4d-Flat Compactifications With Brane Vorticities

TL;DR

This paper explores six-dimensional gravity with branes and sigma models, revealing conditions for four-dimensional flatness, and introduces instanton solutions with branes and vorticities, suggesting a mechanism for adjusting the cosmological constant.

Contribution

It provides explicit solutions involving branes with vorticity in 6D sigma models, and generalizes to multi-instanton configurations on Kähler manifolds.

Findings

Four-dimensional flatness depends on brane tensions and vorticities.

Exact instanton solutions are constructed for sigma models on Kähler manifolds.

Multi-instanton solutions include branes with vorticities at instanton positions.

Abstract

We present solutions in six-dimensional gravity coupled to a sigma model, in the presence of three-brane sources. The space transverse to the branes is a compact non-singular manifold. The example of O(3) sigma model in the presence of two three-branes is worked out in detail. We show that the four-dimensional flatness is obtained with a single condition involving the brane tensions, which are in general different and may be both positive, and another characteristic of the branes, vorticity. We speculate that the adjustment of the effective four-dimensional cosmological constant may occur through the exchange of vorticity between the branes. We then give exact instanton type solutions for sigma models targeted on a general K\"ahler manifold, and elaborate in this framework on multi-instantons of the O(3) sigma model. The latter have branes, possibly with vorticities, at the instanton positions, thus generalizing our two-brane solution.