
We discuss supersymmetric quantum mechanical models with periodic potentials. The important new feature is that it is possible for both isospectral potentials to support zero modes, in contrast to the standard nonperiodic case where either…
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 perform the characterization program for the supersymmetric configurations and solutions of the $\mathcal{N}=1$, $d=5$ Supergravity Theory coupled to an arbitrary number of vectors, tensors and hypermultiplets and with general…
In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, the action can be invariant under change of…
The interplay between supersymmetry and classical and quantum computation is discussed. First, it is shown that the problem of computing the Witten index of $\mathcal N \leq 2$ quantum mechanical systems is $\#P$-complete and therefore…
Supersymmetric quantum mechanics is formulated on a two dimensional noncommutative plane and applied to the supersymmetric harmonic oscillator. We find that the ordinary commutative supersymmetry is partially broken and only half of the…
Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is…
We present two generic classes of supersymmetric solutions of N=2, d=4 supergravity coupled to non-Abelian vector supermultiplets with a gauge group that includes an SU(2) factor. The first class consists of embeddings of the 't…
It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be…