Induced gravity in Z_N orientifold models

TL;DR

This work demonstrates that four-dimensional gravity can be induced on coincident D3-branes in non-compact ${\mathbb Z}_N$ orientifolds of type IIB string theory, with a crucial result: for odd $N$ the one-loop renormalization of the Planck mass receives a torus-only contribution that scales as $\Delta{\mathcal L}_{\text{eff}}^{\text{1-loop}}=\delta_T M_s^2 \sqrt{-g}R$ with $\delta_T = B_2/(6\pi)$ and $B_2$ linked to the Euler characteristic. Twisted sectors localize gravity in four dimensions, and the annulus, Möbius strip, and Klein bottle contributions cancel under tadpole constraints, allowing $N$ to be taken large to realize a sizeable induced gravity effect. The paper provides a concrete string-theoretic realization of a DGP-like mechanism on D3-branes, including a detailed amplitude-based fixation of vertex normalization via the two-graviton amplitude. The results offer a framework for constructing brane-induced gravity models with tunable scales while remaining within a non-compact, orientifolded string-theory setting, motivating future exploration of higher-loop and higher-derivative corrections.

Abstract

We consider non-compact Z_N orientifold models of type IIB superstring theory with four-dimensional gravity induced on a set of coincident D3-branes. For the models with odd N the contribution to the one-loop renormalization of the Planck mass is shown to come only from the torus and to be O(N) as the contributions from annulus, Moebius strip and Klein bottle cancel. One can therefore realize the Dvali-Gabadadze-Porrati idea that four-dimensional gravity is induced by quantum effects at the one-loop level by considering large N.