On the construction of classical superstring field theories

by Sebastian Johann Konopka

Institution: Ludwig-Maximilians-Universität
Year: 2016
Posted: 02/05/2017
Record ID: 2065313
Full text PDF: https://edoc.ub.uni-muenchen.de/19874/


This thesis describes the construction of classical superstring field theories based on the small Hilbert space. First we describe the traditional construction of perturbative superstring theory as an integral over the supermoduli space of type II world sheets. The geometry of supermoduli space dictates many algebraic properties of the string field theory action. In particular it allows for an algebraisation of the construction problem for classical superstring field theories in terms of homotopy algebras. Next, we solve the construction problem for open superstrings based on Witten’s star product. The construction is recursive and involves a choice of homotopy operator for the zero mode of the η-ghost. It turns out that the solution can be extended to the Neveu-Schwarz subsectors of all superstring field theories. The recursive construction involves a hierarchy of string products at various picture deficits. The construction is not entirely natural, but it is argued that different choices give rise to solutions related by a field redefinition. Due to the presence of odd gluing parameters for Ramond states the extension to full superstring field theory is non-trivial. Instead, we construct gauge-invariant equations of motion for all superstring field theories. The realisation of spacetime supersymmetry in the open string sector is highly non-trivial and is described explicitly for the solution based on Witten’s star product. After a field redefinition the non-polynomial equations of motion and the small Hilbert space constraint become polynomial. This polynomial system is shown to be supersymmetric. Quite interestingly, the supersymmetry algebra closes only up to gauge transformations. This indicates that only the physical phase space realizes N = 1 supersymmetry. Apart from the algebraic constraints dictated by the geometry of supermoduli space the equations of motion or action should reproduce the traditional string S-matrix. The S-matrix of a field theory is related to the minimal model of the associated homotopy algebra. Because of the recursive nature of the solution and its construction in terms of products of various picture deficits, it is possible to relate the S-matrices of various picture deficits and, therefore, relate the S-matrix calculated from the bosonic string products at highest picture deficit with the physical vertices at lowest picture deficit through a series of descent equations. For open superstrings one can go beyond the equations of motion. The presence of picture changing operators at internal Ramond lines imposes either a constraint on the Hilbert space or necessitates the introduction of an auxiliary string field at picture −3/2. Based on the full equations of motion for the open string field, an action principle is proposed and shown to be gauge-invariant. Diese Dissertation behandelt die Konstruktion von klassischen Superstringfeldtheorien basierend auf dem kleinen Hilbertraum. Zuerst wird die traditionelle Konstrukti- on der störungstheoretischen Superstringtheorie mittels… Advisors/Committee Members: Sachs, Ivo (advisor).