# Exact Solutions of Einstein-Yang-Mills Theory with Higher-Derivative Coupling

## TL;DR

This paper presents exact solutions to an Einstein-Yang-Mills system with higher-derivative terms, demonstrating spontaneous compactification of ten-dimensional space-time to four-dimensional Minkowski space and AdS_4, with the sphere's radius determined by coupling constants.

## Contribution

It provides explicit classical solutions incorporating higher-derivative Yang-Mills terms, extending previous compactification models with new parameter dependencies.

## Key findings

- Sphere radius is determined by coupling constants, not a modulus.
- Constructed solutions include compactifications to Minkowski and AdS_4 spaces.
- Higher-derivative terms enable new stable compactification configurations.

## Abstract

We construct a classical solution of an Einstein-Yang-Mills system with a fourth order term with respect to the field strength of the Yang-Mills field. The solution provides a spontaneous compactification proposed by Cremmer and Scherk; ten-dimensional space-time with a cosmological constant is compactified to the four-dimensional Minkowski space with a six-dimensional sphere S^6 on which an instanton solution exists. The radius of the sphere is not a modulus but is determined by the gauge coupling and the four-derivative coupling constants and the Newton's constant. We also construct a solution of ten-dimensional theory without a cosmological constant compactified to AdS_4 x S^6.