Dynamics of a Scalar Field along a Flat Direction in de Sitter Space

Abstract

Listen

Translate article

It is known that a scalar potential of a global supersymmetric model often has a special direction called the flat direction/> along which the value of the scalar potential remains unchanged. The potential energy of a supersymmetric model is given by a linear combination of F;* F; and DaDa,z> where F; and Da are auxiliary fields in scalar multiplets and vector multiplets, respectively. Therefore, the flat direction is characterized by conditions*> F;(¢)=0 and Da(¢)=0. If these conditions have non-trivial solutions in terms of the scalar fields ¢, there exists a flat direction. An example in supersymmetric SU(5) grand unified theory (GUT) can easily be found. > The condition of the flat direction imply the supersymmetry is not spontaneously broken,> while the presence of the vacuum expectation value along the direction in general breaks the gauge and global symmetries. It is also possible to show that, in the supersymmetric models, the flat direction does not receive any radiative correction as a result of the non-renormalization theorem.> The unbroken supersymmetry and the absence of the radiative correction are interesting characteristics of the flat direction. With a supersymmetry breaking mass m, on the other hand, the direction receives a logarithmic radiative correction proportional to the breaking mass squared m • In this paper we evaluate the one-loop effective action along the flat direction in the de Sitter space**> using the derivative expansion method. Our original interest is the effective potential along the flat direction in the inflationary expanding universe. Our analysis is relevant for the baryogenesis scenario by the Affieck-Dine mechanism/> in which it is supposed that scalar fields along the flat direction initially have a large expectation value of the order of the GUT scale. Then after inflation and when the Hubble parameter becomes of order of supersymmetric breaking mass scale m (that is of order of the weak scale mw), the scalar fields begin to fall down along the flat direction. The motion of scalar fields (say the squark fields) generates a condensation of the baryon number density and decays into light particles.