# Surface terms in the effective actions via duality constraints

## TL;DR

This paper proposes a method to determine both bulk and boundary terms in string theory effective actions by enforcing gauge invariance and duality symmetries, successfully reproducing the Gibbons-Hawking-York boundary term at leading order.

## Contribution

It introduces a duality-based approach to derive boundary terms in string effective actions, extending the understanding of boundary contributions beyond traditional methods.

## Key findings

- Reproduces the Gibbons-Hawking-York boundary term at leading order.
- Demonstrates the invariance of the effective action under gauge transformations and dualities.
- Provides a unified framework for bulk and boundary term determination.

## Abstract

The effective action of string theory on a spacetime manifold with boundary has both bulk and boundary terms. We propose that both bulk and boundary actions, may be found by imposing the effective action to be invariant under the gauge transformations and under the string dualities. Using this proposal at the leading order of $\alpha'$, the standard Gibbons-Hawking-York boundary term is reproduced.