Measure for moduli The Polyakov string has no nonlocal anomalies

The functional measure of the bosonic Polyakov string contains nonlocal determinantal factors which seem to spoil its gauge invariances even in the critical dimension. We show that in fact both conformal invariance and reparameterization invariance are maintained for every world-sheet topology.     

Loop-corrected string field equations from world-sheet Weyl invariance

We investigate short distance singularities inside the Polyakov path integral in an arbitrary closed bosonic string background due to vertex operators and small handles or holes. The latter are represented in terms of handle or hole operators, which we construct explicitly. The requirement of global Weyl invariance generates loop-corrected equations of motion for the string modes including tadpole terms and self-energy corrections. The relation to theS-matrix and superstrings are discussed briefly.     

Covariant string amplitudes on exotic topologies to one loop

Rules are provided for the calculation of string amplitudes on all exotic topologies to one loop. These topologies include the real projective plane, the disk, the annulus, the Möbius strip, the torus and the Klein bottle. The rules are valid for bosonic strings, superstrings, and heterotic strings either in their critical dimensions or toroidally compactified, and they are applicable to amplitudes with arbitrary external bosonic and fermionic states, including mixed open- and closed-string transitions. The modular invariance of the torus amplitudes is discussed.     

From conformal quantum mechanics on bordered Riemann surfaces to covariant string field theory

The Faddeev-Popov determinant of the reparametrization ghosts of the closed bosonic string on bordered Riemann surfaces is investigated. It is found that the standard ghost action has to be supplemented by additional boundary terms. These additional terms lead to a nontrivial ghost transition amplitude. It is shown that boundary variations of ghost transition amplitudes are generated by the ghost Virasoro operators. The relevance of the boundary variation operator for string field theory is illustrated. A new interpretation of the BRST operator in terms of boundary variations is obtained and the BRST invariance of the transition amplitudes is demonstrated. A generalization of the Siegel gauge of second quantized closed bosonic string field theory is presented.     

Heterotic string theory: (II). The interacting heterotic string

The theory of interacting heterotic strings is presented. Vertex operators are derived in both the bosonic and fermionic formulations of the theory and are shown to be consistent with gauge invariance, Lorentz invariance, and supersymmetry. Three- and four-point amplitudes for the scattering of massless string states are calculated and used to derive the low-energy field theory limit of the heterotic string. Divergences in string theories are discussed and it is shown that one-loop heterotic string amplitudes are finite and modular invariant only for gauge group E₈×E₈ or spin (32)/Z₂.     

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.     

Multiloop amplitudes for the bosonic Polyakov string

We provide a simple formula for multiloop amplitudes of the bosonic, closed oriented Polyakov string (in d = 26) as integrals over moduli space with respect to the Weil-Petersson measure. The integrand consists of Green functions and the determinants of laplacians acting on functions and vectors. We compute these determinants in terms of the lengths of the closed geodesics on the surface. They are finite and different from zero. The one on functions equals the derivative at 1 of the Selberg zeta function. A discussion of lengths of closed geodesics and coordinates for Teichmueller space is given.     

The Mumford form and the Polyakov measure in string theory

An explicit formula is derived for the Mumford form on the moduli space of algebraic curves. According to the Belavin-Knizhnik theorem, this gives a formula for the Polyakov bosonic string measure.     

Gauge string fields

Gauge-invariant actions for free bosonic string fields are derived from the corresponding BRST-invariant gauge-fixed action. The auxiliary components needed to make the action local and maintain unconstrained gauge invariance arise from an SU(1,1)-invariant sector of a pair of opposite-metric fermionic string coordinates or of an extra timelike bosonic one.     

String loop divergences and effective lagrangians

We isolate logarithmic divergences from bosonic string amplitudes on a disc. These divergences are compared with “tadpole” divergences in the effective field theory, with a covariant cosmological term implied by the counting of string coupling constants. We find an inconsistency between the two. This might be a problem in eliminating divergences from the bosonic string.     

The Polyakov path integral over bordered surfaces (the open string amplitudes)

We use the Feynman functional quantization scheme adapted to the gauge theories with reparametrization invariance to the functional covariant first quantization of the open bosonic BDHP string in a position representation. The consistent functional integral representation of the open string propagator is derived and evaluated. This result is used as a starting point for two kinds of constructions of the off-shell multiloop open string amplitudes. The general idea of the presented approach is to consider the off-shell amplitudes as functionals on the space of contours endowed with an intrinsic metric or on the space /₊.     

Generalized conformal invariance conditions on a sigma model of the open bosonic string including the first massive mode

Conformal invariance conditions on a sigma model of the open bosonic string including the tachyon, the abelian gauge field an the first excited massive mode are calculated up to order a′. Inner symmetries are used to compute conformal invariance conditions from renormalization group beta functions.     

String length and covariant string field theory

String length differentials are shown to arise naturally in a BRST hamiltonian approach to the closed bosonic string. A gauge-covariant quadratic action is proposed which is shown to lead to the correct equations of motion. The gauge covariant action is extended to including a three-string interaction vertex, with exact invariance under an extended transformation on the string fields.     

A relation between tree amplitudes of closed and open strings

We derive a formula which expresses any closed string tree amplitude in terms of a sum of the products of appropriate open string tree amplitudes. This formula is applicable to the heterotic string as well as to the closed bosonic string and type II superstrings. In particular, we demonstrate its use by showing how to write down, without any direct calculation, all four-point heterotic string tree amplitudes with massless external particles.     

Interacting physical states of the bosonic string. I

A preliminary discussion on the importance of the contact terms in relation with the existence of many string vacua is presented. The problem of the BRST invariance of the string states transition amplitudes is considered in the sigma model approach to the string. It is shown that the BRST invariance is controlled by a gravitational (Diff) anomaly, and its connections with the standard Virasoro constraints are illustrated. The tachyon amplitudes are analysed and the BRST invariant dilaton vertex operator for non flat world-sheet is constructed.     

Two-point correlator for the D = 1 closed bosonic string

We calculate exactly the two-point correlation function for a random surface discretized via dense planar Feynman graphs when the dimension of the target space is D = 1. The same quantity is computed for the D = 1 bosonic string within the approach of Knizhnik, Polyakov and Zamolodchikov. The agreement is perfect.     

Manifestly covariant field theory of interacting string II

A manifestly covariant field theory is constructed for the interacting bosonic closed string, which possesses a very simple string action invariant under an inhomogeneous nilpotent BRS transformation. The physical on-shell scattering amplitudes in this theory reproduce the Koba-Nielsen amplitudes at the tree level.     

The partition function of the SO(8192) bosonic string

We discuss the partition function of the SO(8192) bosonic string at arbitrary genus. As in the genus-one case, diagrams defined in terms of involutions acting in the same way on the homology basis are weighted by identical mulitplicity factors. This property emerges as the basis feature of the SO(8192) theory. It corresponds to the picture of this model as a parameter-space orbifold of the closed bosonic string. By factorization we recover amplitudes in the degenerate limit.