Non-compact Calabi--Yau Manifolds and Localized Gravity

TL;DR

This paper investigates how gravity can be localized in non-compact Calabi-Yau manifolds within superstring theory, highlighting conditions for an induced Einstein-Hilbert term and implications for realistic string models.

Contribution

It demonstrates that a four-dimensional Einstein-Hilbert term can be generated only in non-compact Calabi-Yau threefolds with non-zero Euler number, linking it to R^4 couplings in ten dimensions.

Findings

Induced Einstein-Hilbert term exists only in four dimensions.

The size of the gravity term can be significantly enhanced by tuning parameters.

The study discusses challenges in constructing realistic string models without compact extra dimensions.

Abstract

We study localization of gravity in flat space in superstring theory. We find that an induced Einstein-Hilbert term can be generated only in four dimensions, when the bulk is a non-compact Calabi-Yau threefold with non-vanishing Euler number. The origin of this term is traced to R^4 couplings in ten dimensions. Moreover, its size can be made much larger than the ten-dimensional gravitational Planck scale by tuning the string coupling to be very small or the Euler number to be very large. We also study the width of the localization and discuss the problems for constructing realistic string models with no compact extra dimensions.