Green-Schwarz Superstring Research Articles

A new sigma model action for the four-dimensional Green-Schwarz heterotic superstring

The sigma model action described in this paper differs in four important features from the usual sigma model action for the four-dimensional Green-Schwarz superstring in a massless background. Firstly, the action is constructed on an N = (2, 0) super-worldsheet using a Kähler potential and a Ogievetsky-Sokatchev constraint; secondly, the target-space background fields are unconstrained; thirdly, the target-space dilaton couples to the two-dimensional curvative; and fourthly, the action reduces in a flat background to a free-field action. A conjecture is made for generalizing this N = (2, 0) sigma model action to the ten-dimensional Green-Schwarz heterotic superstring in a manner that preserves these four new features.

Calculation of Green-Schwarz superstring amplitudes using the N = 2 twistor-string formalism

The free-field N = 2 twistor-string action for the ten-dimensional Green-Schwarz superstring is quantized using standard BRST methods. Unlike the light-cone and semi-light-cone gauge-fixed Green-Schwarz actions, the twistor-string action does not require interaction-point operators at the zeroes of the light-cone momentum, ϖ z x +, which complicated all previous calculations. After defining the vertex operator for the massless physical supermultiplet, as well as two picture-changing operators and an instanton-number-changing operator, scattering amplitudes for an arbitrary number of loops and external massless states are explicitly calculated by evaluating free-field correlation functions of these operators on N = 2 super-Riemann surfaces of the appropriate topology, and intergrating over the global moduli. Although there is no sum over spin structures, only discrete values of the global U(1) moduli contribute to the amplitudes. Because the spacetime supersymmetry generators do not contain ghost fields, the amplitudes are manifestly spacetime-supersymmetric, there is no multiloop ambiguity, and the non-renormalization theorem is easily proven. By choosing the picture-changing operators to be located at the zeroes of ϖ z x +, these amplitudes are shown to agree with amplitudes obtained using the manifestly unitary light-cone gauge formalism.

Twistor-like superstrings with D = 3, 4, 6 target superspace and N = (1, 0), (2, 0), (4, 0) world-sheet supersymmetry

We construct a manifestly N = (4, 0) world-sheet supersymmetric twistor-like formulation of the D = 6 Green-Schwarz superstring, using the principle of double (target-space and world-sheet) Grassmann analyticity. The superstring action contains contains two Lagrange multiplier terms and a Wess-Zumino term. They are written down in the analytic subspace of the world-sheet harmonic N = (4, 0) superspace, the target manifold being too an analytic subspace of the harmonic D = 6, N = 1 superspace. The kappa symmetry of the D = 6 superstring is identified with a Kac-Moody extension of the world-sheet N = (4, 0) superconformal symmetry. It can be enlarged to include the whole world-sheet reparametiization group if one introduces the appropriate gauge Beltrami superfield into the action. To illustrate the basic features of the new D = 6 superstring construction, we first give some details about the simpler (already known) twistor-like formulations of D = 3, N = (1, 0) and D = 4, N = (2, 0) superstrings.

Superstring propagation through supergravitational shockwaves

In all previous works on strings (and superstrings) in curved space-times, explicit calculations were performed only in purely bosonic gravitational backgrounds. Here, we propose to introduce a background containing also fermionic degrees of freedom, solution of the N = 1 supergravity equations in D dimensions. We find an explicit N = 1 linearized supergravity shockwave solution giving the spin-3/2 Rarita-Schwinger field, and an exact (full non-linear) gravitational shockwave bosonic part. We study a Green-Schwarz superstring propagating in such a supergravity background. We write and solve the superstring equations. Contrarely to the purely bosonic shockwave case (in which spinor-string propagation is free), spinor-string coordinates couple here non-trivially to the transverse bosonic coordinates through the fermionic background. We find that outgoing fermionic-modes are mixed with ingoing bosonic (and fermionic) modes. This leads to a new feature of particle transmutation between bosons and fermions, described by the superstring ground states (and also by the excited states). The presence of the bosonic-fermionic background provides in string theory a natural physical mechanism to transform bosons into fermions (and vice versa).

Scattering of superstrings by cosmic strings

We exactly solve the superstring scattering by a straight cosmic string. That is, we exactly quantize the Neveu-Schwarz-Ramond and the Green-Schwarz superstrings propagating in a conical space of deficit angle 8π Gμ, μ being the cosmic-string tension. As for the purely bosonic string, if the superstring touches the cosmic string, the scattering is inelastic, since the internal superstring modes become excited and mixing of particle- and antiparticle-modes takes place, leading to different initial and final particle states. If there is no collision, the superstring only suffers a deflection of ±4 πGμ and the oscillator modes only suffer a polarization change. All the transformations between the ingoing and outgoing states are explicitly computed in closed form. The mass formula and number operators are analyzed. We also generalize all these results to the case when the cosmic string is spinning; the new features, in this case, appear for the time string-coordinate; the propagation of fermionic coordinates is not affected by the cosmic-string spin.

Worldsheet electromagnetism and the superstring tension

A superstring action, invariant under the symmetries corresponding to a free differential N = 1 superalgebra, is constructed. Its worldsheet fields include an electromagnetic gauge potential. Its equations of motion are those of the Green-Schwarz superstring but with the string tension given by the circulation of the worldsheet electric field around the string.

Light-like integrability in loop superspace, Kac-Moody central charges and Chern-Simons terms

We apply the idea of light-like integrability in loop superspace to give a complete derivation of all the constraints of on-shell ten-dimensional supergravity coupled to Yang-Mills. The Yang-Mills Chern-Simons coupling terms are obtained by adding a central extension to the Kac-Moody algebra of the Yang-Mills generators. The form of the loop-superspace covariant derivatives, including the central charge modifications, can also be derived by means of canonical quantization from a Green-Schwarz superstring coupled to a supergravity and super-Yang-Mills background. There the Yang-Mills sector is represented by bosonic group coordinates, which are chiral and describe a gauged Wess-Zumino-Witten model.

COSET CONSTRUCTION OF SUPERSTRINGS VIA THE COADJOINT ORBIT METHOD

The previously proposed general construction of geometric actions on infinite-dimensional group coadjoint orbits in terms of fundamental group one-cocycles is applied to provide an alternative formulation of the Green-Schwarz superstring. It is shown that the latter model can be consistently constructed as geometric action on a certain infinite-dimensional coset space of the semi-direct product of left- and right-handed Virasoro groups with a Kac-Moody group based on an appropriate modification of the super-Heisenberg-Weyl group.

ALTERNATIVE SUPERSTRING LAGRANGIAN FORMULATIONS

Effective Lagrangians for the Green-Schwarz superstring are obtained by using a constrained functional integration formalism.

Towards covariantly quantized D = 10 type-II Green-Schwarz σ-models

The complete gauge algebra of all symmetries which occur in D = 10 Green-Schwarz formulations of closed superstring theories are investigated in the presence of nontrivial backgrounds. Explicit expressions for nonclosure functions required for the Batalin-Vilkovisky quantization technique are obtained. This technique is then employed to covariantly quantize the σ-model describing type II-A Green-Schwarz superstrings propagating in N = 2, D = 10 curved superspace, using a gauge-fixing fermion analogous to the one proposed recently for the quantization of the free D = 10 heterotic string. The ultraviolet properties of the one-loop d = 2 effective action are examined in some detail. In particular, we show that the violation of space-time Lorentz invariance found earlier using a Lorentz noncovariant quantization ansatz disappears in this manifestly covariant formulation.

On the nonperturbative solution of the d = 1 superstring

We construct nonperturbative solutions for the discretized Green-Schwarz superstring in one dimension. This is compared with a modification of the WKB series such that supersymmetry is preserved. The logarithmic divergences due to massless modes appear again, as in the bosonic string case. However, the density of states is different from the bosonic string theory, giving rise to a new series. We comment on the multicritical cases that could arise.

Quantization of manifestly supersymmetric strings

Computation of the number of physical degrees of freedom and of conformal anomaly in recent covariant quantization of Green-Schwarz superstring is presented.

Random superstrings

We propose a lattice formulation of the Green-Schwarz superstring based on the random triangularization of Riemann surfaces. We discuss some of its properties, and outline a framework for a nonperturbative description.

Anomalous anomalies in the Carlip-Kallosh quantization of the Green-Schwarz superstring

The cancellation of conformal and gravitational anomalies in the free Green-Schwarz superstring in the semi-covariant formulation of Carlip and Kallosh is re-examined, and it is found to take place between non-local and local but non-polynomial parts of the effective action. Anomalously, the total effective action does not vanish itself, but contains terms which violate the ten-dimensional Lorentz invariance of the model.

HIGHER-SPIN SYMMETRY IN ONE AND TWO DIMENSIONS (I)

Higher spin theories in one and two dimensions are considered. The analysis of the ghost sector is carried out and a possible analogy with the ghost sector of the superparticle and the Green-Schwarz superstring in the covariant gauge is discussed.

The Green-Schwarz superstring as an asymmetric model of a chiral field

The Green-Schwarz superstring as an asymmetric model of a chiral field

Covariant separation of first-class and second-class constraints for the Green-Schwarz superstring

We define super-Poincaré covariant sets of reducible first-class and second-class constraints for the Green-Schwarz superstring. These constraints can be treated using Dirac's methods and allow, in principle, a fully covariant canonical quantisation.

Formula omitted] covariant computations in the Green-Schwarz superstring

Using the OSp(9, 1 4 ) suggested by Green and Hull we give the correct reclassification of the infinite ghost sector discussed by one of the authors in the Lorentz covariant quantization of the Green-Schwarz superstring. We then show how to perform OSp( 2n 2m ) covariant computations in this infinite sector, without regulators, using supergroup techniques introduced some time ago by one of the authors and his collaborators. In particular the conformal anomaly is shown to be a function of the graded dimension and quadratic index of a spinor representation which are natural OSp( 2n 2m ) invariants. Therefore, like many other supergroup invariants these quantities are equal to the corresponding SO(2 n−12 m) or Sp(2 m−2 n) invariants that are functions of n− m.

New spacetime superalgebras and their KAC̆-Moody extension

We present new spacetime algebras whose existence is due to special Γ-matrix identied which are also necessary for the existence of super p-branes. They contain a pth-rank antisymmetric tensor, and a ( p-1-rank) antisymmetric tensor-spinor generator. Furthermore the translations do not commute with the supercharge. In the case of supermembranes, we find a super-Kač-Moody extension of the new spacetime algebra. We give a realization of the algebra in terms of operators in d=11 superspace, and find a connection with the d=11 supermembrane action which leads to an elegant supergeometric formulation. By double dimensional reduction, we obtain a Kač-Moody algebra for the Type IIA Green-Schwarz superstring. We also discuss the generalization of these results, including the construction of generalized super-Virasoro algebras, for super p-branes.

Current algebra of the d=3 superstring and partial breaking of global supersymmetry

We compute the classical algebra of supercurrents for the N=1, d=3 Green-Schwarz superstring in a physical gauge. The result is a worldsheet-supersymmetry current algebra of type (1, 1), but with an additional central term that implies the (partial) breakdown of (1, 1) to (1, 0) supersymmetry. This confirms a suggestion of Hughes and Polchinski and clarifies the mechanism by which partial breaking of supersymmetry occurs.