2d gravity stress tensor and the problem of the calculation of the multi-loop amplitudes in the string theory

It is shown that the vacuum value of the $2d$ gravity stress tensor in the free field theory is singular in the fundamental region on the complex plane where the genus-$n>1$ Riemann surface are mapped. Because of the above singularity, one can not construct modular invariant multi-loop amplitudes. The discussed singularity is due to the singularity in the vacuum value of the $2d$ gravity field that turns out to be on the genus-$n>1$ Riemann surfaces.Comment: 13 pages, LATEX, November 199

BFKL Pomeron in string models

We consider scattering amplitudes in string models in the Regge limit of high energies and fixed momentum transfers with the use of the unitarity in direct channels. Intermediate states are taken in the multi-Regge kinematics corresponding to the production of resonances with fixed invariant masses and large relative rapidities. In QCD such kinematics leads to the BFKL equation for the Pomeron wave function in the leading logarithmic approximation. We derive a similar equation in the string theory and discuss its properties. The purpose of this investigation is to find a generalization of the BFKL approach to the region of small momentum transfers where non-perturbative corrections to the gluon Regge trajectory and reggeon couplings are essential. The BFKL equation in the string theory contains additional contributions coming from a linear part of the Regge trajectory and from the soft Pomeron singularity appearing already in the tree approximation. In higher dimensions in addition, a non-multi-Regge kinematics corresponding to production of particles with large masses is important. We solve the equation for the Pomeron wave function in the string theory for D=4 and discuss integrability properties of analogous equations for composite states of several reggeised gluons in the multi-colour limit.Comment: 48 pages, 2 figure

Molecular regimes in ultracold Fermi gases

The use of Feshbach resonances for tuning the interparticle interaction in ultracold Fermi gases has led to remarkable developments, in particular to the creation and Bose-Einstein condensation of weakly bound diatomic molecules of fermionic atoms. These are the largest diatomic molecules obtained so far, with a size of the order of thousands of angstroms. They represent novel composite bosons, which exhibit features of Fermi statistics at short intermolecular distances. Being highly excited, these molecules are remarkably stable with respect to collisional relaxation, which is a consequence of the Pauli exclusion principle for identical fermionic atoms. The purpose of this review is to introduce theoretical approaches and describe the physics of molecular regimes in two-component Fermi gases and Fermi-Fermi mixtures, focusing attention on quantum statistical effects.Comment: Chapter of the book: "Cold Molecules: Theory, Experiment, Applications" edited by R. V. Krems, B. Friedrich and W. C. Stwalley (publication expected in March 2009

Parity-violating neutron spin rotation in hydrogen and deuterium

We calculate the (parity-violating) spin rotation angle of a polarized neutron beam through hydrogen and deuterium targets, using pionless effective field theory up to next-to-leading order. Our result is part of a program to obtain the five leading independent low-energy parameters that characterize hadronic parity-violation from few-body observables in one systematic and consistent framework. The two spin-rotation angles provide independent constraints on these parameters. Using naive dimensional analysis to estimate the typical size of the couplings, we expect the signal for standard target densities to be 10^-7 to 10^-6 rad/m for both hydrogen and deuterium targets. We find no indication that the nd observable is enhanced compared to the np one. All results are properly renormalized. An estimate of the numerical and systematic uncertainties of our calculations indicates excellent convergence. An appendix contains the relevant partial-wave projectors of the three-nucleon system.Comment: 44 pages, 17 figures; minor corrections; to be published in EPJ

Three-body problem in Fermi gases with short-range interparticle interaction

We discuss 3-body processes in ultracold two-component Fermi gases with short-range intercomponent interaction characterized by a large and positive scattering length $a$. It is found that in most cases the probability of 3-body recombination is a universal function of the mass ratio and $a$, and is independent of short-range physics. We also calculate the scattering length corresponding to the atom-dimer interaction.Comment: 4 pages, 2 figure

Parity violation in nuclear systems

Parity violation in nuclear systems is reviewed. A few ingredients relevant to the description of the parity-violating nucleon-nucleon force in terms of meson exchanges are reminded. Effects in nuclear systems are then considered. They involve pp scattering, some complex nuclei and the deuteron system.Comment: 4 pages, to be published in the proceedings of the worksho

Is the Luttinger liquid a new state of matter?

We are demonstrating that the Luttinger model with short range interaction can be treated as a type of Fermi liquid. In line with the main dogma of Landau's theory one can define a fermion excitation renormalized by interaction and show that in terms of these fermions any excited state of the system is described by free particles. The fermions are a mixture of renormalized right and left electrons. The electric charge and chirality of the Landau quasi-particle is discussed.Comment: paper 10 pages. This version of the paper will be published in Foundations of Physic

Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring

A ten-dimensional super-Poincare covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincare covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and to construct a suitable $b$ ghost. A super-Poincare covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N<4, confirming the perturbative finiteness of superstring theory. One can also prove the Type IIB S-duality conjecture that $R^4$ terms in the effective action receive no perturbative contributions above one loop.Comment: 45 pages harvmac tex, added minor clarification

Parity nonconservation in deuteron photoreactions

We calculate the asymmetries in parity nonconserving deuteron photodisintegration due to circularly polarized photons gamma+d to n+p with the photon laboratory energy ranging from the threshold up to 10 MeV and the radiative capture of thermal polarized neutrons by protons n+p to gamma+d. We use the leading order electromagnetic Hamiltonian neglecting the smaller nuclear exchange currents. Comparative calculations are done by using the Reid93 and Argonne v18 potentials for the strong interaction and the DDH and FCDH "best" values for the weak couplings in a weak one-meson exchange potential. A weak NDelta transition potential is used to incorporate also the Delta(1232)-isobar excitation in the coupled-channels formalism.Comment: 14 pages, 13 figures (18 eps files), LaTeX2

Parity nonconserving cold neutron-parahydrogen interactions

Three pion dominated observables of the parity nonconserving interactions between the cold neutrons and parahydrogen are calculated. The transversely polarized neutron spin rotation, unpolarized neutron longitudinal polarization, and photon-asymmetry of the radiative polarized neutron capture are considered. For the numerical evaluation of the observables, the strong interactions are taken into account by the Reid93 potential and the parity nonconserving interactions by the DDH model along with the two-pion exchange.Comment: 17 pages, 2 figure