Partition-function representation for the open superstring effective action:: Cancellation of Möbius infinites and derivative corrections to Born-Infeld lagrangian

Abstract

We justify the σ-model partition-function representation for the open superstring effective action (EA) for massless vector fields. We first consider the open Bose string theory and interpret Möbius infinites present in on-shell amplitudes before Möbius gauge fixing as a part of power 2-d UV infinities of the regularized Bose string theory. This helps to clarify the relation between the partition function Z and the EA. We find that in the Bose string theory Z does not exactly coincide with EA (they differ in one of F 2 ∂F ∂F-terms). This difference (connected with the fact that the open Bose string Möbius volume is linearly divergent) disappears in the open superstring theory where the super-Möbius volume is finite. The cancellation of power infinities in the superstring theory implies the absence of Möbius infinities and hence the possibility to compute the superstring amplitudes without fixing a (super) Möbius gauge. This proves the equivalence between the renormalized Z and the EA (renormalization of pure logarithmic infinities corresponds to subtraction of massless exchanges). This equivalence is checked by explicit computations and applied to establish the absence of the leading field-strength derivative-dependent correction ∂F ∂F f( F) to the Born-Infeld term in the open superstring EA (there are, however, ∂∂F ∂∂FFF terms in the EA). We also emphasize the advantages of the σ-model approach based on the generating functional Z over the standard vertex operator approach. In particular, we find that the manifestly 2-d supersymmetric and gauge-invariant Z (defined as the 2-d expectation value of the 1-d supersymmetric generalization of the “ tr P exp”- factor) automatically contains the contact terms which are necessary to add to the standard expressions for the amplitudes in order to ensure their 2-d supersymmetry and gauge invariance without need to rely on analytic continuation in momenta.