Abstract
In some string theories, e.g. SO(32) heterotic string theory on Calabi-Yau manifolds, a massless field with a tree level potential can acquire a tachyonic mass at the one loop level, forcing us to quantize the theory around a new background that is not a solution to the classical equations of motion and hence is not described by a conformally invariant world-sheet theory. We describe a systematic procedure for carrying out string perturbation theory around such backgrounds.
Highlights
The above example provides the motivation for our analysis, we shall address this in a more general context
We describe a systematic procedure for carrying out string perturbation theory around such backgrounds
We consider a general situation in string theory where at tree level we have a massless real scalar with a non-zero four point coupling represented by a potential
Summary
We shall carry out our analysis under several simplifying assumptions. These are made mainly to keep the analysis simple, but we believe that none of these (except 4) is necessary. To deal with these divergences we need to first regularize these divergences, solve for λ, and at the end remove the regulator For this we shall work with a choice of gluing compatible local coordinates according to the procedure described in section 3.2 of [35] and express a general amplitude contributing to the right hand side of (2.4) as a sum of products of ‘one particle irreducible’ (1PI) amplitudes joined by the propagator. We expect the individual contributions to Γto be free from divergence associated with zero momentum propagator in the Λ → ∞ limit, since the contribution to ∆ ̄ from a massive state of mass m is given by 1 − e−Λm2/2 /m2, while the contribution from the other massless states are expected to vanish due to the assumed vanishing of the corresponding tadpoles From this argument it is clear that the Λ dependence of Γwill come through exponentially suppressed terms for large but finite Λ. All physical amplitudes will turn out to be free from this ambiguity
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
