# One loop amplitude from null string

## TL;DR

This paper extends the CHY formalism to one-loop amplitudes using null string theory, revealing differences in modular invariance and deriving n-gon scattering amplitudes, thus supporting the n-gons conjecture.

## Contribution

It introduces a novel one-loop formalism based on null string theory, connecting it with CHY and ambitwistor string theories, and derives n-gon amplitudes.

## Key findings

- Null string theory reproduces CHY results at one-loop.
- Modular invariance does not hold in null string theory.
- Derived n-gon scattering amplitudes confirming the n-gons conjecture.

## Abstract

We generalize the CHY formalism to one-loop level, based on the framework of the null string theory. The null string, a tensionless string theory, produces the same results as the ones from the chiral ambitwistor string theory, with the latter believed to give a string interpretation of the CHY formalism. A key feature of our formalism is the interpretation of the modular parameters. We find that the $S$ modular transformation invariance of the ordinary string theory does not survive in the case of the null string theory. Treating the integration over the modular parameters this way enable us to derive the n-gons scattering amplitude in field theory, thus proving the n-gons conjecture.