The Low Energy Effective Action From the Heterotic Superstring

[摘要] The heterotic superstring has been considered to be a candidate for a quantised unified theory of all physical interactions at high energies, including the unification of quantised gravity. The low energy phenomenology of such a theory is most easily described in terms of an effective quantum field theory, which describes the scattering of the massless modes of the string theory, as well as satisfying the anomaly freedom, supersymmetry, unitarity, etc. of the string theory. Previous attempts at the derivation of the low energy effective theory have concentrated on the bosonic sector of the action, and on the possible ambiguities in the dervivation of this action. This thesis describes an attempt to derive the effective field theory including the fermionic sector of the theory, with the hope that the resulting action will demonstrate the supersymmetry of the heterotic superstring, as well as the anomaly freedom. After an introduction to the construction of the free heterotic superstring, and the corresponding interacting string theory, two amplitudes are calculated. It is shown that these amplitudes naturally expand in a power series in the string parameter a'. The attempt at constructing a low energy theory which will reproduce these amplitudes order by order in this parameter will then be made. The effective theory which has the same matter spectrum as the massless modes of the heterotic string is stated, and this free theory is quantised. The techniques of constrained quantisation are used to evaluate the propagators for the various fields of the theory. A comment will be made on the problems of quantisating higher derivative theories, and an ansatz will be made to avoid these problems. The interacting field theory, which is uniquely determined by the Noether method is stated. It is noted that the required anomaly freedom of this action can only be included at the expense of supersymmetry, by the addition of a term of higher order in the parameter a'. The lowest order action thus derived is then used to construct the lowest order amplitudes in the a' parameter, (that is 0(a')), which are compared with the corresponding string results. It is shown that the effective field theory gives the same amplitudes as the string theory. The field theory is then extended in an attempt to match the next highest order amplitudes in the a' parameter, and also to retrieve the lost supersymmetry of the lowest order action. In this regard, known supersymmetric actions are used to construct the amplitudes at the appropriate level in the a' parameter, and these amplitudes are compared with the string results. These matching calculations are shown to fail implying that these actions do not correspond to the low energy effective action for the heterotic string theory. A more general action is constructed, subject to a guiding assumption that the action only contains the two-form form of the covariant derivative of the gravitino, and without regard to supersymmetry, which is then used to construct amplitudes which are compared to the string result. A match to the string amplitude is then found for specific values for the general coefficients introdced in this action. A comparison with the two actions previously used as trial low energy effective field theories is drawn, and the similarities and differences noted. Finally some comments are made on the possibility of ambiguities which may be inherent in the procedure described in this thesis for deriving the low energy effective action. Some examples of field redefinitions which do not show the same properties as the field redefinitions used in the purely bosonic cases previously treated in the literature. The implications for the amplitude matching procedure are then noted. The conclusions of this work are then presented.

[发布机构] University:University of Glasgow

[关键词] Theoretical physics