Soliton Solutions of the N=2 Supersymmetric KP Equation

Abstract

The N=2 super-KP equation associated with nonstandard flows is bilinearized using the Hirota method and soliton solutions are obtained. The bilinearization has been done for component fields and its KdV limit is discussed by comparing the soliton solutions obtained by this procedure with those found from the N=1 superspace formalism. The equivalence of these two procedures in the KdV limit is observed.     

New Realization of N=2 Supersymmetric QuantumMechanics and Shape Invariance

The new supercharges are constructed and the weight function is defined to study the N=2 one-dimensional supersymmetric quantum mechanics. Several examples are discussed in the new realization.     

Matone's Relation ofN =2 Super Yang-Mills and Spectrum of Toda Chain

InN=2 super Yang-Mills theory, the Matone's relation relates instanton corrections of the prepotential to instanton corrections of scalar field condensation <
Trφ²>. This relation has been proved to hold for Omega deformed theories too, using localization method. In this paper, we first give a case study supporting the relation, which does not rely on the localization technique. Especially, we show that the magnetic expansion also satisfies a relation of Matone's type. Then we discuss implication of the relation for the spectrum of periodic Toda chain, in the context of recently proposed Nekrasov-Shatashvili scheme.     

N=2超对称量子力学的新实现和形状不变性

构造新的超荷和定义权重函数,并研究了N=2一维超对称量子力学.在新的实现中讨论了若干实例.     

Hidden Symmetries and Integrable Hierarchy of the $${\mathcal{N}}$$ = 4 Supersymmetric Yang-Mills Equations

We describe an infinite-dimensional algebra of hidden symmetries of supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite sequence of flows on the solution space of the SYM equations. The dependence of the SYM fields on the parameters along the flows can be recovered by solving the equations of the hierarchy. We embed the SYM equations in the infinite system of the hierarchy equations and show that this SYM hierarchy is associated with an infinite set of graded symmetries recursively generated from supertranslations. Presumably, the existence of such nonlocal symmetries underlies the observed integrable structures in quantum SYM theory. On leave from Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Russia. Address after October 1st, 2006: Theoretical Physics Group, The Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom.     

A Note on the Third Family of N=2 Supersymmetric KdV Hierarchies

Abstract

We propose a hamiltonian formulation of the N = 2 supersymmetric KP type hierarchy recently studied by Krivonos and Sorin. We obtain a quadratic hamiltonian structure which allows for several reductions of the KP type hierarchy. In particular, the third family of N = 2 KdV hierarchies is recovered. We also give an easy construction of Wronskian solutions of the KP and KdV type equations.     

Twisted N=2 Supersymmetry with Central Charge and Equivariant Cohomology

We present an equivariant extension of the Thom form with respect to a vector field action, in the framework of the Mathai-Quillen formalism. The associated Topological Quantum Field Theories correspond to twisted N=2 supersymmetric theories with a central charge. We analyze in detail two different cases: topological sigma models and non-abelian monopoles on four-manifolds. Received: 2 April 1996 / Accepted: 15 July 1996     

Seiberg-Witten/Whitham Equations and Instanton Corrections in N=2 Supersymmetric Yang-Mills Theory

We obtain the instanton correction recursion relations for the low energy effective prepotential in pure N=2 SU(n) supersymmetric Yang-Mills gauge theory from Whitham hierarchy and Seiberg-Witten/Whitham equations. These formulae provide us a powerful tool to calculate arbitrary order instanton corrections coefficients from the perturbative contributions of the effective prepotential in Seiberg-Witten gauge theory. We apply this idea to evaluate one- and two- order instanton corrections coefficients explicitly in SU(n) case in detail through the dynamical scale parameter expressed in terms of Riemann's theta-function.     

The (N=1) Supersymmetric Sine-Gordon model in two dimensions. II

In this second paper the technical part of the results about the SupersymmetricN=1 massless Sine-Gordon field theory, at finite (space) volume, is given. The proof that the theory exists and is analytic in the coupling constant and that, at finite (space) volume, its Witten index is 1, is, therefore, completed.     

The (N=1) Supersymmetric Sine-Gordon model in two dimensions. I

In this paper and its companion (II) we prove that the SupersymmetricN=1 massless Sine-Gordon field theory, at finite (space) volume, exists and is analytic in the coupling constant . Moreover at finite (space) volume is Witten index is=1.     

Fermionic flows and tau function of the N = (1|1) superconformal Toda lattice hierarchy

An infinite class of fermionic flows of the N = (1|1) superconformal Toda lattice hierarchy is constructed and their algebraic structure is studied. We completely solve the semi-infinite N = (1|1) Toda lattice and chain hierarchies and derive their tau functions, which may be relevant for building supersymmetric matrix models. Their bosonic limit is also discussed.     

Hierarchy of quark masses in the isotopic doublets in N=1 supergravity models

In the framework of some generic softly broken SUSY models we study the SU (2) × U(1) breaking by radiative corrections, starting with the Yukawa couplings which at the Planck scale M_P satisfy h^t = h^b. Physically acceptable solutions exist with the heirarchy of VEVs: ν₂/ν₁ ≈ m_t/m_b provided m_t ⩾ 50 GeV. When the SUSY breaking is driven only by the gaugino mass the solutions uniquely predict ν₂=O(10)ν₁ and the top mass in the range 50–65 GeV. Also, the mass ratio in the second quark generation can be accounted for.     

{\mathcal{N} = 2} Supersymmetric AdS4 Solutions of M-theory

We analyse the most general ${\mathcal{N} = 2}$ supersymmetric solutions of D = 11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold Y ₇. We show that the necessary and sufficient conditions for supersymmetry can be phrased in terms of a local SU(2)-structure on Y ₇. Solutions with non-zero M2-brane charge also admit a canonical contact structure, in terms of which many physical quantities can be expressed, including the free energy and the scaling dimensions of operators dual to supersymmetric wrapped M5-branes. We show that a special class of solutions is singled out by imposing an additional symmetry, for which the problem reduces to solving a second order non-linear ODE. As well as recovering a known class of solutions, that includes the IR fixed point of a mass deformation of the ABJM theory, we also find new solutions which are dual to cubic deformations. In particular, we find a new supersymmetric warped AdS₄ × S ⁷ solution with non-trivial four-form flux.     

Geometry of Real Forms of the Complex Neumann System

In the paper, we study real forms of the complex generic Neumann system. We prove that the real forms are completely integrable Hamiltonian systems. The complex Neumann system is an example of the more general Mumford system. The Mumford system is characterized by the Lax pair (L^?(λ), M^?(λ)) of 2 × 2 matrices, where and U^?(λ), V^?(λ), W^?(λ) are suitable polynomials. The topology of a regular level set of the moment map of a real form is determined by the positions of the roots of the suitable real form of U^?(λ), with respect to the position of the values of suitable parameters of the system. For two families of the real forms of the complex Neumann system, we describe the topology of the regular level set of the moment map. For one of these two families the level sets are noncompact.

In the paper, we also give the formula which provides the relation between two systems of the ?rst integrals in involution of the Neumann system. One of these systems is obtained from the Lax pair of the Mumford type, while the second is obtained from the Lax pair whose matrices are of dimension (n+1) × (n+1).     

On （2＋1）-Dimensional Non-isospectral Toda Lattice Hierarchy and Integrable Coupling System

By considering （2＋1）-dimensional non-isospectral discrete zero curvature equation, the （2＋1）-dimensional non-isospectral Toda lattice hierarchy is constructed in this article. It follows that some reductions of the （2＋1）- dimensional Toda lattice hierarchy are given. Finally, the （2＋1）-dimensional integrable coupling system of the Toda lattice hierarchy is obtained through enlarging spectral problem.     

Supersymmetric,regularization of one-loop Green's functions in N = 4 Yang-Mills theory

Supersymmetric dimensional regularization via dimensional reduction is used for explicit calculation of one-loop two-point Green's functions in an N = 4 supersymmetric Yang-Mills theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 74–79, June, 1989.In conclusion, the authors would like to thank Prof. I. V. Trutin for numerous invaluable discussions.     

N = 1 superstring in 2 + 2 dimensions

In this paper we construct a (2,2) dimensional string theory with manifest N = 1 spacetime supersymmetry. We use Berkovits' approach of augmenting the spacetime supercoordinates by the conjugate momenta for the fermionic variables. The worldsheet symmetry algebra is a twisted and truncated “small” N = 4 superconformal algebra. The realisation of the symmetry algebra is reducible with an infinite order of reducibility. We study the physical states of the theory by two different methods. In one of them, we identify a subset of irreducible constraints, which is by itself critical. We construct the BRST operator for the irreducible constraints, and study the cohomology and interactions. This method breaks the SO(2,2) spacetime symmetry of the original reducible theory. In another approach, we study the theory in a fully covariant manner, which involves the introduction of infinitely many ghosts for ghosts.