N = 4 Supergravitation einer T² - kompaktifizierten sechsdimensionalen Theorie,
N = 4 supergravity of a T² - compactified sixdimensional theory [German], Thesis
Abstract: Supergravitational theories can be considered as low energy limit of string theories which are supposed to be good candidates in order to unify quantum theory and Einstein's general relativity. Unfortunately string theories and - in the same way - supergravitational theories live in more than four space- time dimensions so that one has to reduce the whole theory from D > 4 dimensions down to D = 4 dimensions. In this thesis the bosonic part of a sixdimensional supergravity shall be reduced to four dimensions on a two- dimensional torus T². The resulting action can be compared with a general action which describes every N = 4 supergravity so that all components, which form the general action, can be determined with the help of all terms appearing in the reduced action. For this purpose one has to treat the massless and massive case separatly. At first one can determine some components of the general theory in the massless case. Indeed, this task seems to become very difficult because there are two-form fields in the reduced theory which do not appear in the general action (the same problem appears for electric and magnetic vectors). In order to solve this problem one has to dualize these fields: Two-form fields are dual to scalars and magnetic vectors are dual to electric vectors. After having performed these dualizations it is possible to determine all terms which construct the massless theory and to rewrite the reduced theory in the general form of the N = 4 supergravity in four dimensions. These terms have to be valid for the massive theory,too, because this theory has to go over to the massless theory in the limit of vanishing masses. But there are additional parameters which do not appear in the massless case. Using the formerly determined terms it is possible to determine these missing parameters. This finally leads to the conclusion that actually the action which has been deduced by dimensional reduction can be rewritten in the general way every N = 4 supergravity can be formed in four dimensions.