Muenster, Korbinian (2013): String field theory: algebraic structure, deformation properties and superstrings. Dissertation, LMU München: Faculty of Physics 

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Muenster_Korbinian.pdf 11MB 
Abstract
This thesis discusses several aspects of string field theory. The first issue is bosonic openclosed string field theory and its associated algebraic structure  the quantum openclosed homotopy algebra. We describe the quantum openclosed homotopy algebra in the framework of homotopy involutive Lie bialgebras, as a morphism from the loop homotopy Lie algebra of closed string to the involutive Lie bialgebra on the Hochschild complex of open strings. The formulation of the classical/quantum openclosed homotopy algebra in terms of a morphism from the closed string algebra to the open string Hochschild complex reveals deformation properties of closed strings on open string field theory. In particular, we show that inequivalent classical open string field theories are parametrized by closed string backgrounds up to gauge transformations. At the quantum level the correspondence is obstructed, but for other realizations such as the topological string, a nontrivial correspondence persists. Furthermore, we proof the decomposition theorem for the loop homotopy Lie algebra of closed string field theory, which implies uniqueness of closed string field theory on a fixed conformal background. Second, the construction of string field theory can be rephrased in terms of operads. In particular, we show that the formulation of string field theory splits into two parts: The first part is based solely on the moduli space of world sheets and ensures that the perturbative string amplitudes are recovered via Feynman rules. The second part requires a choice of background and determines the real string field theory vertices. Each of these parts can be described equivalently as a morphism between appropriate cyclic and modular operads, at the classical and quantum level respectively. The algebraic structure of string field theory is then encoded in the composition of these two morphisms. Finally, we outline the construction of type II superstring field theory. Specific features of the superstring are the appearance of Ramond punctures and the picture changing operators. The sewing in the Ramond sector requires an additional constraint on the state space of the world sheet conformal field theory, such that the associated symplectic structure is nondegenerate, at least onshell. Moreover, we formulate an appropriate minimal area metric problem for type II world sheets, which can be utilized to sketch the construction of a consistent set of geometric vertices. The algebraic structure of type II superstring field theory is that of a $\mathcal{N}=1$ loop homotopy Lie algebra at the quantum level, and that of a $\mathcal{N}=1$ homotopy Lie algebra at the classical level.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  String Field Theory, Superstrings, Homotopy Algebras, Deformation Theory 
Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date of oral examination:  23. July 2013 
1. Referee:  Sachs, Ivo 
MD5 Checksum of the PDFfile:  e9cccb67ae406c2e66978a1ad999c008 
Signature of the printed copy:  0001/UMC 21510 
ID Code:  16096 
Deposited On:  19. Sep 2013 08:37 
Last Modified:  20. Jul 2016 10:34 