Hidden N=(2|2) supersymmetry of the N=(1|1) supersymmetric Toda lattice hierarchy
An N=(2|2) superfield formulation of the N=(1|1) supersymmetric Toda lattice hierarchy is proposed, and its five real forms are presented.
nlin.SI↗
arXiv subjects
Olaf Lechtenfeld
Publications and source records attributed to Olaf Lechtenfeld.
Open N=2 strings in a B-field background and noncommutative self-dual Yang-Mills
In the presence of D-branes, fermionic N=2 strings in 2+2 dimensions can be coupled to a K"ahler NS-NS two-form B. We present the corresponding action which produces N=2 supersymmetric boundary conditions and discuss the Seiberg-Witten zero-slope limit. After recalling the constraints on the Chan-Paton gauge group, we demonstrate for U(n) groups that the open N=2 string with a nonzero B-field coincides on tree level with noncommutative self-dual Yang-Mills. Several misconceptions of hep-th/0011206 are corrected.
hep-th↗
Real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy in real N=1 and twisted N=2 superspaces
Three nonequivalent real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy (solv-int/9907021) in real N=1 superspace are presented. It is demonstrated that they possess a global twisted N=2 supersymmetry. We discuss a new superfield basis in which the supersymmetry transformations are local. Furthermore, a representation of this hierarchy is given in terms of two twisted chiral N=2 superfields. The relations to the s-Toda hierarchy by H. Aratyn, E. Nissimov and S. Pacheva (solv-int/9801021) as well as to the modified and derivative NLS hierarchies are established.
solv-int↗
On the Integrability of Covariant Field Theory for Open N=2 Strings
We discuss the integrability of the Berkovits-Siegel open string field equations and derive an infinite set of their non-local (solution-generating) symmetries. The string field equations are embedded in an infinite system of overdetermined equations (BS hierarchy) associated with hidden string symmetries. The latter enforce the vanishing of most scattering amplitudes for the open N=2 string.
hep-th↗
N=2 Quantum String Scattering
We calculate the genus-one three- and four-point amplitudes in the 2+2 dimensional closed N=(2,2) worldsheet supersymmetric string within the RNS formulation. Vertex operators are redefined with the incorporation of spinor helicity techniques, and the quantum scattering is shown to be manifestly gauge and Lorentz invariant after normalizing the string states. The continuous spin structure summation over the monodromies of the worldsheet fermions is carried out explicitly, and the field-theory limit is extracted. The amplitude in this limit is shown to be the maximally helicity violating amplitude in pure gravity evaluated in a two-dimensional setting, which vanishes, unlike the four-dimensional result. The vanishing of the genus-one N=2 closed string amplitude is related to the absence of one-loop divergences in dimensionally regulated IIB supergravity. Comparisons and contrasts between self-dual field theory and the N=2 string theory are made at the quantum level; they have different S-matrices. Finally, we point to further relations with self-dual field theory and two-dimensional models.
hep-th↗
Mathematics and Physics of N=2 Strings
Open and closed strings with two worldsheet supersymmetries in 2+2 dimensional spacetime are reviewed in the NSR formulation. I briefly discuss their quantization, mutual and self-interactions, classical spacetime dynamics and interpretation in terms of self-dual Yang-Mills and gravity. A stringy origin of the infinite self-dual gravity hierarchy is presented. An outlook to the loop level concludes.
hep-th↗
Closed N=2 Strings: Picture-Changing, Hidden Symmetries and SDG Hierarchy
We study the action of picture-changing and spectral flow operators on a ground ring of ghost number zero operators in the chiral BRST cohomology of the closed N=2 string and describe an infinite set of symmetry charges acting on physical states. The transformations of physical string states are compared with symmetries of self-dual gravity which is the effective field theory of the closed N=2 string. We derive all infinitesimal symmetries of the self-dual gravity equations in 2+2 dimensional spacetime and introduce an infinite hierarchy of commuting flows on the moduli space of self-dual metrics. The dependence on moduli parameters can be recovered by solving the equations of the SDG hierarchy associated with an infinite set of abelian symmetries generated recursively from translations. These non-local abelian symmetries are shown to coincide with the hidden abelian string symmetries responsible for the vanishing of most scattering amplitudes. Therefore, N=2 string theory "predicts" not only self-dual gravity but also the SDG hierarchy.
hep-th↗
Ward identities and the vanishing theorem for loop amplitudes of the closed N=2 string
The existence of a ground ring of ghost number zero operators in the chiral BRST cohomology of the N=2 string is used to derive an infinite set of Ward identities for the closed-string scattering amplitudes at arbitrary genus. These identities are sufficient to rederive the well known vanishing theorem for loop amplitudes with more than three external legs.
hep-th↗
Supersymmetric KP hierarchy in N=1 superspace and its N=2 reductions
A wide class of N=2 reductions of the supersymmetric KP hierarchy in N=1 superspace is described. This class includes a new N=2 supersymmetric generalization of the Toda chain hierarchy. The Lax pair representations of the bosonic and fermionic flows, local and nonlocal Hamiltonians, finite and infinite discrete symmetries, first two Hamiltonian structures and the recursion operator of this hierarchy are constructed. Its secondary reduction to new N=2 supersymmetric modified KdV hierarchy is discussed.
solv-int↗
Towards a stringy extension of self-dual super Yang-Mills
Motivated by the search for a space-time supersymmetric extension of the N=2 string, we construct a particle model which, upon quantization, describes (abelian) self-dual super Yang-Mills in 2+2 dimensions. The local symmetries of the theory are shown to involve both world-line supersymmetry and kappa symmetry.
hep-th↗
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.
solv-int↗
Non-local symmetries of the closed N=2 string
By carefully analysing the picture-dependence of the BRST cohomology an infinite set of symmetry charges of the closed N=2 string is identified. The transformation laws of the physical vertex operators are shown to coincide with the linearised non-local symmetries of the Plebanski equation (which is the effective field theory of the closed N=2 string). Moreover, the corresponding Ward identities are powerful enough to allow for a rederivation of the well known vanishing theorem for the tree-level correlation functions with more than three external legs.
hep-th↗
Manifestly invariant actions for harmonic self-dual gauge theory
We discuss alternative descriptions of four-dimensional self-dual Yang-Mills fields in harmonic space with additional commuting spinor coordinates. In particular, the linear analyticity equation and nonlinear covariant harmonic-field equations are studied. A covariant harmonic field can be treated as an infinite set of ordinary four-dimensional fields with higher spins. We analyze different constructions of invariant harmonic-field actions corresponding to the self-dual harmonic equations.
hep-th↗
String-induced Yang-Mills coupling to self-dual gravity
By considering N=2 string amplitudes we determine the (2+2)-dimensional target space action for the physical degrees of freedom: self-dual gravity and self-dual Yang-Mills, together with their respective infinite towers of higher-spin inequivalent picture states. Novel `stringy' couplings amongst these fields are essential ingredients of an action principle for the effective target space field theory. We discuss the covariant description of this theory in terms of self-dual fields on a hyperspace parametrised by the target space coordinate and a commuting chiral spinor.
hep-th↗
Extended Self-Dual Yang-Mills from the N=2 String
We show that the physical degrees of freedom of the critical open string with N=2 superconformal symmetry on the worldsheet are described by a self-dual Yang-Mills field on a hyperspace parametrised by the coordinates of the target space R^{2,2} together with a commuting chiral spinor. A prepotential for the self-dual connection in the hyperspace generates the infinite tower of physical fields corresponding to the inequivalent pictures or spinor ghost vacua of this string. An action is presented for this tower, which describes consistent interactions amongst fields of arbitrarily high spin. An interesting truncation to a theory of five fields is seen to have no graphs of two or more loops.
hep-th↗
Scalar Deformations of Schwarzschild Holes and Their Stability
We construct two solutions of the minimally coupled Einstein-scalar field equations, representing regular deformations of Schwarzschild black holes by a self-interacting, static, scalar field. One solution features an exponentially decaying scalar field and a triple-well interaction potential; the other one is completely analytic and sprouts Coulomb-like scalar hair. Both evade the no-hair theorem by having partially negative potential, in conflict with the dominant energy condition. The linear perturbation theory around such backgrounds is developed in general, and yields stability criteria in terms of effective potentials for an analog Schrödinger problem. We can test for more than half of the perturbation modes, and our solutions prove to be stable against those.
gr-qc↗
On the Self-Dual Geometry of N=2 Strings
We discuss the precise relation of the open N=2 string to a self-dual Yang-Mills (SDYM) system in 2+2 dimensions. In particular, we review the description of the string target space action in terms of SDYM in a ``picture hyperspace'' parametrised by the standard vectorial R^{2,2} coordinate together with a commuting spinor of SO(2,2). The component form contains an infinite tower of prepotentials coupled to the one representing the SDYM degree of freedom. The truncation to five fields yields a novel one-loop exact lagrangean field theory.
hep-th↗
Chiral BRST Cohomology of N=2 Strings at Arbitrary Ghost and Picture Number
We compute the BRST cohomology of the holomorphic part of the N=2 string at arbitrary ghost and picture number. We confirm the expectation that the relative cohomology at non-zero momentum consists of a single massless state in each picture. The absolute cohomology is obtained by an independent method based on homological algebra. For vanishing momentum, the relative and absolute cohomologies both display a picture dependence -- a phenomenon discovered recently also in the relative Ramond sector of N=1 strings by Berkovits and Zwiebach.
hep-th↗