New moduli spaces from string background independence consistency conditions

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.

Building string field theory around non-conformal backgrounds

“…Our studies in Ref. [ 8] show that for k = 2 we have n ≥ 1. The real dimensionality of B k n exceeds by k that of the moduli space M k+n of punctured spheres.…”

“…(2.10) of Ref. [ 8]. There are (k 1 k 2 + k 1 + k 2 ) minus signs that arise from moving all the F states to the right.…”

“…The Batalin Vilkovisky algebra of surfaces with ordinary punctures [ 3], was extended to this more general case in Ref. [ 8]. The main results are summarized below.…”

“…covariant derivatives gives Much of the work in [ 8] went into constructing the hamiltonian B µν and showing that it was defined by moduli spaces of surfaces having two special punctures. We now show that higher conditions arise and could be used to define moduli spaces of surfaces having more than two special punctures.…”

“…⋆ We write B = k,p B k p where B k p denotes a moduli space of spheres with k special punctures and p ordinary punctures. In this complex we have an antibracket operation, which corresponds to the sewing of ordinary punctures of the corresponding surfaces, and an operator K that acting on a moduli space of surfaces it adds one special puncture to the each of the surfaces [ 8]. The operator K satisfies the identity K 2 = 0, and this is related to the fact that any space in the complex is defined to be antisymmetric under the exchange of the labels on any two of the special punctures.…”