Related papers: An Index for Superconformal Quantum Mechanics
We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all…
As shown by Witten the N=1 supersymmetric gauged WZW model based on a group G has an extended N=2 supersymmetry if the gauged subgroup H is so chosen that G/H is Kahler. We extend Witten's result and prove that the N=1 supersymmetric gauged…
We compute the Hilbert series of three-dimensional $\mathcal{N}=3$ quiver gauge theories by taking a specific limit of the superconformal index. Our approach introduces auxiliary fugacities associated with symmetries which, while not…
This article studies some features of quantum field theories with internal supersymmetry, focusing mainly on 2-dimensional non-linear sigma models which take values in a coset superspace. It is discussed how BRST operators from the target…
We present ${\cal N}{=}\,4$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds constructed within the Hamiltonian approach. The structure functions entering the supercharges and the Hamiltonian obey modified covariant…
We study the geometry of the gauged quiver quantum mechanics realizing $D(2,1;0)$ superconformal symmetry. These models arise as effective descriptions of multi-centered D-brane systems in type II Calabi-Yau compactifications, in the…
We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace both in the case where there are not central charges…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
We carry out a general analysis of the representations of the superconformal algebras OSp(8/4,R) and OSp(8*/2N) in terms of harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different…
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…
A novel approach is proposed to analyze a rather vast counter-rotating Hamiltonian interaction in the context of cavity quantum electrodynamics. The method relies upon the supersymmetric mapping of the corresponding rotating interaction and…
In this paper we explore the relation between conformal superalgebras with 64 supercharges and maximal supergravity theories in three, four and six dimensions using twistorial oscillator techniques. The massless fields of N=8 supergravity…
We study the superconformal index of 4d $\mathcal{N}=4$ $USp(2N_c)$ and $SO(N_c)$ SYM from a matrix model perspective. We focus on the Cardy-like limit of the index. Both in the symplectic and orthogonal case the index is dominated by a…
The new approach to quantum mechanical problems is proposed. Quantum states are represented in an algebraic program, by lists of variable length, while operators are well defined functions on these lists. Complete numerical solution of a…
Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation…
We compute the Witten index of the Berenstein-Maldacena-Nastase matrix quantum mechanics, which counts the number of ground states as well as the difference between the numbers of bosonic and fermionic BPS states with nonzero spins. The…
Using the harmonic superspace approach, we construct the three-dimensional N=4 supersymmetric quantum mechanics of the supermultiplet (3,4,1) coupled to an external SU(2) gauge field. The off-shell N=4 supersymmetry requires the gauge field…
The conformal symmetry SO(d,2) of the massless particle in d dimensions, or superconformal symmetry OSp(N|4), SU(2,2|N), OSp(8|N) of the superparticle in d=3,4,6 dimensions respectively, had been previously understood as the global Lorentz…
We propose an exactly-solvable model of the quantum oscillator on the class of K\"ahler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum…
The quantum nonrelativistic spin-1/2 planar systems in the presence of a perpendicular magnetic field are known to possess the N=2 supersymmetry. We consider such a system in the field of a magnetic vortex, and find that there are just two…