Abstract
We propose a novel Kaluza–Klein scheme which assumes the internal space to be maximally non-Riemannian, meaning that no Riemannian metric can be defined for any subspace. Its description is only possible through Double Field Theory but not within supergravity. We spell out the corresponding Scherk–Schwarz twistable Kaluza–Klein ansatz, and point out that the internal space prevents rigidly any graviscalar moduli. Plugging the same ansatz into higher-dimensional pure Double Field Theory and also to a known doubled-yet-gauged string action, we recover heterotic supergravity as well as heterotic worldsheet action. In this way, we show that 1) supergravity and Yang–Mills theory can be unified into higher-dimensional pure Double Field Theory, free of moduli, and 2) heterotic string theory may have a higher-dimensional non-Riemannian origin.
Highlights
Kaluza–Klein theory attempts to unify General Relativity and electromagnetism into higher-dimensional pure gravity
In this paper we propose a novel Kaluza–Klein scheme to unify Stringy Gravity and Yang–Mills, which postulates a non-Riemannian internal space and does not suffer from any moduli problem
Within the framework of Double Field Theory (DFT) initiated in [5,6,7,8,9], O(D, D) T-duality becomes the manifest principal symmetry and the effective action itself is to be identified as an integral of a stringy scalar curvature beyond Riemann
Summary
Kaluza–Klein theory attempts to unify General Relativity and electromagnetism into higher-dimensional pure gravity. The (aesthetically unpleasing) cylindrical extra dimension brings along an unwanted additional massless scalar field, i.e. radion or graviscalar modulus, which is not observed in nature: it would spoil the Equivalence Principle by appearing on the right-hand side of the geodesic equation This moduli stabilization problem is essentially rooted in the fact that there is no natural scale in pure gravity which would fix or stabilize the radius of the cylinder. By Stringy Gravity, we mean the string theory effective action of the NS-NS (or purely bosonic) closed-string massless sector, conventionally represented by the three fields, {gμν, Bμν , φ}. They transform into one another under T-duality and form a (reducible) O(D, D) multiplet [3, 4]. We focus on computing +G(0) and −G(0) separately in higher dimensions with the Scherk–Schwarz twisted non-Riemannian Kaluza–Klein ansatz
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