Open String Renormalization Group Flow as a Field Theory

Abstract

This article shows that the integral flow-lines of the RG-flow of open string theory can be interpreted as the solitons of a Hořova–Lifshitz sigma-model of open membranes. The authors argue that the effective background description of this model implies the g-theorem of open string theory. Its close connection to boundary string field theory is described. Additionally, the study endows the Hilbert space of the open membrane with a graded non-commutative, associative, cyclic algebra and construct an open membrane field theory, whose action measures the energy difference between different backgrounds in open string field theory. The authors use an identity-based membrane field to proof Sen's conjecture. Finally, the ideas are applied to the topological string and it is shown that the membrane action is quantized in equivariant K-theory of the moduli space of framed instantons.