A Note on Circle Compactification of Tensile Ambitwistor String

TL;DR

This paper investigates the circle compactification of the bosonic tensile ambitwistor string, revealing how the radius influences the effective field theory and demonstrating its point-particle-like behavior despite string characteristics.

Contribution

It provides new insights into the spectrum, gauge symmetry enhancement, and the field theory nature of the tensile ambitwistor string through current algebra and partition function analysis.

Findings

The circle radius acts as a tuning parameter for the effective field theory.

A subsector exhibits gauge symmetry enhancement to $ISO(2)_L\times SU(2)_R$.

The partition function matches that of a field theory, indicating point-particle behavior.

Abstract

We discuss a number of problems associated with the circle compactification of the bosonic tensile ambitwistor string with the asymmetric vacuum choice. By considering the spectrum and physical state conditions, we show that the circle radius plays a role as a tuning parameter which determines the low energy effective field theory. At the self dual point, we construct the current operators and compute OPEs between them. While the final outcome remains as yet inconclusive, several new results are obtained. Through the current algebra analysis we show that there is a subsector of the massless states where the gauge symmetry is enhanced to $ISO(2)_L\times SU(2)_R$. Using the fact that the one loop partition function is not modular invariant, we show that tensile ambitwistor string partition function is exactly the same as a field theory partition function. Our result proves that despite the existence of winding modes, which is a typical characteristic of a string, the tensile ambitwistor string behaves as a point particle theory.