Related papers: Second Hopf map and supersymmetric mechanics with …
We study rigid surface operators in the $N=4$ supersymmetric Yang-Mills theories with gauge groups $SO(n)$ and $Sp(2n)$. Using maps $X_S$ and $Y_S$ between these two theories, Wyllard made explicit proposals for how the $S$-duality map…
We construct a simple Lorentz-invariant action for maximally supersymmetric self-dual Yang-Mills theory that manifests colour-kinematics duality. We also show that this action double copies to a known action for maximally supersymmetric…
The general features of the degeneracy structure of ($p=2$) parasupersymmetric quantum mechanics are employed to yield a classification scheme for the form of the parasupersymmetric Hamiltonians. The method is applied to parasupersymmetric…
We consider the light-cone (LC) gauge and LC quantization of the dimensional reduction of super Yang Mills theory from four to two dimensions. After integrating out all unphysical degrees of freedom, the non-local LC Hamiltonian exhibits an…
We present a novel $\mathcal{N} = 2 $ $\mathbb{Z}_2^2$-graded supersymmetric quantum mechanics ($\mathbb{Z}_2^2$-SQM) which has different features from those introduced so far. It is a two-dimensional (two-particle) system and is the first…
Using a complex deformation q=exp(is) of su(2) we obtain extensions of the finite-dimensional representations towards the infinite-dimensional ones. A generalised q-deformation of su(2), as a Hopf algebra is introduced. We present the…
New gaugings of four dimensional N=8 supergravity are constructed, including one which has a Minkowski space vacuum that preserves N=2 supersymmetry and in which the gauge group is broken to $SU(3)xU(1)^2$. Previous gaugings used the form…
The SU(2) collective coordinates expansion of the Born-Infeld\break Skyrmion Lagrangian is performed. The classical Hamiltonian is computed from this special Lagrangian in approximative way: it is derived from the expansion of this…
Energy eigenstates for N=2 supersymmetric gauged quantum mechanics are found for the gauges groups SU(n) and U(n). The analysis is aided by the existence of an infinite number of conserved operators. The spectum is continuous. Perturbative…
We discuss 4D N=2 non-abelian gauge theories where one supersymmetry is preserved while the other one is spontaneously broken and non-linearly realized. The goldstino resides in a Maxwell multiplet of the Bagger-Galperin type. We introduce…
We construct a supersymmetric version of instanton operators in five-dimensional Yang-Mills theories. This is possible by considering a five-dimensional generalization of the familiar four-dimensional topologically twisted theory, where the…
The new method of solving quantum mechanical problems is proposed. The finite, i.e. cut off, Hilbert space is algebraically implemented in the computer code with states represented by lists of variable length. Complete numerical solution of…
We propose Lagrangian and Hamiltonian formulations of a N=4 supersymmetric three-dimensional isospin-carrying particle moving in the non-Abelian field of a Wu-Yang monopole and in some specific scalar potential. This additional potential is…
Irreducible gauge theories in both the Lagrangian and Hamiltonian versions of the Sp(2)-covariant quantization method are studied. Solutions to generating equations are obtained in the form of expansions in power series of ghost and…
Twisted Hopf algebra $sl_\xi(2)$ gives rise to a deformation of the Yangian ${\cal Y}(sl(2))$. The corresponding deformations of the integrable XXX-spin chain and the Gaudin model are discussed.
We consider the description of second-class constraints in a Lagrangian path integral associated with a higher-order $\Delta$-operator. Based on two conjugate higher-order $\Delta$-operators, we also propose a Lagrangian path integral with…
The spectrum of IIB supergravity on AdS${}_5 \times S^5$ contains a number of bound states described by long double-trace multiplets in $\mathcal{N}=4$ super Yang-Mills theory at large 't Hooft coupling. At large $N$ these states are…
We propose a natural framework of SU(5) supersymmetric grand unified theory with the minimal particle contents, which does not contain dimension five proton decay operators. The suitable fermion mass hierarchy can be reproduced by higher…
We present maximal supergravity in two dimensions with gauge group SO(9). The construction is based on selecting the proper embedding of the gauge group into the infinite-dimensional symmetry group of the ungauged theory. The bosonic part…
Beta-functions are derived for the flow of N=2 SUSY SU(2) Yang-Mills in 4-dimensions with massless matter multiplets in the fundamental representation of the gauge group. The beta-functions represent the flow of the couplings as the VEV of…