Related papers: Harmonic Superfields in N=4 Supersymmetric Quantum…
The kinematical and dynamical symmetries of equations describing the time evolution of quantum systems like the supersymmetric harmonic oscillator in one space dimension and the interaction of a non-relativistic spin one-half particle in a…
We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is…
Using the superfield gauging procedure, we construct new ${\cal N}\,{=}\,2$ and ${\cal N}\,{=}\,4$ superfield systems that generalize Calogero models. In the bosonic limit, these systems yield rational Calogero models and hyperbolic…
The study of spontaneous supersymmetry breaking (SSB) on the lattice is obstructed by a severe sign problem. Quantum computing provides a promising alternative approach. In particular, properties of supersymmetry relate SSB to the…
We study the quantum structure of four-dimensional ${\cal N}=2$ superfield sigma-model formulated in harmonic superspace in terms of the omega-hypermultiplet superfield $\omega$. The model is described by harmonic superfield sigma-model…
Recent papers have established the relationship between projective superspace and a complexified version of harmonic superspace. We extend this construction to the case of general nonlinear sigma models in both frameworks. Using an analogy…
In this set of five lectures we present a basic toolbox to discuss the dynamics of four dimensional supersymmetric quantum field theories. In particular we overview the program of geometrically engineering the four dimensional…
The perspectives of numerical simulations in supersymmetric quantum field theories with vector-like gauge symmetries are discussed. A numerical simulation algorithm for SU(2) gauge theory with gluinos is studied and the first results on the…
In the previous works, we proposed the stochastic quantization method (SQM) approach to N=1 supersymmetric Yang-Mills theory (SSYM). In four dimensions, in particular, we obtained the superfield Langevin equation and the corresponding…
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 review a performance of Fock space methods in calculating spectra of a range of supersymmetric models with gauge symmetry. Examples include: a) SU(2) Supersymmetric Yang Mills Quantum Mechanics in four euclidean dimensions, b) Quantum…
We study the $N=1$ supersymmetric $G_2$ gauge theories with $N_f$ flavors of quarks in the fundamental vector representation. We find dynamically generated superpotentials, smooth quantum moduli space, quantum moduli space with additional…
We present the description in central charge superspace of N=4 supergravity with antisymmetric tensor coupled to an arbitrary number of abelian vector multiplets. All the gauge vectors of the coupled system are treated on the same footing…
Various applications of quantum algebraic techniques in nuclear structure physics, such as the su$_q$(2) rotator model and its extensions, the use of deformed bosons in the description of pairing correlations, and the construction of…
Starting from the most general harmonic superspace action of self-interacting Q^+ hypermultiplets in the background of N=2 conformal supergravity, we derive the general action for the bosonic sigma model with a generic 4n dimensional…
The multiphoton algebras for one-dimensional Hamiltonians with infinite discrete spectrum, and for their associated kth-order SUSY partners are studied. In both cases, such an algebra is generated by the multiphoton annihilation and…
We develop classical globally supersymmetric theories. As much as possible, we treat various dimensions and various amounts of supersymmetry in a uniform manner. We discuss theories both in components and in superspace. Throughout we…
This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries.…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
The progress brought to the study of chiral fermions and gauge theories by quantization methods with a bulk time suggests their usefulness in supersymmetric theories. Using superspace methods, we show how an explicitly supersymmetric…