Communications in Mathematical Physics

, Volume 330, Issue 3, pp 1227–1262 | Cite as

Homotopy Classification of Bosonic String Field Theory

  • Korbinian MünsterEmail author
  • Ivo Sachs


We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.


Modulus Space Open String Topological String Closed String Coder Cycl 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Arnold Sommerfeld Center for Theoretical PhysicsMunichGermany

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