Strongly Topological Interactions of Tensionless Strings

TL;DR

This paper explores the tensionless limit of classical string theory, revealing it as a topological quantum theory where amplitudes depend only on topological features, not on metric details.

Contribution

It introduces a formulation of tensionless strings as a topological theory using vector densities, and demonstrates the metric independence of quantum amplitudes.

Findings

String amplitudes depend only on topological features.

Quantum theories can be inequivalent due to different vector densities.

No integration over vector density zeroes is needed in amplitudes.

Abstract

The tensionless limit of classical string theory may be formulated as a topological theory on the world-sheet. A vector density carries geometrical information in place of an internal metric. It is found that path-integral quantization allows for the definition of several, possibly inequivalent quantum theories. String amplitudes are constructed from vector densities with zeroes for each in- or out-going string. It is shown that independence of a metric in quantum mechanical amplitudes implies that the dependence on such vector density zeroes is purely topological. For example, there is no need for integration over their world-sheet positions.