Path-Integral Quantization of the (2,2) String

A complete treatment of the (2,2) NSR string in flat (2+2) dimensional space-time is given, from the formal path integral over N=2 super Riemann surfaces to the computational recipe for amplitudes at any loop or gauge instanton number. We perform in detail the superconformal gauge fixing, discuss the spectral flow, and analyze the supermoduli space with emphasis on the gauge moduli. Background gauge field configurations in all instanton sectors are constructed. We develop chiral bosonization on punctured higher-genus surfaces in the presence of gauge moduli and instantons. The BRST cohomology is recapitulated, with a new space-time interpretation for picture-changing. We point out two ways of combining left- and right-movers, which lead to different three-point functions.Comment: 36 pages, LaTeX; published version (typos & eq.(7.12) corrected

Yukawa Corrections from Four-Point Functions in Intersecting D6-Brane Models

We discuss corrections to the Yukawa matrices of the Standard Model (SM) fermions in intersecting D-brane models due to four-point interactions. Recently, an intersecting D-brane model has been found where it is possible to obtain correct masses and mixings for all quarks as well as the tau lepton. However, the masses for the first two charged leptons come close to the right values but are not quite correct. Since the electron and muon are quite light, it is likely that there are additional corrections to their masses which cannot be neglected. With this in mind, we consider contributions to the SM fermion mass matrices from four-point interactions. In an explicit model, we show that it is indeed possible to obtain the SM fermion masses and mixings which are a better match to those resulting from experimental data extrapolated at the unification scale when these corrections are included. These corrections may have broader application to other models.Comment: 24 pages, 4 figure

Covariant one-loop fermion emission amplitudes in closed string theories

We calculate the 2 fermion-2 boson and the 4 fermion scattering amplitudes at one loop in the NSR formulation of the heterotic and type II superstring theories using the covariant fermion emission vertex. The results are shown to agree with well known amplitudes calculated in the light-cone gauge in the Green-Schwarz formulation. The agreement of the 4-fermion amplitude entails the use of a new ϑ-function identity which we also prove

Two-loop dilaton tadpole induced by Fayet-Iliopoulos D-terms in compactified heterotic string theories

We calculate the two-loop dilaton tadpole induced by Fayet-Iliopoulos D-terms in heterotic string theories compactified on arbitrary supersymmetry preserving backgrounds. The result turns out to be a total derivative in the moduli and hence receives contribution solely from the boundary of the moduli space. This contribution is shown to be proportional to the square of the coefficient of the one-loop Fayet-Iliopoulos D-term in agreement with what is expected from effective lagrangian considerations

Spin field correlators on an arbitrary genus Riemann surface and non-renormalization theorems in string theories

We calculate the n-point correlation functions of spin fields on an arbitrary genus Riemann surface. We also calculate the corresponding correlators for the spin fields associated with the local supersymmetry ghosts using a specific ansatz for screening the background ghost charge. Using these results we show by explicit calculation that to all orders in the string perturbation theory all n-point amplitudes involving massless fields in the superstring and the heterotic string theory vanish identically for 0≤n≤3

Catoptric tadpoles

Fermionic string perturbation theory is known to suffer from an ambiguity in the form of a total derivative in the moduli space. For a class of backgrounds (including R10, orbifolds and theories with no U(1) factors in gauge group) we show that these ambiguities for the partition function of heterotic string theory at any genus are proportional to massless physical tadpoles in the theory at lower genera and hence vanish in stable vacua. We also find that in R10 the cosmological constant at a given genus is proportional to the cosmological constant at lower genera. This enables us to give an inductive argument for the vanishing of the cosmological constant in R10 to all orders in string perturbation theory. We also address the ambiguity and finiteness of n-point functions. Our results indicate that in R10 the ambiguity can be absorbed by a renormalization of the string coupling constant and the string tension. The expected sources of divergence in the n-point function in arbitrary tachyon-free backgrounds, besides the usual infrared divergences for d≤4, are shown to be proportional to tadpoles of physical massless fields. For type II strings in arbitrary backgrounds, we show by explicit calculations that the ambiguity vanishes at g=2

Fivebrane Lagrangian with Loop Corrections in Field-Theory Limit

Equations of motion and the lagrangian are derived explicitely for Dual D=10, N=1 Supergravity considered as a field theory limit of a Fivebrane. It is used the mass-shell solution of Heterotic String Bianchi Identites obtained in the 2-dimensional $\sigma$-model two-loop approximation and in the tree-level Heterotic String approximation. As a result the Dual Supergravity lagrangian is derived in the one-loop Five-Brane approximation and in the lowest 6-dimensional $\sigma$-model approximaton.Comment: 21 page

Vacuum Energy Cancellation in a Non-supersymmetric String

We present a nonsupersymmetric orbifold of type II string theory and show that it has vanishing cosmological constant at the one and two loop level. We argue heuristically that the cancellation persists at higher loops.Comment: 31 pages harvmac big, 6 figures. New version includes the 2-loop analysis of hep-th/9810129 and elimination of one of the two heuristic arguments for higher loop cancellatio

The mutual information of a stochastic binary channel: validity of the Replica Symmetry Ansatz

We calculate the mutual information (MI) of a two-layered neural network with noiseless, continuous inputs and binary, stochastic outputs under several assumptions on the synaptic efficiencies. The interesting regime corresponds to the limit where the number of both input and output units is large but their ratio is kept fixed at a value $\alpha$. We first present a solution for the MI using the replica technique with a replica symmetric (RS) ansatz. Then we find an exact solution for this quantity valid in a neighborhood of $\alpha = 0$. An analysis of this solution shows that the system must have a phase transition at some finite value of $\alpha$. This transition shows a singularity in the third derivative of the MI. As the RS solution turns out to be infinitely differentiable, it could be regarded as a smooth approximation to the MI. This is checked numerically in the validity domain of the exact solution.Comment: Latex, 29 pages, 2 Encapsulated Post Script figures. To appear in Journal of Physics

Higher Loop Spin Field Correlators in D=4 Superstring Theory

We develop calculational tools to determine higher loop superstring correlators involving massless fermionic and spin fields in four space time dimensions. These correlation functions are basic ingredients for the calculation of loop amplitudes involving both bosons and fermions in D=4 heterotic and superstring theories. To obtain the full amplitudes in Lorentz covariant form the loop correlators of fermionic and spin fields have to be expressed in terms of SO(1,3) tensors. This is one of the main achievements in this work.Comment: 59 pages, 1 figure; v2: final version published in JHE