\(N=2\) strings and selfdual field theories (Q2781762)

This book is also the author's doctoral dissertation submitted to the University of Hannover in 2001. As such it consists to a large part of an up-to-date review of the \(N=2\) supersymmetric string. This object was introduced already in 1976, but has remained in the shadow of the \(N=1\) superstring models ever since, the main reason being that it is consistent only in 2 complex Euclidean or, equivalently, 4 real ultrahyperbolic dimensions. As a consequence its dynamical degrees of freedom may be represented by a single scalar field corresponding to the motion of its centre of mass, and it is not of interest for particle phenomenology. The author's own investigations start from the interesting fact that the tree level amplitudes of the \(N=2\) string are reproduced by a self-dual gravitational and self-dual Yang-Mills theory in the target space for the closed and open string sector, respectively.NEWLINENEWLINE The final chapter of the book is concerned with the question whether the same effective field theories also describe the one-loop amplitudes, in particular the 4-point amplitude. The effective field theory amplitudes have been known to be finite in 4 dimensions and to vanish in 2 (real) dimensions. The string amplitudes can be calculated only in the infinite tension limit and their values depend on the choice of the integration measure in the metric moduli space. For closed strings the natural requirement of modular invariance yields a vanishing amplitude, thus implying the 2-dimensional field theory interpretation, whereas for open strings the requirement of modular invariance is not justified and has to be replaced by an investigation of the ghost zero modes in the path integral. This yields a non-modular invariant integration measure and nonvanishing one-loop amplitudes consistent with the 4-dimensional effective field theory.NEWLINENEWLINE All the mathematical tools required in this technically rather involved investigation are developed in the first four chapters of the book and six appendices. But due to its conciseness a previous acquaintance with string theory will definitely be helpful to the reader.