On off-shell structure of open string sigma model

TL;DR

This paper investigates the off-shell structure of the open string sigma model, analyzing the effective action, scattering amplitudes, and boundary interactions, and demonstrates consistency with on-shell conditions and mass spectra.

Contribution

It provides a detailed analysis of the off-shell structure, computes the cubic and quadratic terms, and discusses the effects of nonrenormalizable boundary interactions in open string sigma models.

Findings

Cubic term in the effective action vanishes for some off-shell configurations.

Quadratic boundary action reproduces on-shell conditions for massive fields.

Tachyon quadratic term correctly yields the tachyon mass.

Abstract

We analyze several problems related to off-shell structure of open string sigma model by using a combination of derivative expansion and expansion in powers of the fields. According to the sigma model approach to bosonic open string theory, the tachyon effective action $S(T)$ coincides with the renormalized partition function $Z(T)$ of sigma model on a disk, up to a term vanishing on shell. On the other hand, $Z(T)$ is a generating functional of perturbative open string scattering amplitudes. If $S(T) = Z(T)$, then there should be no contribution of exchange diagrams to string amplitudes computed using $S(T)$. We compute the cubic term in the effective action, and show that it vanishes if some but not all external legs are on shell, and, therefore, any exchange diagram involving the cubic term vanishes too. Then, we discuss a problem of turning on nonrenormalizable boundary interactions, corresponding to massive string modes. We compute the quadratic term for a symmetric tensor field, and show that despite nonrenormalizability of the model one can consistently remove all divergent terms, and obtain a quadratic action reproducing the on-shell condition for the field. We also briefly discuss fermionic (NS) sigma model, compute the tachyon quadratic term, and show that it reproduces the correct tachyon mass. We note that turning on a massive symmetric tensor field leads to the appearance of a term linear in it, which can be removed by adding a higher-derivative term to the boundary of the disc.