# Frustrated conformal transformations and holomorphic maps on ambitwistor space

## TL;DR

This paper introduces frustrated conformal transformations within twistor theory, linking instantons to maps on ambitwistor space, and presents a solution based on the BPST instanton.

## Contribution

It defines a new class of conformal transformations called frustrated conformal transformations and connects them to ambitwistor space via instanton solutions.

## Key findings

- Frustrated conformal transformations are characterized by instanton data.
- A specific solution using the BPST instanton is constructed.
- The work extends the Penrose-Ward correspondence to these transformations.

## Abstract

We study some aspects of conformal transformations in the context of twistor theory, leading to the definition of a frustrated conformal transformation. This equation relies on two instantons for the left and right copies of $Sp(1)$, one being self-dual and the other anti-self-dual. Solutions to this equation naturally generate maps on ambitwistor space due to an analog of the Penrose-Ward correspondence. A solution based on the BPST instanton is presented.