Snowmass White Paper: String Perturbation Theory

Abstract

The purpose of this White Paper is to review recent progress towards elucidating and evaluating string amplitudes, relating them to quantum field theory amplitudes, applying their predictions to string dualities, exploring their connection with gravitational physics, and deepening our understanding of their mathematical structure. We also present a selection of targets for future research.

High Energy String Scattering in AdS

“…Perturbative string theory in flat backgrounds is relatively well understood. In principle worldsheet methods can be used to compute perturbative expansions for a variety of scattering amplitudes [1]. The situation in curved spacetime is very different.…”

TF1 Snowmass Report: Quantum gravity, string theory, and black holes

“…Since string theory is a theory of gravity, string compactification can be viewed as providing a rich set of probes of its behavior: one can use compactifications on various geometries X i , and their relationships to one another, to probe how this particular theory of quantum gravity "sees" spatial geometry and topology. This viewpoint has led to the discovery of many new mathematical phenomena and structures (including mirror symmetry, vertex algebras, moonshine [39], aspects of the geometry of the moduli space of Riemann surfaces associated with string perturbation theory [40], and too many others to list here). We will have to mention just a few out of many promising developments, described more completely in [41].…”

Unitarity cuts of the worldsheet

“…At this stage one might reasonably ask why this issue has not caused severe problems before. After all, there is an enormously rich literature on scattering amplitudes in string theory, see, e.g., [7][8][9][10][11][12][13] for reviews. However, most of those results have been obtained either at tree-level or in the low-energy expansion at loop-level.…”