The polyakov path integral over bordered surfaces

The geometrical approach to the functional integral over Faddeev-Popov ghost fields is developed and applied to construct the BRST extension of the off-shell closed string amplitudes in the constant curvature gauge. In this gauge the overlap path integral for off-shell amplitudes is evaluated. It leads to the nonlocal sewing procedure generating all off-shell amplitudes from the cubic interaction vertex. The general scheme of the reconstruction of a covariant closed string field theory from the off-shell amplitudes is discussed within the path integral framework.     

The Polyakov path integral over bordered surfaces

Following the general scheme of the convariant path integral quantization of gauge systems, two alternative formulations of the first quantized closed bosonic string in a position representation are presented. In both approaches the covariant path integral representations of the propagator and of the higher order off-shell amplitudes are constructed. For a wide class of gauges the explicit formulae for off-shell amplitudes are obtained. This paper is the continuation of our previous work where the corresponding problems in the open string case were considered [20].     

On a modification of the boundary-state formalism in off-shell string theory

We examine the application of boundary states in computing amplitudes in off-shell open string theory. We find a straightforward generalization of a boundary state which produces the correct matrix elements with on-shell closed string states.     

Evaluation of the one loop string path integral

We evaluate Polyakov's path integral for the sum over all closed surfaces with the topology of a torus, in the critical dimensiond = 26. The result is applied to the partition function and cosmological constant of the free bosonic string, and to tachyon scattering amplitudes.     

Off-shell effective actions in string theory

A new, “off-shell”, approach to conformal invariance, β-functions and field equations in first quantized string theory is presented. The method, valid to all orders in the weak-field expansion and non-perturbatively in α′, is illustrated for a tachyon background at genus zero and one level. For a particular choice, we derive a Zamolodchikov-type equation for the effective action.     

Point-like structure and off-shell dual strings

We argue that in a consistent off-shell dual formalism the amplitude for the emission of a scalar off-shell state by a string consists of two components. One of these contains the particle poles in the off-shell leg and the other is intimately related to the insertion of a point-like energy density on the string. As a result, the amplitude for a string to emit a zero momentum scalar state into the vacuum (which may be relevant for spontaneous symmetry breaking) is described by the amplitude for a finite fraction of the energy in the string to collapse to a spatial point at some time (this fraction and its space-time position being integrated over). The off-shell amplitudes have an elegant formulation in terms of a set of “confined modes” which can be assigned quark flavour quantum numbers to reproduce the Chan-Paton scheme.We suggest the dual model be modified by allowing for the coupling of scalar closed strings to the vacuum and the resulting effect on the space-time structure of dual Green functions is described.We find that even the emission of a single zero-momentum closed string modifies the elastic amplitude in a significant manner, leading to a power-behaved fixed-angle cross section in contrast to the usual exponential decrease of the dual model. This arises from point-like scattering between energy densities accumulating in the colliding strings. The relationship between the fixed angle and Regge limits is discussed. The fixed angle behaviour is found to be the asymptotic limit in momentum transfer of a fixed pole that arises in the Regge limit.     

Non-archimedean string dynamics

Explicit formulas for the N-point tree amplitudes of the non-archimedean open string are derived. These amplitudes can be generated from a simple non-local lagrangian involving a single scalar field (the tachyon) in ambient space-time. This lagrangian is studied and is found to possess a tachyon free vacuum with no “particles” but with soliton solutions. The question of generalizing the adelic product formular to N-point amplitudes is taken up. The infinite product of 5-point amplitudes is shown to converge in a suitably chosen kinematic region whence it can be analytically continued. Though the precise form of the product formula for the 5-point (and N-point)amplitudes is not found, it is shown that the product is not equal to one as it is for the 4-point amplitudes but rather involves the famous zeros of the Riemann zeta function. Chan-Paton rules for non-archimedean open strings are given. A string over the (global) field of rational numbers is constructed. Other problems that are addressed are the introduction of supersymmetry, the nature of a p-adic string lagrangian, and the possibility of strings over other locally compact fields.     

Reciprocal space-time and momentum-space singularities in the narrow resonance approximation

A general scheme is proposed which makes explicit the relationship between the singularities of off-shell amplitudes in position-space and momentum-space in the narrow resonnace approximation. In some ways this may be viewed as a duality scheme for amplitudes involving external quarks, in which narrow resonances in certain channels build the Fourier transform of power singularities in x² (x^μ being a position vector). This scheme is made precise by dual string off-shell amplitudes. As well as highlighting possible connections between the general dual framework and the structure of confined field theories we are able to pinpoint certain grave shortcomings of present dual models.     

On Wess–Zumino terms of brane–antibrane systems

We calculate the disk level S-matrix element of one closed string RR field, two open string tachyons and one gauge field in type II superstring theory. An expansion for the S-matrix element has been found that its four leading order terms are reproduced exactly by the symmetric trace tachyon DBI and the Wess–Zumino actions of D-brane–anti-D-brane systems. Using this consistency, we have also found the first higher derivative correction to the some of the WZ terms.     

Field theory of the interacting string: The closed string

We recast dual models in the language of a quantum field theory of functional fields, restricting ourselves for simplicity to the closed string model. We derive the dynamics for both scalar and spinor functional fields from a unique parametrization invariant action. Passages to the Hamiltonian formalism and second quantization are explicitly worked out for the closed mesonic string in the front form. The results are equivalent to those obtained earlier by GGRT, i.e. no ghost fields at the price of an anomalous number of space-time dimensions and a tachyon. Finally, we use the parametrization invariance requirement on the action to derive couplings of closed strings to local fields by extending a global U(1) invariance built in the free action into a local one in the functional sense. We construct the self-couplings of closed string fields by requiring these to be consistent with the gauge invariance of the external fields. This procedure uniquely leads (for the open string) to the string splitting picture of Nambu and Mandelstam. The closed string is found to cross itself and then split up into two others. Both open and closed strings have quartic interactions corresponding to strand (for the open string) and lobe (for the closed string) exchanges. The case of the interacting fermionic model is not treated here.     

Finite temperature corrections to the coupling constant and ground state mass in string theory

Finite temperature corrections to open string coupling constant and tachyon mass are calculated. We find that temperature contributions do have singularities (this was not the case in field theory). We study the low-temperature limit of the coupling constant and find that, in this limit, it decreases with temperature. We study the corrections to closed strings.     

Off shell states in the dual model

We present a class of Lorentz invariant, gauge invariant off-shell amplitudes for the ordinary Veneziano and Ramond-Neveu-Schwarz dual models. They correspond to interactions with the string which are local in space-time.     

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 /₊.     

Behavior of boundary string field theory associated with integrable massless flow

We put forward an idea that the boundary entropy associated with integrable massless flow of thermodynamic Bethe ansatz (TBA) is identified with tachyon action of boundary string field theory. We show that the temperature parametrizing a massless flow in the TBA formalism can be identified with tachyon energy for the classical action at least near the ultraviolet fixed point, i.e., the open string vacuum.     

J/gy suppression as evidence for high densities in nuclear collisions

It is shown that the scattering amplitudes of some degenerate massive string states can be expressed in terms of that of higher spin states at the same mass level. This phenomenon is discussed from σ-model point of view and demonstrated explicitly by using massive Ward identities generated by zero-norm states atD=26. The subtlety of the scalar propagating state is briefly pointed out. We also compare our on-shell gauge symmetry derived from σ-model with off-shell gauge symmetry of covariant string field theory.     

Pomerons and BCFW recursion relations for strings on D-branes

We derive pomeron vertex operators for bosonic strings and superstrings in the presence of D-branes. We demonstrate how they can be used in order to compute the Regge behavior of string amplitudes on D-branes and the amplitude of ultrarelativistic D-brane scattering. After a lightning review of the BCFW method, we proceed in a classification of the various BCFW shifts possible in a field/string theory in the presence of defects/D-branes. The BCFW shifts present several novel features, such as the possibility of performing single particle momentum shifts, due to the breaking of momentum conservation in the directions normal to the defect. Using the pomeron vertices we show that superstring amplitudes on the disc involving both open and closed strings should obey BCFW recursion relations. As a particular example, we analyze explicitly the case of 1→1$1\to 1$ scattering of level one closed string states off a D-brane. Finally, we investigate whether the eikonal Regge regime conjecture holds in the presence of D-branes.     

Tachyons, Lamb shifts and superluminal chaos

An elementary account on the origins of cosmic chaos in an open and multiply connected universe is given; there is a finite region in the open 3-space in which the world-lines of galaxies are chaotic, and the mixing taking place in this chaotic nucleus of the universe provides a mechanism to create equidistribution. The galaxy background defines a distinguished frame of reference and a unique cosmic time order; in this context superluminal signal transfer is studied. Tachyons are described by a real Proca field with negative mass square, coupled to a current of subluminal matter. Estimates on tachyon mixing in the geometric optics limit are derived. The potential of a static point source in this field theory is a damped periodic function. We treat this tachyon potential as a perturbation of the Coulomb potential, and study its effects on energy levels in hydrogenic systems. By comparing the induced level shifts to high-precision Lamb shift measurements and QED calculations, we suggest a tachyon mass of 2.1 keV/c² and estimate the tachyonic coupling strength to subluminal matter. The impact of the tachyon field on ground state hyperfine transitions in hydrogen and muonium is investigated. Bounds on atomic transition rates effected by tachyon radiation as well as estimates on the spectral energy density of a possible cosmic tachyon background radiation are derived. Received 13 August 1999 and Received in final form 7 February 2000     

One-loop correction of the tachyon action in boundary superstring field theory

We compute one-loop correction to the string field theory action of the tachyon for unstable D-branes in the framework of the boundary superstring field theory. We would expect that the one-loop correction comes from the partition function of the two-dimensional worldsheet theory on the annulus. The annulus correction suggests that the genus expansion is, somehow, governed by the effective string coupling defined in terms of the tachyon λ=g_sexp(−T²/4).     

Scalar field potentials for closed and open cosmological models

We develop a technique for the reconstruction of the potential for a scalar field or a tachyon field, reproducing a given cosmological evolution in a closed and open isotropic cosmological models. Such potentials are explicitly written down for the cases of the evolutions driven by a generic barotropic fluid and by radiation plus a cosmological constant, for the case of a scalar field. For tachyon and pseudo-tachyon fields the potentials are reconstructed for some special cases, corresponding to particular values of the barotropic index.     

Tadpole resummations in string theory

While R–R tadpoles should be canceled for consistency, string models with broken supersymmetry generally have uncanceled NS–NS tadpoles. Their presence signals that the background does not solve the field equations, so that these models are in “wrong” vacua. In this Letter we investigate, with reference to some prototype examples, whether the true values of physical quantities can be recovered resumming the NS–NS tadpoles, hence by an approach that is related to the analysis based on String Field Theory by open–closed duality. We show that, indeed, the positive classical vacuum energy of a Dp-brane of the bosonic string is exactly canceled by the negative contribution arising from tree-level tadpole resummation, in complete agreement with Sen's conjecture on open-string tachyon condensation and with the consequent analysis based on String Field Theory. We also show that the vanishing classical vacuum energy of the SO(8192) unoriented bosonic open-string theory does not receive any tree-level corrections from the tadpole resummation. This result is consistent with the fact that this (unstable) configuration is free from tadpoles of massless closed-string modes, although there is a tadpole of the closed string tachyon. The application of this method to superstring models with broken supersymmetry is also discussed.