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Quantum Open-Closed Homotopy Algebra and String Field Theory
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We reformulate the algebraic structure of Zwiebach's quantum open-closed string field theory in terms of homotopy algebras. We call it the quantum open-closed homotopy algebra (QOCHA) which is the generalization of the open-closed homotopy algebra (OCHA) of Kajiura and Stasheff. The homotopy formulation reveals new insights about deformations of open string field theory by closed string backgrounds. In particular, deformations by Maurer Cartan elements of the quantum closed homotopy algebra define consistent quantum open string field theories.
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Universal quadratic field equations via homotopy algebras
The bar-cobar construction turns the equations of motion of any homotopy-algebra gauge theory into universal quadratic Maurer-Cartan equations, with solutions equivalent to the original theory.
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