Advances in Theoretical and Mathematical Physics

Volume 21 (2017)

Number 7

Special Issue: Proceedings of the Strings 2016 Conference in Beijing

Guest Editors: J. Maldacena (Institute for Advanced Study), H. Ooguri (California Institute of Technology), H. Babak (Harvard University), S. Li (Tsinghua University), W. Song (Tsinghua University), and H. Lin (Tsinghua University)

Why the cosmological constant is so small: A string theory perspective

Pages: 1803 – 1818



S.-H. Henry Tye (Jockey Club Institute for Advanced Study and Department of Physics, Hong Kong University of Science and Technology, Hong Kong; and Laboratory for Elementary-Particle Physics, Cornell University, Ithaca, New York, U.S.A.)


With no free parameter (except the string scale $M_S$), dynamical flux compactification in Type IIB string theory determines both the cosmological constant (vacuum energy density) $\Lambda$ and the Planck mass $M_P$ in terms of $M_S$, thus yielding their relation. Following elementary probability theory, we find that a good fraction of the meta-stable de Sitter vacua in the cosmic string theory landscape tend to have an exponentially small cosmological constant $\Lambda$ compared to either the string scale $M_S$ or the Planck scale $M_P$, i.e., $\Lambda \ll M^4_S \ll M^4_P$. Here we illustrate the basic stringy idea with a simple scalar field $\phi^3$ (or $\phi^4$) model coupled with fluxes to show how this may happen and how the usual radiative instability problem is bypassed (since there are no parameters to be fine-tuned). These low lying semi-classical de Sitter vacua tend to be accompanied by light scalar bosons/axions, so the Higgs boson mass hierarchy problem may be ameliorated as well.

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Published 19 March 2018