Симметрии и точные решения в теории гетеротической струны

• Автор: Эррера-Агилар Альфредо
• Шифр специальности: 01.04.02
• Научная степень: Кандидатская
• Год защиты: 1999
• Место защиты: Дубна
• Количество страниц: 94 с.

То ту mother

It is difficult for me to express in words the real feelings of gratitude that I owe to many people who, in one form or another, have played such a significant role in my studies. The point is that when you are studying abroad, it is not only your studies but your whole that is abroad. This means that I do not only have contact with teachers, professors and scientists, but also interact with a whole set of people, who have greatly supported me in my studies and life in Russia. However, there are several persons who played a crucial role in this stage of my life and I want to make some special mentions.
First of all I would like to thank my advisor and friend Dr. 0. V. Kechkin for introducing me to my present field of research, for his great patience to me during my learning and for sharing with me not only his time in hours and hours of work, but also his valuable friendship.
I would like also to thank N. Makhaldiani for his help during the preparation of my candidacy exams, for inspiring me a general interest in science and for his helpful discussions on my work.
I am really grateful to Profr. V.G. Kadyshevsky for giving me the opportunity of carrying out my Ph.D. training at JINR and supporting my application for a fellowship. I really appreciated the unique atmosphere of the Institute and its ability to inspire research students from around the world.
It is a pleasure to thank Profr. B.S. Ishkhanov and Profr. I. V. Puzynin for creating such favorable working conditions both at DEPNI, NPI-MSU and LCTA, JINR; for stimulating the collaboration between both Institutes and for encouraging me during my studies. Special thanks are due to all my former teachers at Russian Peoples ’ Friendship University and, in particular, to Profr. G.N. Shikin, my first advisor, and Profr. Yu. P. Rybakov for their support.
Particularly warm thanks go to those people with whom I shared part of my life outside the physical community, I mean my family and friends. Perhaps I received the biggest support from them and for this reason, I would like to say: thanks a lot to everybody!

Finally I acknowledge the financial support from JINR, CONACYT and SEP.

Contents

Introduction

1 String Motivated Gravity Models

1.1 From String Theory to M-theory
1.2 Effective Field Theory of Heterotic String
2 New Formulation of Heterotic String Theory
2.1 New Chiral Matrix
2.2 Matrix Ernst Potentials
2.3 Israel-Wilson-Perjés Solutions
2.3.1 N=4, D=4 Supergravity
3 Symmetries of Heterotic String Theory
3.1 Charging Symmetries
3.2 Linearizing Potentials
3.3 Class of Invariant Fields under Charging Symmetries
3.4 Solution Generating Technique
4 Truncated Models
4.1 Ernst Formulation of EKRD Theory
4.1.1 Dualization Procedure
4.1.2 Axisymmetric Case
4.1.3 0(d+l,d+l)-symmetry in SL(2,R) Form
4.2 0(2,2)-Symmetric EKR Theory
4.2.1 Kramer-Neugebauer Maps
4.2.2 Double Ernst Solution
4.3 Ernst Formulation of EMDA Theory
4.3.1 Charging symmetries
4.3.2 Linearizing potentials

CHAPTER 2. NEW FORMULATION OF HETEROTIC STRING THEORY
where R2 — x2 + y2 + (z + ia)2, M is a complex d + 1-dimensional constant matrix with arbitrary components mpp = fhpq + inpq, and a is a real constant. We choose M and R in this way in order to deal with rotating black hole-type solutions (in this case we have a ring singularity) when the NUT charges of the field system are set to zero (general Israel-Wilson-Perjes solutions include both NUT charge and angular momentum). Since all variables entering the action (2.27) and the equations of motion (2.28) are real, in this work we shall restrict ourselves to a real class of solutions. However, because of the indefinite character of S, matrix b is complex in general, as well as the potential A. We can proceed as follows: Let us require just the first two rows of b to be real (leaving the remaining components imaginary), then we perform the matrix product (2.45) and set the factors that multiply the imaginary components of b to zero. It turns out that this condition imposes the following restriction on the matrix M

mu 1
m i2 m2 2 mr+i

(2.49)
where Od_i denotes a (d — l)-dimensional square array of zeroes and r = 2
At this stage we are able to calculate the three-fields G, B, A, , u, v and s from the relations (2.48) and (2.45). By studying their asymptotic behaviour one can establish the following relation between the integration constants and the physical parameters of the theory

Ra lhr+1

ràjT+1

-u-fp-
Cr Ras

ÂLas

2(m2ibu + m22b2I)/Ras -2(rhr+lylbu + mr+li2b2I)/Ra
çl_ )
Ras
Id-i , ?
mu D
Ras P ’ 1 as
( Q'e/Ra
I Ql/Ra, I