Related papers: Quantum integrability and supersymmetric vacua
We discuss a number of exact results in N=1 supersymmetric field theories. We review the results obtained by Seiberg in Super-Yang-Mills (SYM) theories with matter in fundamental representation. We then consider Kutasov-type SYM theories,…
We continue our work on the study of spherically symmetric loop quantum gravity coupled to two spherically symmetric scalar fields, one that acts as a clock. As a consequence of the presence of the latter, we can define a true Hamiltonian…
We consider bosonized $QCD_2$, and prove that after rewritting the theory in terms of gauge invariant fields, there exists an integrability condition valid for the quantum theory as well. Furthermore, performing a duality type…
Recently a significant progress in matching the anomalous dimensions of certain class of operators in N=4 SYM theory and rotating strings was made. The correspondence was established mainly using Bethe ansatz technique applied to the spin s…
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution…
We demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting N = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic…
The form of the spectral curve for $4d$ $N=2$ supersymmetric Yang-Mills theory with matter fields in the fundamental representation of the gauge group suggests that its $1d$ integrable counterpart should be looked for among (inhomogeneous)…
We consider a non-supersymmetric example of the AdS/CFT duality which generalizes the supersymmetric exactly marginal deformation constructed in hep-th/0502086. The string theory background we use was found in hep-th/0503201 from the AdS_5…
We consider the harmonic-superspace ($HS$) system of equations that contains superfield $SYM^1_6$ constraints and equations of motion. A dynamical equation in the special $A$-frame is equivalent to the zero-curvature equation corresponding…
In this paper the quantum integrals of the Hamiltonian of the quantum many-body problem with the interaction potential K/sinh^2(x) (Sutherland operator) are constructed as images of higher Casimirs of the Lie algebra gl(N) under a certain…
The strongly coupled vacua of an N=1 supersymmetric gauge theory can be described by imposing quantization conditions on the periods of the gauge theory resolvent, or equivalently by imposing factorization conditions on the associated N=2…
We extend the formalism of Hamiltonian string bit models of quantum gravity type in two spacetime dimensions to include couplings to particles. We find that the single-particle closed and open universe models respectively behave like empty…
We consider quantum spin chains and their translationally invariant pure states. We prove Haag duality for quasilocal observables localized in semi-infinite intervals when the von Neumann algebras generated by observables localized in these…
The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theories with matter is analysed as an isomonodromy problem. We show that the holomorphic section describing the effective action can be deformed by moving its singularities on…
We study the effective superpotential of N=1 supersymmetric gauge theories with a mass gap, whose analytic properties are encoded in an algebraic curve. We propose that the degree of the curve equals the number of semiclassical branches of…
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components…
We demonstrate the existence of a novel set of discrete symmetries in the context of N = 2 supersymmetric (SUSY) quantum mechanical model with a potential function f(x) that is a generalization of the potential of the 1D SUSY harmonic…
In pure N=1 supersymmetric Yang-Mills with gauge group SU(N), the domain walls which separate the N vacua have been argued, on the basis of string theory realizations, to be D-branes for the confining string. In a certain limit, this means…
We prove a `Whitney' presentation, and a `Coulomb branch' presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm{Gr}(k;n)$, inspired from physics, and stated in an earlier paper. The first presentation…
In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted…