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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.
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