Algebraic Structure of String Field Theory [electronic resource] / by Martin Doubek, Branislav Jurčo, Martin Markl, Ivo Sachs.

Relativistic Point Particle -- String Theory -- Open and closed strings -- Open-closed BV equation -- A- and L-algebras -- Homotopy involutive Lie bialgebras -- Operads -- Feynman transform of a modular operad -- Structures relevant to physics.

This book gives a modern presentation of modular operands and their role in string field theory. The authors aim to outline the arguments from the perspective of homotopy algebras and their operadic origin. Part I reviews string field theory from the point of view of homotopy algebras, including A-infinity algebras, loop homotopy (quantum L-infinity) and IBL-infinity algebras governing its structure. Within this framework, the covariant construction of a string field theory naturally emerges as composition of two morphisms of particular odd modular operads. This part is intended primarily for researchers and graduate students who are interested in applications of higher algebraic structures to strings and quantum field theory. Part II contains a comprehensive treatment of the mathematical background on operads and homotopy algebras in a broader context, which should appeal also to mathematicians who are not familiar with string theory.