The stringy origins of Galileons and their novel limit

Damien Easson,Andrew Svesko,Tucker Manton,Maulik Parikh

doi:10.1088/1475-7516/2021/05/031

The stringy origins of Galileons and their novel limit

Damien Easson, Andrew Svesko + Show 2 more

Open Access

https://doi.org/10.1088/1475-7516/2021/05/031

Copy DOI

Abstract

We show generalized Galileons — a particular subclass of Horndeski gravity — arise from a consistent Kaluza-Klein reduction of the low-energy effective action of heterotic string theory to first order in α'. This suggests Horndeski theories of gravity have a string-theoretic origin. The form of the Galileonic terms is precisely fixed by parameters of the embedding spacetime, so that only a specific subset of Horndeski theories is permitted by string theory. A novel limit of the model is considered by performing a dimensionfulrescaling of α'.

Highlights

A local modification to general relativity3 [20], Galileons have proven useful in describing the inflationary phase of the universe [21,22,23], dark energy [24], and bouncing cosmologies [25,26,27,28] as the generalized Galileons “naturally” violate the null energy condition (NEC)
Some progress was made in understanding the fundamental origins of Galileons by recognizing they arise from higher-dimensional Lovelock theories of gravity via a standard KaluzaKlein (KK) dimensional reduction [29]
Truncating the gravi-dilaton sector of D-dimensional superstring theory to the α correction, we found that a consistent diagonal dimensional reduction of this theory generically leads to a Horndeski theory of gravity

Summary

Horndeski from Lovelock: A Review

In D ≥ 5 dimensions, Lovelock theories of gravity generalize Einstein’s general relativity to Einstein-Lovelock theories of gravity. We will present an explicit example of Horndeski theory arising from the dimensional reduction of Einstein-Gauss-Bonnet gravity. Of particular interest to us is the ‘diagonal’ reduction of the EinsteinHilbert and Gauss-Bonnet terms over a flat n-dimensional Euclidean space (a n-torus) An expression for this quantity was previously given in [35]; in their calculation they discarded total derivative terms which we will need to know explicitly. While a pure Gauss-Bonnet term in p + 1 ≤ 4 is purely topological, here LGB will have an effect on lower dimensional spacetime dynamics as it couples to the scalar φ in a non-trivial way.

Galileons from Strings

Novel α -Corrected String Theory?

Discussion and Conclusion

A Kaluza-Klein Reduction of Einstein-Gauss-Bonnet

Equations of Motion