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Planar homotopy algebras and open-string field theory
Planar homotopy algebras and open-string field theory
This thesis is concerned about the existence of a open-string field theory that is consistent at the quantum level without coupling to the closed string. We want to achieve this via a restriction to planar Feynman graphs. Our aim is to formulate this theory in the mathematical language of homotopy algebras. We further ask whether such a formulation is applies also to general gauge theories, in particular in the limit of large gauge groups. Finally, we will discuss the problems of such a formulation, as well as how these can be solved by lifting the restriction to planar diagrams only. This work should also serve as an extensive introduction to the Batalin-Vilkovisky formalism. We look at different mathematical aspects of this formalism and its relation to homotopy algebras.
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Chiaffrino, Christoph
2020
English
Universitätsbibliothek der Ludwig-Maximilians-Universität München
Chiaffrino, Christoph (2020): Planar homotopy algebras and open-string field theory. Dissertation, LMU München: Faculty of Physics
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Abstract

This thesis is concerned about the existence of a open-string field theory that is consistent at the quantum level without coupling to the closed string. We want to achieve this via a restriction to planar Feynman graphs. Our aim is to formulate this theory in the mathematical language of homotopy algebras. We further ask whether such a formulation is applies also to general gauge theories, in particular in the limit of large gauge groups. Finally, we will discuss the problems of such a formulation, as well as how these can be solved by lifting the restriction to planar diagrams only. This work should also serve as an extensive introduction to the Batalin-Vilkovisky formalism. We look at different mathematical aspects of this formalism and its relation to homotopy algebras.