New Moduli Spaces from String Background Independence Consistency Conditions

TL;DR

This paper develops a new framework for string field theory using moduli spaces of punctured Riemann surfaces with special punctures, aiming for background-independent formulations and exploring their algebraic properties.

Contribution

It introduces a novel construction of moduli spaces with multiple special punctures and links them to background independence in string field theory, including recursion relations and cohomology implications.

Findings

Moduli spaces with two special punctures satisfy specific antisymmetry and recursion relations.

The theory supports a background-independent approach to string field theory.

Partial antibracket cohomology theorem for the string action is established.

Abstract

In string field theory an infinitesimal background deformation is implemented as a canonical transformation whose hamiltonian function is defined by moduli spaces of punctured Riemann surfaces having one special puncture. We show that the consistency conditions associated to the commutator of two deformations are implemented by virtue of the existence of moduli spaces of punctured surfaces with two special punctures. The spaces are antisymmetric under the exchange of the special punctures, and satisfy recursion relations relating them to moduli spaces with one special puncture and to string vertices. We develop the theory of moduli spaces of surfaces with arbitrary number of special punctures and indicate their relevance to the construction of a string field theory that makes no reference to a conformal background. Our results also imply a partial antibracket cohomology theorem for the string action.