Twistors and Actions on Coset Manifolds

TL;DR

This paper introduces a new twistor-based framework for constructing symmetric particle and string actions on coset spaces, enabling quadratic kinetic terms and simplifying quantization, with explicit application to AdS spaces.

Contribution

It defines twistors on coset spaces as hypersurfaces in a vector space, leading to manifestly symmetric actions with quadratic kinetic terms, and provides a general algorithm with an explicit AdS case.

Findings

Constructed actions with quadratic kinetic terms for particles on coset spaces.

Applied the method explicitly to particles on AdS_p, resulting in a gauge theory.

Revealed a connection to nonlocal world-line sigma-models.

Abstract

Particle and string actions on coset spaces typically lack a quadratic kinetic term, making their quantization difficult. We define a notion of twistors on these spaces, which are hypersurfaces in a vector space that transform linearly under the isometry group of the coset. By associating the points of the coset space with these hypersurfaces, and the internal coordinates of these hypersurfaces with momenta, it is possible to construct manifestly symmetric actions with leading quadratic terms. We give a general algorithm and work out the case of a particle on AdS_p explicitly. In this case, the resulting action is a world-line gauge theory with sources, (the gauge group depending on p) which is equivalent to a nonlocal world-line sigma-model.