High-energy zero-norm states and symmetries of string theory

High-energy limit of zero-norm states in the old covariant first quantized spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed-angle behavior of four-point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to verify our results.     

Quantum deformation of space-time symmetries and interactions

We discuss quantum deformations of Lie algebra as described by the noncoassociative modification of its coalgebra structure. We consider for simplicity the quantum D = 1 Galilei algebra with four generators: energy H, boost B, momentum P and central generator M (mass generator). We describe the nonprimitive coproducts for H and B and show that their noncocommutative and noncoassociative structure is determined by the two-body interaction terms. Further we consider the case of physical Galilei symmetry in three dimensions. Finally we discuss the noninteraction theorem for manifestly covariant two-body systems in the framework of quantum deformations of D = 4 Poincaré algebra and a possible way out.     

The role of classical symmetries in the low-energy limit of superstring theories

Due to the appearance of certain classical symmetries in the low-energy limit of superstring theories, some relevant parameters remain undetermined. The breakdown of these symmetries is investigated in the loop expansion. This then enables one to clarify which properties of the low-energy theory are artifacts of the classical approximation. The results are relevant for the relations between gauge coupling constants and the magnitude of the supersymmetry breakdown scale.     

Space-time symmetries of superstring and Jordan algebras

The sequence of Jordan algebras , whose elements are the 3×3 Hermitian matrices over the division algebras , , , and , is considered. These algebras are naturally related to supersymmetric structures in space-time dimensions of 3, 4, 6, and 10, as the Lorentz groups in these dimensions can be expressed in a unified way as a subgroup of the structure group of the Jordan algebras . The generators of the complete structure group and the automorphism group can be separated into bosonic and fermionic generators, depending on their transformation properties under the Lorentz subgroup. A peculiar connection between these fermionic generators and the supersymmetry generators of the superstring action is introduced and discussed.     

Consistency of open superstring theories

The infinities and the anomalies in the G≠SO(32) open superstring arise from the same limit of the one-loop Riemann surfaces. The dilaton tadpole infinity is removable by an appropriate choice of background, as in the work of Fischler and Susskind. However, we find that the anomalies arise from the tadpole of an unphysical field, and cannot be removed by any choice of background. Thus, the spacetime anomalies are due to a world-sheet superconformal anomaly of topological origin. We also give a general discussion of the relation between anomalies and surface terms in moduli space, and point out several new applications.     

Axions,dilatons and Wess-Zumino terms in superstring theories

The nature of the gauge singlet pseudoscalar and scalar particles in the four-dimensional low energy effective theory derived from the superstring is clarified. Including the Wess-Zumino terms of the intermediate ten-dimensional field theory does not affect the result of naive dimensional reduction that one pseudoscalar does not couple to $\text{F}\text{F}\text{̃}$ and is a true Goldstone boson, while the other pseudoscalar couples identically to both the hidden and observable gauge sectors, and is a true axion. The absence of any new physics in the Wess-Zumino terms of the ten-dimensional anomaly-free supergravity theory is emphasized.     

Symmetry structures of superstring field theories

A new extended formulation of free supersymmetric string field theories is presented. The hidden symmetries are exhibited and their quantization is given. The rigid space-time supersymmetry of the free theory is discussed.     

Low energy aspects of superstring theories

The effective theory obtained as low energy limit of theE ₈×E ₈ superstring is analyzed from the phenomenological point of view. The supersymmetry breaking manifests itself in the low energy sector only after the radiative corrections involving the goldstino field have been taken into account. A universal mass for the scalar fields, generally smaller thanm _3/2, is generated. An intermediate scale can be obtained through the radiative breaking of part of the gauge group. As a consequence, the additional particles present in the spectrum get a heavy mass, and effective interactions are induced, which make possible the breaking of the electroweak group and the radiative generation of gaugino masses.     

Fermonic zero-norm states and enlarged supersymmetries of Type II string

We calculate the NS–R fermionic zero-norm states of the type II string spectrum. The massless and some possible massive zero-norm states are seen to be responsible for the space-time supersymmetry. The existence of other fermionic massive zero-norm states with higher spinor–tensor indices correspond to new enlarged boson–fermion symmetries of the theory at high energy. We also discuss the R–R charges and R–R zero-norm states and justify the idea that the perturbative string does not carry the massless R–R charges. Received: 12 July 1999 / Revised version: 16 September 1999 / Published online: 17 March 2000     

Non-trivial coupling of internal and space-time symmetries

Previous results which exhibit the impossibility of combining internal and space-time symmetries are reanalysed. Starting with McGlinn's (1964) work, where this trivial coupling appears as a direct product of these symmetries, it is shown that, by suitable generalisations such as the use of the framework of group extensions, and by the introduction of a new quantal observable, i.e. a ‘mass-breaking operator’, one can prove the existence of a non-trivial coupling scheme which admits mass splitting for the members of some super-multiplet. This leads to a new classification scheme for elementary particles. Contrary to the conventional classification models, where the choice of the underlying symmetry group does not emerge directly from the comparison of theoretical predictions with the experimental data, our scheme admits the possibility of determining the relevant symmetry from the mass spectrum.     

Non-trivial coupling of internal and space-time symmetries

Previous results which exhibit the impossibility of combining internal and space-time symmetries are reanalysed. Starting with McGlinn's (1964) work, where this trivial coupling appears as a direct product of these symmetries, it is shown that, by suitable generalisations such as the use of the framework of group extensions, and by the introduction of a new quantal observable, i.e. a mass-breaking operator, one can prove the existence of a non-trivial coupling scheme which admits mass splitting for the members of some super-multiplet. This leads to a new classification scheme for elementary particles. Contrary to the conventional classification models, where the choice of the underlying symmetry group does not emerge directly from the comparison of theoretical predictions with the experimental data, our scheme admits the possibility of determining the relevant symmetry from the mass spectrum.     

Properties of the covariant formulation of superstring theories

The covariant two-dimensional action principle that describes the dynamics of free superstrings in a Minkowski background is reviewed. Covariant gauge conditions are formulated, which simplify the equations of motion of the superspace coordinates to free equations. In this gauge there are bosonic and fermionic constraints whose generators give a supersymmetric generalization of the Virasoro algebra. As in certain supersymmetric field theories, closure of the algebra requires using the equations of motion. Covariant constrained bracket relations are obtained for the classical theory, but it is very difficult to extend them to quantum mechanical commutation relations. Interaction vertices satisfying supersymmetry and the necessary gauge conditions are constructed. They reduce in a special frame to ones found in earlier work in the light-cone gauge, and then can be interpreted quantum mechanically.     

General symmetries of a string fluid space-time

It is shown that a string fluid is the simplest anisotropic fluid with vanishing heat flux. Furthermore it has the property that the Ricci tensor is obtained from the energy momentum tensor, and vice versa, if one interchanges the fluid variables. We use previous works on the collineations of anisotropic fluids, which include the string fluid as a particular case, to compute the kinematic and the dynamic effects of certain collineations of a string fluid. It is found that the possible spacetimes, which can carry a string fluid, are severely restricted and the possible string fluids in spacetimes, which can admit them are more or less fixed. We recover previous results on the effect of symmetries in string fluid spacetimes and get many new ones, for example the matter inheritance collineations. The study and the results are presented in a systematic manner, which allows the comprehension and the comparison of the restrictions imposed by each collineation. Finally one can use the same method of work for a systematic study of similar problems.     

Equivalence of dual-field theoretical limits of superstring theories

The equivalence of type IA and type IB field-theoretical limits of superstring theories is shown by using a new type of duality transformation. Compactifications of the type IB theory to four dimensions are studied and it is shown that they induce the same vacuum configurations as the type IA theory provided the field equations are satisfied.