# Scalar model of effective field theory in curved space

## TL;DR

This paper analyzes the low-energy effective behavior of a light scalar field coupled to a heavy scalar in curved space, demonstrating IR decoupling and non-local effects similar to flat space, with implications for effective field theories.

## Contribution

It provides a detailed analysis of IR decoupling and non-local effects in the effective field theory of scalars in curved space, extending previous flat space results.

## Key findings

- One-loop mixed diagrams produce IR non-local contributions.
- Effective self-interaction can be derived by integrating out the heavy scalar.
- The IR decoupling and non-local effects are similar in flat and curved space.

## Abstract

We consider, in more details than it was done previously, the effective low-energy behavior in the quantum theory of a light scalar field coupled to another scalar with much larger mass. The main target of our work is an IR decoupling of heavy degrees of freedom, including in the diagrams with mixed light-heavy contents in the loops. It is shown that the one-loop diagrams with mixed internal lines produce an IR non-local contributions which are exactly the same as the ones in the theory of the light scalar alone, with the effective self-interaction which can be obtained by the functional integration of the heavy scalar, almost neglecting its kinetic term. The same effect takes place in curved space, regardless of a larger amount of non-localities which show up in the effective model.