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G. S. Danilov

Publications and source records attributed to G. S. Danilov.

14 recordsLinked to original sources
arXiv2015

Calculation of multi-loop superstring amplitudes

Multi-loop interaction amplitudes in the theory of the closed, oriented superstrings are obtained by the integration of local amplitudes which are represented by a sum of the spinning string local amplitudes. The last local amplitudes are given explicitly through super-Schottky group parameters and interaction vertex coordinates on the $(1|1)$ complex supermanifold. The integration is ambiguous under those replacements of the integration variables which admix Grassmann variables to the boson ones. So the calculation is guided by a preservation of local symmetries of the superstring. The obtained amplitudes are free from divergences and consistent with the world-sheet symmetries. The vacuum amplitude and 1-, 2- and 3-point amplitudes of massless states vanish once the integration over certin modular variables and interaction vertex coordinates.

hep-th↗
arXiv2012

Calculation and modular properties of multi-loop superstring amplitudes

Multi-loop superstring amplitude are calculated in the convenient gauge where Grassmann moduli are carried by the 2D gravitino field. Generally, instead of the modular symmetry, the amplitudes hold the symmetry under modular transformations added by relevant transformations of the 2D local supersymmetry. If a number of loops is larger than 3, the integration measures are not modular forms. In this case the expression for the amplitude contains an integral over the bound of the fundamental region of the modular group.

hep-th↗
arXiv2009

Resonance capture by hydrogenous impurities and losses of ultracold neutrons in solid material traps

The capture of trapped ultracold neutrons (UCNs) by closed hydrogenous impurities within a solid coating of the trap is discussed as a possible cause of observed anomalously large losses of UCNs in solid material UCN traps. Then significant losses of UCNs arise only if resonances occur in the UCN-impurity scattering amplitude. For a large size impurity, higher partial waves in the UCN-impurity interaction are important, and they are taken into account in the present paper. The method of the calculation is applicable to irregular shape impurities as well. A small distortion of an impurity shape, if it splits the resonance, can increase the UCN losses by a few times. UCN losses in the beryllium trap are calculated assuming they are due to the UCN capture by ice spherical impurities within the coating of the trap walls. Both s- and p-wave resonances contribute significantly to the UCN losses considered. As an example, observed anomalous large UCN losses are achieved if the average radius of the impurity is about 600 Angstroms and the impurity density is about 3*10^{14}/cm^3. A distortion of the spherical shape of the impurity could increase the UCN losses and therefore decrease the impurity density.

nucl-th↗
arXiv2006

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.

hep-ph↗
arXiv2003

On cruel mistakes in the calculation of multi-loop superstring amplitudes, the ambiguity of the modular integral and the integration over the module space

Widely spread cruel misconceptions and mistakes in the calculation of multi-loop superstring amplitudes are exposed. Correct calculations are given. It is shown that the cardinal mistake in the gauge fixing procedure presents ab ovo in the Verlinde papers. The mistake was reproduced in following proposals including the recent papers. The modular symmetry of the multi-loop superstring amplitudes is clarified, an incorrectness of previous conjectures being shown. It is shown that the Berezin-type integral versus boson and fermion moduli is doubt under non-split transformations mixing fermion integration variables to the boson integration ones. In particular, due to singularities in moduli of the given spin structure, the integral can be finite or divergent dependently on the integration variables employed. Hence, unlike naive expectations, the multi-loop superstring amplitude is ambiguous. Nevertheless, the ambiguity is totally resolved by the requirement to preserve local symmetries of the superstring amplitude. In the Verlinde world-sheet description it includes, among other thing, the requirement that the amplitude is independent of the gravitino field locations. In action the resolution of the ambiguity in the Verlinde scheme is achieved by going to the supercovariant gauge. As it has been argued earlier, the resulted arbitrary-loop amplitudes are finite.

hep-th↗
arXiv2001

Using of unitarity equations for the calculation of fermion interaction amplitudes in the superstring theory

The unitarity equations for the boson interaction amplitudes in the superstring theory are used to calculate the interaction amplitudes including the Ramond states, which are 10-fermion and Ramond bosons. The n-loop, 4-point amplitude with two massless Neveu-Schwarz bosons and two massless Ramond states is obtained explicitly. It is shown that, in addition, the unitarity equations require some integral relations for local functions determining the amplitude. For the tree amplitude the validness of the above integral relations is verified.

hep-th↗
arXiv2001

Manifest calculation and the finiteness of the superstring Feynman diagrams

The multi-loop amplitudes for the closed, oriented superstring are represented by finite dimensional integrals of explicit functions calculated through the super-Schottky group parameters and interaction vertex coordinates on the supermanifold. The integration region is proposed to be consistent with the group of the local symmetries of the amplitude and with the unitarity equations. It is shown that, besides the SL(2) group, super-Schottky group and modular one, the total group of the local symmetries includes an isomorphism between sets of the forming group transformations, the period matrix to be the same. The singular integration configurations are studied. The calculation of the integrals over the above configurations is developed preserving all the local symmetries of the amplitude, the amplitudes being free from divergences. The nullification of the 0-, 1-, 2- and 3-point amplitudes of massless states is verified. Vanishing the amplitudes for a longitudinal gauge boson is argued.

hep-th↗
arXiv1998

Finiteness of multi-loop superstring amplitudes

Superstring amplitudes of an arbitrary genus are calculated through super-Schottky parameters by a summation over the fermion strings. For a calculation of divergent multi-loop fermion string amplitudes a supermodular invariant regularization procedure is used. A cancellation of divergences in the superstring amplitudes is established. Grassmann variables are integrated, the superstring amplitudes are obtained to be explicitly finite and modular invariant.

hep-th↗
arXiv1995

Unimodular transformations of the supermanifolds and the calculation of the multi-loop amplitudes in the superstring theory

The modular transformations of the $(1|1)$ complex supermanifolds in the like-Schottky modular parameterization are discussed. It is shown that these "supermodular" transformations depend on the spinor structure of the supermanifold by terms proportional to the odd modular parameters. The above terms are calculated in the explicit form. They are urgent for the divergency problem in the Ramond-Neveu-Schwarz superstring theory and for calculating the fundamental domain in the modular space. The supermodular transformations of the multi-loop superstring partition functions calculated by the solution of the Ward identities are studied. The above Ward identities are shown to be covariant under the supermodular transformations. So the partition functions necessarily possess the covariance under the transformations discussed. It is demonstrated explicitly the covariance of the above partition functions at zero odd moduli under those supermodular transformations, which turn a pair of even genus-1 spinor structures to a pair of the odd genus-1 spinor ones. The brief consideration of the cancellation of divergences is given.

hep-th↗
arXiv1995

Electromagnetic fields providing charge screening and confinement in two-dimensional massless electrodynamics

The charge screening, confinement of fermion quantum numbers and the chiral condensate formation in two-dimensional QED is studied in details. It is shown that charge screening and confinement of fermion number in two-dimensional QED is due to an appearance of gauge fields which nullify the Dirac determinant. An appearance of the fields of another type but with the same property yield the chiral condensate formation. In addition, these second type fields ensure the "softness" of the charge screening in a process which is analogous to the $e^+e^-$ annihilation.

hep-th↗
arXiv1995

The calculation of Feynman diagrams in the superstring perturbation theory

The method of the calculation of the multi-loop superstring amplitudes is proposed. The amplitudes are calculated from the equations that are none other than Ward identities. They are derived from the requirement that the discussed amplitudes are independent from a choice of gauge of both the vierbein and the gravitino field. The amplitudes are calculated in the terms of the superfields vacuum correlators on the complex (1|1) supermanifolds. The superconformal Schottky groups appropriate for this aim are built for all the spinor structures. The calculation of the multi- loop boson emission amplitudes in the closed, oriented Ramond-Neveu-Schwarz superstring theory is discussed in details. The main problem arises for those spinor structures that correspond to the Ramond fermion loops. Indeed, in this case the superfield vacuum correlators can not be derived by a simple extension of the boson string results. The method of the calculation of the above correlators is proposed. The discussed amplitudes due to all the even spinor structures is given in the explicit form.

hep-th↗
arXiv1994

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.

hep-th↗
arXiv1993

Explicit Calculation of Multiloop Amplitudes in the Superstring Theory

Multiloop superstring amplitudes are calculated in the explicit form by the solution of Ward identities. A naive generalization of Belavin-Knizhnik theorem to the superstring is found to be incorrect since the period matrix turns out to be depended on the spinor structure over the terms proportional to odd moduli. These terms appear because fermions mix bosons under the two-dim. supersymmetry transformations. The closed, oriented superstring turns out to be finite, if it possesses the ten-dimensional supersymmetry, as well as the two-dimentional one. This problem needs a further study.

hep-th↗