The interacting gauge covariant bosonic string

The interaction of the gauge covariant open bosonic string is presented in oscillator form, and in functional form. In the latter form, the string is described by commuting and anticommuting coordinates. The interaction is essentially the condition that the strings should overlap.     

The bosonic string in non-conformal gauges

The lagrangian and hamiltonian formalism for a free bosonic relativistic string are considered for arbitrary non-orthonormal or non-orthonormal gauges. We show in detail how one can write an arbitrary metric tensor as a reparametrization of a conformally flat one. By means of this decomposition, the lagrangian and hamiltonian formalisms are explicitly solved. From the result of this classical analysis we are then able to conclude that the quantization yields the same physical results as in the standard orthonormal gauge.We also comment on singularities in Liouville theories for strings.     

Factorization of bosonic string amplitudes

We consider the bosonic string path integral over degenerating Riemann surfaces. We first review the factorization of conformal field theory on a degenerating surface. A careful treatment of the degeneration of the measure for moduli leads to a modification of the usual ghost insertions so as to assure covariance under a change of conformal frame. More generally, amplitudes with BRST invariant but conformally non-invariant operators are well defined with the covariant ghost insertions. As a detailed application we study the string modifications to the background field equations. We find to first order in the tadpole and all orders in string coupling that the ratio of the graviton source, dilaton source, and zero-point amplitude agrees with that found from general covariance and the soft-dilaton theorem in the low-energy field theory. We also discuss the unitarity of the bosonic string theory,     

Modifying the bosonic string vacuum

A nontrivial string vacuum can induce effects in open bosonic string theories which can be interpreted in terms of nonlocality of the mapping of the string world sheet into spacetime. This is achieved by modifying the sum over Riemann surfaces to include boundaries on which the bosonic fields satisfy a Dirichlet condition, as well as holes with the usual Neumann condition and crosscaps. Such effects profoundly alter the large-angle behaviour of string amplitudes. With suitable normalization, they also lead to a cancellation of the one-loop divergence associated with the vacuum emission of a soft dilaton.     

Vertex operators of closed bosonic string

A closed bosonic string emission and absorption vertex operator is constructed in the framework of the path-integral formulation of string theories. The vertex operator is a functional of an external string wave function as well as a string coordinate and a metric variable. Conformal invariance is the guiding principle of the construction. By demanding the metric variable to be decoupled from the theory a set of Virasoro conditions is obtained for the external string wave function and a number of conformal breaking terms to be added to the generating functional.     

The massive bosonic string in the center-of-mass gauge

The open Nambu string is revisited in the spirit of an early approach by Rohrlich. Strictly timelike motions only are considered. The proper-time of the center-of-mass is taken as preferred parameter. We propose a canonical formalism in terms of a countable infinity of variables, among them the modes. But the barycentric coordinates have noncommuting components, which makes possible a consistent quantization (in any dimension, four in particular) within the framework of a transverse space of states. If a maximal number of modes is further fixed, a transverse Hilbert space emerges, where spacetime displacements preserve the (positive-definite) scalar product.This article is dedicated to Fritz Rohrlich.     

Classical geometry of bosonic string dynamics

We develop a treatment of bosonic strings on a general curved background in which the volume element and the coordinates of the worldsheet are related in a similar way as canonically conjugate quantities in mechanics. The resultant formalism is a particular variant of the multi-phase-space approach to classical field theory put forward by Kijowski, Tulczyjew, and others. We study conservation laws within this framework and find that all conserved quantities are related to point symmetries, i.e., isometries of the underlying spacetime. Thus, the symmetries of relativistic mechanics coming from Killing tensors have no analogue here. We furthermore deduce from the present scheme the covariant version of the usual phase space.     

Pseudo-supergravity extension of the bosonic string

We construct a “pseudo-supersymmetric” fermionic extension of the effective action of the bosonic string in arbitrary spacetime dimension D. The theory is invariant under pseudo-supersymmetry transformations up to the quadratic fermion order, which is sufficient in order to be able to derive Killing spinor equations in bosonic backgrounds, and hence to define BPS type solutions determined by a system of first-order equations. The pseudo-supersymmetric theory can be extended by coupling it to a Yang-Mills pseudo-supermultiplet. This also allows us to construct “α^′ corrections” involving quadratic curvature terms. An exponential dilaton potential term, associated with the conformal anomaly for a bosonic string outside its critical dimension, can also be pseudo-supersymmetrised.     

Spin content of the bosonic string

A new form is derived for the generating function, χ^[λ](x) = Σ_n=0^∞xⁿχ_n^[λ], which counts the number of times, χ_n^[λ], that the irreducible O(D − 1) rotation group representation [λ] appears at the nth mass level for the bosonic string. The derivation goes through for arbitrary old spatial dimensions, D − 1 = 2v + 1. Simplifications of the results are noted for large v and the relation to a previously obtained formula for χ^[λ](x) is explained.     

BRST invariant mixed string vertex for the bosonic string

We construct a BRST invariant (N + M)-string vertex including both open and closed string states. When we saturate it with N open string and M closed string physical states it reproduces their corresponding scattering amplitude. As a particular case we obtain a BRST invariant vertex for the open-closed string transition.     

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.     

On gauge invariant bosonic string quantization

It is argued that gauge invariance of the first quantized bosonic string is preserved by a mutual cancellation of the conformai and reparametrization anomalies. Implications for a geometric interpretation of second quantized string field theories are discussed in the conclusions.Invited talk presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Conformal gravity and the bosonic string

We show that the Callan et al. effective equations of motion for the bosonic closed string in a non-trivial background may not be derived only from the bosonic part of theN=1 supergravity action of Manton and Chapline, but also from just a general conformally invariant theory of gravity. In our scheme the invariance under gauge transformations of the antisymmetric tensor field turns out to be a consequence of the metricity condition.     

New critical dimensions forq-deformed bosonic string

Applying the mass shell condition forq-deformed open and closed strings, new critical space-time dimensions are derived. Supported by the Algerian Ministry of High Education and Research under contract N^oD2501/17/01/93. Permanent address.     

Off-shell string amplitudes and singular states in bosonic string theory

The off-shell amplitudes with N external scalar particles are investigated. The dependence of the momenta is emphasized.     

Finite temperature closed bosonic string in a finite volume

Paying attention to the modular invariance and using a covariant canonical gauge (the proper time gauge), we calculate the free energy of a noninteracting gas of closed bosonic strings in a 25-dimensional torus of finite size. The result differs in form from the modular non-invariant result of Polchinski, but can be shown to be equal to it.     

Symmetries of the interacting gauge-covariant bosonic string

We derive in detail the local gauge transformations and interaction lagrangian of the second-quantized bosonic string. We verify at lowest non-trivial order in the coupling constant the gauge invariance of the interacting action, and the closure of the field transformations. This gives the structure constants of the corresponding local gauge group. This group has its generators labelled by all the string states of the theory. We show that the fermionic part of the interaction is just the overlap condition for the ghost coordinates of the three strings, multiplied by an appropriate extra ghost at the point common to the three strings. Our treatment is based on an extensive use of Goto-Naka-type overlap equations. It avoids the use of ill-defined infinite matrices or series, and can be straightforwardly extended to other string theories. We explicitly derive the conformal transformation relating the gauge-covariant three-point function to the old Caneschi-Schwimmer-Veneziano vertex. We also deal with the closed bosonic string.     

Non-commutative geometry and the closed bosonic string

We propose an action for an interacting closed bosonic string. Our formalism relies heavily on ideas discussed by Witten for the open bosonic string. We also obtain the gauge fixed quantum action for the fully interacting open bosonic string.