The soliton supermultiplet in 4 + 1 dimensions

We consider the SO(4) = SU(2) ? USp(2) Clifford algebra, obtained by the supersymmetry algebra for the N = 2 supersymmetric Yang-Mills theory in 4+1 dimensions, which, in the phase of unbroken gauge symmetry, has a topological charge as central charge. We find that, even if the Higgs mechanism is absent, the massive soliton supermultiplet contains the same number of states as the massless supermultiplet of elementary particles.     

A note on 1/4-BPS states

We study classical solutions of super Yang–Mills theories that are invariant under 1/4 of the supersymmetry generators. Expressions for the mass and electric charge of the configurations are derived as functions on the monopole moduli space. These functions also provide a method of determining the number of normalisable bosonic zero modes.     

Index theorems and supersymmetry in the soliton sector

For arbitrary two-dimensional supersymmetric theories with soliton solutions, we use the Callias-Bott-Seeley trace theorem to calculate the O(?) correction to the soliton mass. At the same order the Bogomolny bound is shown, by an explicit computation, to be saturated. The non-vanishing of the mass correction is traced to the existence of supersymmetry violating surface terms in the soliton lagrangian, while the saturation of the Bogomolny bound is a consequence of the absence of spontaneous breaking of $\text{N =}\text{1}\text{2}$ supersymmetry in a related lagrangian. We argue that this supersymmetry remains unbroken to all orders in perturbation theory. Topological arguments à la Witten are not able to exclude non-perturbative breaking.     

Supergravity as a gauge theory of supersymmetry

In a new approach to supergravity we consider the gauge theory of the 14-dimensional supersymmetry group. The theory is constructed from 14×4 gauge fields, 4 gauge fields being associated with each of the 14 generators of supersymmetry. The gauge fields corresponding to the 10 generators of the Poincaré subgroup are those normally associated with general relativity, and the gauge fields corresponding to the 4 generators of supersymmetry transformations are identified with a Rarita-Schwinger spinor. The transformation laws of the gauge fields and the Lagrangian of lowest degree are uniquely constructed from the supersymmetry algebra. The resulting action is shown to be invariant under these gauge transformations if the translation associated field strength vanishes. It is shown that the second-order form of the action, which is the same as that previously proposed, is invariant without constraint.     

On the supersymmetric solitons and monopoles

The basic results in a new trend in supersymmetry and soliton theory are presented. It is shown that the soliton expectation value of the energy operator is the mass of the soliton without quantum corrections. A new supersymmetric monopole model in three dimensions is constructed by generalization of the supersymmetric sine-Gordon model in one space dimension.     

ℤ n 3 -graded colored supersymmetry

We build generalizations of the Grassmann algebras from a few following simple assumptions: the algebras are graded, maximally symmetric and contain an ordinary Grassmann algebra as a subalgebra. These algebras are graded by and display surprising properties that indicate their possible application to the modeling of quark fields. We build the generalized supersymmetry generators based on these algebras and their derivation operators. These generators are cubic roots of the usual supersymmetry generators.     

Transformation properties of the supercurrent

It is shown that the spinor current, if correctly defined, belongs to a supermultiplet, together with the energy-momentum tensor and the axial-vector current. The transformation properties of this supermultiplet under both restricted and general supersymmetry transformations are given. The generators of special supersymmetry transformations can be obtained as first moments of the time component of the spinor current. The transformation laws of the supermultiplet containing the spinor current provide the local version of the supersymmetry algebra.     

Fermion zero modes and ‘hidden’ symmetry

The origin of the fermion zero modes in the soliton fields is investigated in 2- and 4-dimensional models and a connection is found with the existence of ‘hidden’ supersymmetry properties of the Lagrangians.     

Supersymmetric skyrmions in four dimensions

Possible topological solitons (skyrmions) of four-dimensional supersymmetric nonlinear σ-models are investigated. The requirements of supersymmetry limit our study to the CP¹ model. A stable soliton seems possible, but in the absence of a demonstrated lower-bound for the mass, the stability of the soliton is unproved. The semi-classical spectrum of the CP¹ skyrmion, as well as its supersymmetric extension, is studied.     

Observables in topological Yang-Mills theorieswith extended shift supersymmetry

We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Witten's equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator. Received: 8 March 2005, Published online: 21 October 2005 Supported in part by the Conselho Nacional de Desenvolvimento Científico e Tecnológico CNPq, Brazil     

Super-Kac-Moody algebras and supersymmetric 2d-free fermions

Explicit representations of super-Kac-Moody algebra are constructed in terms of 2d-free fermions which form a non-linear representation of supersymmetry with the fermions grouped with the generators of the algebra into superfields. It is shown how the most general construction of this type corresponds to homogeneous spacesG/H and how supersymmetry alone is responsible for that structure.This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contracts DE-AC03-76SF00098     

Lattice models with N=2 supersymmetry

We introduce lattice models with explicit N=2 supersymmetry. In these interacting models, the supersymmetry generators Q+/- yield the Hamiltonian H=(Q(+),Q(-)) on any graph. The degrees of freedom can be described as either fermions with hard cores, or as quantum dimers; the Hamiltonian of our simplest model contains a hopping term and a repulsive potential. We analyze these models using conformal field theory, the Bethe ansatz, and cohomology. The simplest model provides a manifestly supersymmetric lattice regulator for the supersymmetric point of the massless (1+1)-dimensional Thirring (Luttinger) model. Generalizations include a quantum monomer-dimer model on a two-leg ladder.     

D=1 chiral supersymmetry with a central charge

We analyse a model which provides a realisation of Witten'sD=0+1 supersymmetry extended by a central charge, which is interpreted as defining a superselection rule, and study the interactions of its superfields. At the same time, this model allows us to discuss some general properties of extended supersymmetry theories.     

Partially broken global supersymmetry and the superstring

We study the partial spontaneous breaking of a global supersymmetry algebra. A formalism developed by Volkov for nonlinearly realized spacetime symmetries is very useful. The case analyzed in detail is two-dimensional (2,2) supersymmetry with a central charge spontaneously broken to (0,2). This algebra, which is realized in supersymmetric Nielsen-Olesen strings, leads to the Green-Schwarz superstring action.     

一维介观结链中电荷孤子的控制

研究了一维介观结链中的电势分布随各岛上门电压和电子数分布的变化关系,并发现在一个岛上加一个门电压会产生一个静电势孤子.通过调节门电压可以较好地控制静电势孤子的形状及其位置,从而达到对电荷孤子的有效控制. 关键词： 电荷孤子 介观结 单电荷隧穿     

Complex solitary waves and soliton trains in KdV and mKdV equations

We demonstrate the existence of complex solitary wave and periodic solutions of theKorteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. The solutions ofthe KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under thesimultaneous actions of parity (??) and time-reversal (??) operations. The corresponding localized solitons arehydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishingintensity. The ????-odd complex soliton solution is shown to beiso-spectrally connected to the fundamental sech² solution through supersymmetry. Physically, thesecomplex solutions are analogous to the experimentally observed grey solitons of non-liner Schödinger equation, governing the dynamics of shallow waterwaves and hence may also find physical verification.     

Fluctuations of fractional charge in soliton anti-soliton systems

The total charge in a soliton-anti-soliton system has integer eigenvalues. However, when soliton-induced charge fractionization occurs, it is possible to make a Bogoliubov transformation on the eigenstates of the total charge, so that in the limit of infinite soliton anti-soliton separation., the transformed states become eigenstates of a charge operator suitably localized at the soliton. In the limit, the localized charge operator has fractional eigenvalues, without fluctuations.     

Tachyonic squarks in split supersymmetry

The decoupling of scalar particles in split supersymmetry makes the spectrum of squarks irrelevant for low energy processes. Nevertheless, the structure of the vacuum is sensitive to the spectrum of squarks, even when the supersymmetry breaking scale is large. In this Letter, we show that in certain regions of the parameter space, squarks could develop radiatively tachyonic masses, thus breaking electric charge and color. We discuss the constraints that follow from the requirement of charge and color conservation, and we comment on the implications for model building.     

Supersymmetric sound in condensed matter

The effect of a net conserved charge density is considered in supersymmetric relativistic field theories. If the charge is supersymmetric and if it distributes itself homogeneously, there appear both goldstino and Goldstone modes, associated with the spontaneously broken supersymmetry algebra.     

Nonsupersymmetric string solitons

We begin a search for nonsupersymmetric/supersymmetric dual string pairs by constructing candidate critical nonsupersymmetric strings as solitons in supersymmetric string theories. Using orbifold techniques, one can construct cosmic string solutions which lie in supersymmetric vacua but which do not fall in supermultiplets. We discuss two three-dimensional examples in detail. The effective worldsheet actions for the soliton strings have (0,2) and (1,1) supersymmetry and the correct numbers of massless bosons and fermions to be critical heterotic and type II strings, respectively.