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.     

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.     

Equivalence between the unified dual model and Pomeron-Reggeon amplitudes

We show that a recently proposed unified dual model for interacting open and closed strings actually describes Pomeron-Reggeon amplitudes of the conventional Veneziano model. We prove, in particular, that the Pomeron amplitudes are given by the Shapiro-Virasoro model.     

Symmetry breaking at enhanced symmetry points

The influence of world-sheet boundary condensates on the toroidal compactification of bosonic string theories is considered. At the special points in the moduli space at which the closed-string theory possesses an enhanced unbroken G × G symmetry (where G is a semi-simple product of simply laced groups) a scalar boundary condensate parameterizes the coset G × G/G. Fluctuations around this background define an open-string generalization of the corresponding chiral non-linear sigma model. Tree-level scattering amplitudes of on-shell massless states (‘pions’) reduce to the amplitudes of the principal chiral model for the group G in the low-energy limit. Furthermore, the condition for the vanishing of the renormalization group beta function at one loop results in the familiar equation of motion for that model. The quantum corrections to the open-string theory generate a mixing of open and closed strings so that the coset-space pions mix with the closed-string G × G gauge fields, resulting in a Higgs-like breakdown of the symmetry to the diagonal G group. The case of non-oriented strings is also discussed.     

Adèlic formulas for string amplitudes in fields of algebraic numbers

On the basis of the analysis on adèle groups (Tate's formula) for any field of algebraic numbers, a regularization of infinite adèlic products of gamma and beta functions of local fields is proposed. The formulas obtained are applied to representations of the four-point crossing symmetric Veneziano and Virasoro-Shapiro amplitudes through regularized adèlic products of the corresponding string (open and closed, resp.) amplitudes.     

String Scattering from Decaying Branes

We develop the general formalism of string scattering from decaying D-branes in bosonic string theory. In worldsheet perturbation theory, amplitudes can be written as a sum of correlators in a grand canonical ensemble of unitary random matrix models, with time setting the fugacity. An approach employed in the past for computing amplitudes in this theory involves an unjustified analytic continuation from special integer momenta. We give an alternative formulation which is well-defined for general momenta. We study the emission of closed strings from a decaying D-brane with initial conditions perturbed by the addition of an open string vertex operator. Using an integral formula due to Selberg, the relevant amplitude is expressed in closed form in terms of zeta functions. Perturbing the initial state can suppress or enhance the emission of high energy closed strings for extended branes, but enhances it for D0-branes. The closed string two point function is expressed as a sum of Toeplitz determinants of certain hypergeometric functions. A large N limit theorem due to Szegö, and its extension due to Borodin and Okounkov, permits us to compute approximate results showing that previous naive analytic continuations amount to the large N approximation of the full result. We also give a free fermion formulation of scattering from decaying D-branes and describe the relation to a grand canonical ensemble for a 2d Coulomb gas.     

Four-dimensional heterotic strings and conformal field theory

The techniques of (super) conformal field theory are applied to 4-dimensional heterotic string theories. We discuss certain aspects of 4-dimensional strings in the framework of the bosonic lattice approach such as the realization of superconformal symmetry, character valued partition functions, construction of vertex operators and ghost picture changing. As an application we compute all possible 3- and 4-point tree amplitudes of the massless fields and derive from them the low energy effective action of the massless modes. Some effects for the massless spectrum due to one-loop string effects are also mentioned.     

On the adelic string amplitudes

Some remarkable properties of the adelic string amplitudes for the physical domain of the Mandelstam variables are considered. It is shown that the p-adic four-point functions are always negative. Also, a formula is obtained which expresses the product of moduli of the p-adic amplitudes and the Veneziano amplitude in terms of the zeta functions. This product is absolutely convergent unlike the divergent product of these amplitudes without moduli, recently considered by Freund and Witten. Using the zeta function representation, p-adic interpolation of the Veneziano amplitude is also considered.     

Holomorphic factorization and open strings

It is established that, apart from a function of the period matrix of the double of the surface, the open bosonic string integrand at an arbitrary order of string perturbation theory is the modulus squared of a necessarily complex function of real moduli coordinates and that no surface terms contribute to any obstruction to this factorization. This function is related to the modulus of the holomorphic function in the moduli space of the double of the surface guaranteed to exist by the previously established result of holomorphic factorization for closed strings.     

A fresh look at generalized Veneziano amplitudes

The dual resonance model, which was a precursor of string theory was based upon the idea that two-particle scattering amplitudes should be expressible equivalently as a sum of contributions of an infinite number of s channel poles each corresponding to a finite number of particles with definite spin, or as a similar sum of t channel poles. The famous example of Veneziano [Nuovo Cimento A 57 (1968) 190] satisfies all these requirements, and is additionally ghost free. We recall other trajectories which provide solutions to the duality constraints, e.g. the general Mobiüs trajectories and the logarithmic trajectories, which were thought to be lacking this last feature. We however demonstrate, partly empirically, the existence of a regime within a particular deformation of the Veneziano amplitude for logarithmic trajectories for which the 4-point amplitude remains ghost free.     

Quantisation of the string fragmentation model

We quantise the classical Artru-Mennessier string model with a Feynman sum over histories method. This procedure yields both propagation amplitudes and a Veneziano mass spectrum for mesons, with resonance poles for unstable states. Applied to the processe ⁺ e ^?→hadrons our amplitudes justify previous applications of string models and in particular the relative amplitudes for different string configurations are in agreement with a recent conjecture of Andersson and Hofmann which can account for the observed Bose-Einstein correlations ine ⁺ e ^? annihilation.     

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.     

Strings in horizons, dissipation and a possible interpretation of the Hagedorn temperature

We consider the entanglement of closed bosonic strings intersecting the event horizon of a Rindler spacetime, and, by using some simplified (rather semiclassical) arguments and some elements of the string field theory, we show the existence of a critical temperature beyond which closed strings cannot be in thermal equilibrium. The order of magnitude of this critical value coincides with the Hagedorn temperature, which suggests an interpretation consistent with the fact of having a partition function that is ill defined for temperatures higher than it. Possible implications of the present approach for the microscopical structure of stretched horizons are also pointed out.     

All NSR-models in terms of bosonic strings: An explicit derivation

We construct the open and closed string NSR-models in terms ofD15 bosonic string theories. All anticommuting NSR-operators are obtained after fermionizing 4 bosonic dimensions, and the NSR-Hilbert spaces are embedded as linear subspaces of the bosonic Hilbert spaces. We thus show the existence of various 10D supersymmetric sectors of the state spaces ofD=26 consistent bosonic strings.     

Amplitudes for the Bosonic String with Boundaries

We deal with the problem of the computation of amplitudes for the bosonic Polyakov string with boundaries and show that both conformal invariance and reparametrisation invariance are maintained in critical dimensional d = 26 as the case without boundaries. The amplitudes of the bosonic, closed oriented Polyakov string with boundaries are formulated aa integral over moduli space with respect to the Weil-Petersson measure.     

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.     

PartiallyU(1) compactified scalar massless field on the compact Riemann surface and the bosonic string amplitudes

The theory of the partiallyU(1) compactified scalar massless field on the compact Riemann surface with Nambu-Goto action is defined. The partition function is determined completely by a choice of the finite-dimensional approximations. The correlation functions are the only correctly defined objects of the theory. The averages of the correlation function asymptotic values provide the amplitudes. For the compact Riemann surfaces of any genus the usual bosonic string amplitudes are the special cases of the above amplitudes.