Charles B. Thorn

Quantum dynamics of a massless relativistic string

Abstract We develop the classical and quantum mechanics of a massless relativistic string, the light string, which is characterized by an action proportional to the area of the world sheet swept out by the string in space time. We show that, classically, there are only D -2 dynamically independent components among the D functions x μ ( σ , τ ) which represent the world sheet ( D is the dimension of space time). Quantizing only these independent components, we find that the angular momentum operators suggested by the correspondence principle generate O( D -1,1) only when the first excited state is a photon, i.e., a spin-one massless state, and when D = 26. By allowing additional degrees of freedom in the quantum mechanics, we are able to quantize the string in a Lorentz covariant manner for any value of D and any mass for the first excited state. In this latter scheme the full Fock space contains negative norm states. However, when D ⩽ 26 for a massless first excited state and D ⩽ 25 for a real massive first excited state, the physical states span a positive subspace of the Fock space. The excitation spectrum of the light string coincides with the space of physical states in the dual resonance model for unit intercept of the leading Regge trajectory. We point out the connection of this work to previous studies of the physical states in dual models.

Compatibility of the Dual Pomeron with Unitarity and the Absence of Ghosts in the Dual Resonance Model

Abstract It is shown that the number of states coupling in the Veneziano model when the space time dimension, d, is 26 (d = 10 for the Neveu-Schwarz model) is reduced in such a way that the Pomeron is probably a pole. A simple consequence of this counting is the absence of ghosts for d ⩽ 26 (d ⩽ 10 for Neveu-Schwartz).

STRING FIELD THEORY

Abstract We present an account of string field theory which aims to introduce the reader to the important concepts of the subjects as well as to aid access to the literature. Light cone string theory is briefly reviewed, but the emphasis is on the covariant approach exploiting world sheet BRST invariance to define string field derivations, integration, and products. Although we try to present the ideas in a general way, we draw on Wittens formulation of open string field theory for most of our examples. We include brief self-contained reviews of both the operator and Lagrangian versions of the BRST formalism employed in this article. There is a detailed account of perturbation theory for Wittens theory, including a few explicit sample calculations. Open problems faced by open superstring field theory and by closed string field theory are discussed. We sketch some of the ideas for attacking them but do not give a definitive resolution. Finally, some formulae relevant to the “bosonization of superghosts” are derived in a self-contained appendix.

Light-cone superstring in AdS space–time

We consider fixing the bosonic light-cone gauge for string in AdS space in the phase space framework, i.e., by choosing x+=τ, and by choosing σ so that P+ is distributed uniformly (its density P+ is independent of σ). We discuss classical bosonic string in AdSd and superstring in AdS5×S5. In the latter case the starting point is the action found in hep-th/0007036, where the κ-symmetry is fixed by a fermionic light-cone type gauge. We derive the light-cone Hamiltonian in the AdS5×S5 case and in the case of superstring in AdS3×S3. We also obtain a realization of the generators of the basic superalgebra psu(2,2|4) in terms of AdS5×S5 superstring coordinate 2-d fields in the light-cone gauge.

The vertex function in Witten's formulation of string field theory

Abstract Conformal mapping techniques are employed to obtain the oscillator representation of the three open string vertex in Wittens formulation of string field theory. It is argued that the physical state couplings are identical to those of the dual resonance model, and this is confirmed for the low lying states with our explicit construction.

Superstring field theory

We construct a class of cubic gauge-invariant actions for superstring field theory, gauge fix one of them and show that it reproduces the known superstring S-matrix. In our construction boson string fields are taken in the 0 picture and fermion string fields in the −12 picture. For 0 picture the bosonic kinetic term requires an insertion carrying −2 units of picture number. We construct all possible picture-changing operators with the required properties. We use the simplest of these to construct the superstring action we choose to analyze here. In the gauge b1 + b−1 = 0, the conformal mappings needed to evaluate the tree diagrams are algebraic, and this enables a completely explicit derivation of the Koba-Nielsen amplitudes. In this gauge the action formally linearizes, a phenomenon familiar from other Chern-Simons type theories. Nontrivial scattering amplitudes are obtained by approaching this gauge as a limit.

Making the massless string massive

We investigate the possibility of associating a finite rest mass density with the relativistic string at the classical level. We choose a modification of the massless Lagrangian which reduces in the non-relativistic limit to the usual non-relativistic string. After studying some simple classical motions of this system, we quantize the massive string in a similar way to the massless case. The Regge trajectories are linear as in the massless case, but their intercepts are shifted downward from unity by an amount proportional to the square of the rest mass density parameter. Our naive quantization procedure is covariant only in 25 space-time dimensions. However, we are able to use the extra degree of freedom implicit in the mass density to modify the Lorentz generators so that covariance is maintained for any dimension less than 25. We envisage hadronic interactions to be introduced through the breaking and joining of strings, as in the massless case, and we discuss the problems associated with the construction of covariant amplitudes when D < 25.

An exact operator solution of the quantum Liouville field theory

Exact, closed form results are given expressing the quantum Liouville field theory in terms of a canonical free pseudoscalar field. The classical conformal transformation properties and Baechlund transformation of the Liouville model are briefly reviewed and then developed into explicit operator statements for the quantum theory. This development leads to exact expressions for the basic operator functions of the Liouville field: partial/sub ..mu../Phi, and e/sup n/phi. An operator product analysis is then used to construct the Liouville energy-momentum tensor operator, which is shown to be equal to that of a free pseudoscalar field. Dynamical consequences of this equilvalence are discussed, including the relation between the Liouville and free field energy eigenstates. Liouville correlation functions are partially analyzed, and remaining open questions are discussed.

Quantum Bäcklund transformation for the Liouville theory

Abstract The classical Backlund transformation, which maps the Liouville model onto a free field theory, is developed into an explicit operator relation for quantum fields. Conformal transformation properties and canonical commutation relations are preserved by this operator mapping.

Reformulation of the dual pion model

The dual pion model is reformulated in another Fock space. The basic conjecture about the decoupling of the ground state is proved, and all the on-shell gauge operators are found.