Related papers: Bosonic quantum integrable systems and gauge theor…
We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions…
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 introduce a variational approach for the Quantum Inverse Scattering Method to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake this in a manner which does not rely on any prior knowledge of integrability…
In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As…
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d $\mathcal{N} = 1$…
A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to…
We consider the superfield formulation of supersymmetric gauge and matter field theories on a three-dimensional sphere with rigid ${\cal N}=2$ supersymmetry, as well as with ${\cal N}> 2$. The construction is based on a supercoset…
We define a semi-Hopf algebra which is more general than a Hopf algebra. Then we construct the supersymmetry algebra via the adjoint action on this semi-Hopf algebra. As a result we have a supersymmetry theory with quantum gauge group,…
A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic…
We construct the general supersymmetry algebra via the adjoint action on a semi-Hopf algebra which has a more general structure than a Hopf algebra. As a result we have an extended supersymmetry theory with quantum gauge group, i.e.,…
We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin…
We consider the exact solution of a model of correlated electrons based on the superalgebra $Osp(2|2)$. The corresponding Bethe ansatz equations have an interesting form. We derive an expression for the ground state energy at half filling.…
The supersymmetric generalization of a recently proposed Abelian axial gauge model with antisymmetric tensor matter fields is presented.
A unified integrable system, generating a new series of interacting matter-radiation models with interatomic coupling and different atomic frequencies, is constructed and exactly solved through algebraic Bethe ansatz. Novel features in Rabi…
We formulate in terms of the quantum inverse scattering method the algebraic Bethe ansatz solution of the one-dimensional Hubbard model. The method developed is based on a new set of commutation relations which encodes a hidden symmetry of…
We construct a supermatrix model whose classical background gives two-dimensional noncommutative supersphere. Quantum fluctuations around it give the supersymmetric gauge theories on the fuzzy supersphere constructed by Klimcik. This model…
In this paper we propose a simple method for building exactly solvable multi-parameter spectral equations which in turn can be used for constructing completely integrable and exactly solvable quantum systems. The method is based on the use…
We study some graded geometric constructions appearing naturally in the context of gauge theories. Inspired by a known relation of gauging with equivariant cohomology we generalize the latter notion to the case of arbitrary Q-manifolds…
We study an integrable conformal OSp(2m + 2|2m) supercoset model as an analog to the AdS_5 X S^5 superstring world-sheet theory. Using the known S-matrix for this system, we obtain integral equations for states of large particle density in…
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…