# S and T Self-dualities in Dilatonic f(R) Theories

## TL;DR

This paper investigates higher-dimensional dilatonic f(R) theories that exhibit exact S and T self-dualities, identifying conditions under which these dualities exist without instabilities.

## Contribution

It demonstrates that such theories can be constructed without Ostrogradsky instabilities and clarifies the specific conditions for the coexistence of S and T dualities.

## Key findings

- Theories with higher powers of scalar Ricci curvature can have exact S and T dualities.
- No theories with both S and T dualities exist unless the action is linear in scalar curvature.
- The constructed theories are free of Ostrogradsky instabilities.

## Abstract

We search for theories, in general spacetime dimensions, that would incorporate a dilaton and higher powers of the scalar Ricci curvature such that they have exact S and/or T self-dualities. The theories we find are free of Ostrogradsky instabilities. We also show that within the framework we are confining ourselves a theory of the form mentioned above can not have both T and S dualities except for the case where the action is linear in the scalar curvature.