Related papers: New insight into WDVV equation
Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus…
We survey a number of results regarding the representation theory of $W$-algebras and their connection with the resent development of the four dimensional $N=2$ superconformal field theories in physics.
The superfield formulation of two - dimensional $N=4$ Extended Supersymmetric Quantum Mechanics (SQM) is described. It is shown that corresponding classical Lagrangian describes the motion in the conformally flat metric with additional…
The Verlinde formula computes the dimension of certain vector spaces ("conformal blocks") associated to a Rational Conformal Field Theory. In this paper we show how this can be made rigorous for one particular such theory, the WZW model.…
N = 3 Weyl multiplet in four dimensions was first constructed in J van Muiden et al (2017) where the authors used the current multiplet approach to obtain the linearized transformation rules and completed the nonlinear variations using the…
We construct $N=4$ supersymmetric KdV equation as a hamiltonian flow on the $N=4\;SU(2)$ super Virasoro algebra. The $N=4$ KdV superfield, the hamiltonian and the related Poisson structure are concisely formulated in $1D \;N=4$ harmonic…
We derive a general theorem relating the energy and momentum with the velocity of any solitary wave solution of the generalized KdV equation in $N$-dimensions that follows from an action principle. Further, we show that our $N$-dimensional…
We discuss a quantum extension of the holographic RG flow equation obtained previously from the classical Hamiltonian constraint in the bulk AdS supergravity. The Wheeler-DeWitt equation is proposed to generate the extended RG flow and to…
Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried using both, the topological algebra and its central extension, which arise from the twisting of $N=2$ supersymmetry in four…
Based upon the general supercharges which involve not only generators C_j of the Clifford algebra C(4,0) with positive metric, but also operators of third order, C_j C_k C_l, the general form of N=4 supersymmetric quantum mechanics (SSQM),…
We showed in hep-th/0303210 that the Dijkgraaf-Vafa theory can be regarded as large-N reduction in the case of $\mathcal{N}=1$ supersymmetric U(N) gauge theories, with single adjoint matter. We generalize this to gauge theories with gauge…
We study four-point correlators in superconformal theories in various dimensions. We develop an efficient method to solve the superconformal Ward identities in Mellin space. For 4d $\mathcal{N}=4$ SYM and the 6d $\mathcal{N}=(2,0)$ theory,…
Abstract We present the construction of the first-order $D=4$, $\mathcal{N}=1$ supergravity action by gauging the Maxwell-Weyl superalgebra. The four-form lagrangian is constructed by using the curvatures of the algebra and the local scale…
Uniform estimates for the decay structure of the $n$-soliton solution of the Korteweg-deVries equation are obtained. The KdV equation, linearized at the $n$-soliton solution is investigated in a class $\WW$ consisting of sums of travelling…
We develop a unified framework for the design and analysis of high-order nonconforming virtual element methods for nonlinear fourth-order reaction--diffusion problems in two dimensions, with emphasis on clamped, Navier, and…
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann algorithm, formulated specially for multiple subdomains splitting for general parabolic and hyperbolic problems. This method is based on a non-overlapping spatial domain…
We study existence results for a fourth order problem describing single-component film models assuming initial data in Wiener spaces.
Supersymmetry of the Wess-Zumino (N=1, D=4) multiplet allows field equations that determine a larger class of geometries than the familiar Kahler manifolds, in which covariantly holomorphic vectors rather than a scalar superpotential…
Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant ``discrete quantum mechanical systems" are introduced and discussed in some detail. They arise in the problem of…
We provide evidence for the existence of a new strongly-coupled four dimensional $\mathcal{N}=2$ superconformal field theory arising as a non-trivial IR fixed point on the Coulomb branch of the mass-deformed superconformal Lagrangian theory…