The Cosmological Constant and Dark Dimensions from Non-Supersymmetric Strings

TL;DR

The paper constructs a non-supersymmetric string model in which the open-string gauge/matter sector contributes zero to the one-loop vacuum energy and the closed-string gravitational sector is suppressed by large extra dimensions, yielding a small observed cosmological constant. It combines Brane Supersymmetry Breaking with Scherk–Schwarz breaking to achieve Bose–Fermi degeneracy in the open sector and a dark-dimensional gravity sector with $\Lambda_{\text{closed}}$ set by the dark-dimensional radius, stabilised to exponentially large values via non-perturbative effects. A four-dimensional $\mathcal{N}=1$ EFT is developed to describe moduli stabilisation and to realize two large extra dimensions with a de Sitter saddle, matching the Dark Energy scale within controlled $g_s$ and $\alpha'$ expansions. The framework yields testable implications for table-top gravity experiments and cosmology, while highlighting open questions about higher-loop cancellations and embedding the Standard Model with realistic chirality and couplings. The approach provides a concrete string-theoretic route to address the cosmological constant problem and its connection to extra-dimensional physics.

Abstract

We present a string theory construction in which the particle physics contributions to the one-loop vacuum energy exactly cancel, whilst the gravitational contributions are suppressed in the size of one or two large extra dimensions. This provides an ultraviolet realisation of the Dark Dimension and Supersymmetric Large Extra Dimensions scenarios, with, moreover, an explanation as to why the Standard Model contributions to the vacuum energy cancel without the need of eV mass-splittings. Gravity propagates in micron sized dark dimension(s), whilst the visible and hidden sectors are supported on D-branes. Supersymmetry is broken in the dark dimension(s) à la Scherk-Schwarz, whereas supersymmetry is broken at the string scale, à la Brane Supersymmetry Breaking, in the D-branes sector, without inducing tadpoles. Vacuum energy from the visible sector is cancelled by the vacuum energy of the hidden sector branes. We also discuss moduli stabilization in this set-up, finding that the interplay between the Scherk-Schwarz one-loop contribution and non-perturbative effects can fix the size of the dark dimension(s) to be exponentially large in the inverse string-coupling, leading to an exponentially small total vacuum energy, with all moduli stabilised in a dS saddle.

Figures (4)

• Figure 1: The O-plane/D-brane configuration corresponding to the non-supersymmetric USp(16) model by CDP Coudarchet:2021qwc. The tension and charge combinations result in a cancellation of the disk tadpoles. The branes are dynamically attracted to the $\overline{\text{O}7}^+$-plane, giving rise to a USp(16) gauge group. Tadpoles arise, however, at one-loop, corresponding to a one-loop vacuum energy $\Lambda_{\text{open}}\sim M_s^4$.
• Figure 2: The O-plane/D-brane configuration for the USp(8)$\times$SO(8) deformation of the CDP model. Thanks to an exact matching between the numbers of bosons and fermions at every mass level, when counting contributions from both the USp(8) and SO(8) stacks, the one-loop vacuum energy from the open-string sectors cancels exactly, $\Lambda_{\text{open}}=0$. However, the SO(8) branes are dynamically attracted to the $\overline{\text{O}7}^+$-plane, so the configuration is unstable. The endpoint of the instability is the CDP model illustrated in Figure \ref{['fig:USp16']}, which has $\Lambda_{\text{open}}\sim M_s^4$.
• Figure 3: The O-plane/D-brane configuration for our USp(8) $\times$ SO(1)$^8$ construction, which has $\Lambda_{\text{open}}=0$. After dimensionally reducing and T-dualising, there are 16 copies of the CDP distribution of O$^-$/$\overline{\text{O}}^\mp$-planes shown in Figure \ref{['fig:USp16']} (we show 4 of them). Together with the USp(8) brane stack on one of the $\overline{\text{O}3}^+$-planes, there are eight single SO(1) branes placed on separate $\overline{\text{O}3}^-$-planes. The numbers of bosons and fermions coming from the brane stacks match at all mass levels. The configuration is moreover stable, as the SO(1) branes are stuck on the $\overline{\text{O}3}^-$-planes.
• Figure 4: The dependence of the leading order term in the one-loop effective potential on the complex structure $U_3$ through the function $\mathcal{E}_3(U_3)$, with its saddles and its manifest $\text{Re}\,U_3\rightarrow\text{Re}\,U_3+1$ symmetry. The saddle point $U_3^*=\frac{1}{2}(1+i)$ in the fundamental domain is highlighted with a white dot.