A Small Cosmological Constant, Grand Unification and Warped Geometry

TL;DR

The work presents a warped 5D brane-world mechanism to attenuate the observed 4D vacuum energy by an exponential warp factor, with the inter-brane separation tied to the GUT scale. Lifting to IIB string theory using D3-brane stacks yields a spontaneously broken SU(5) SUSY GUT that naturally contains the MSSM spectrum and achieves Higgs doublet–triplet splitting through geometric separation, while bulk scalars do not spoil the suppression. The open-string sector supplies heavy GUT states (X,Y and color-triplet Higgs) and light MSSM matter fields via nontrivial compactification topology, and a consistent proton lifetime can be maintained with $M_{ ext{open}}ootnotesize{ ext{(open-string mass)}} \gtrsim M_{ m GUT}$. The framework thus connects the tiny cosmological constant, the Planck scale, and the GUT scale in a concrete string-theoretic setting, and offers plausible avenues for SUSY breaking within the same construction.

Abstract

We explore a mechanism to obtain the observational small value for the 4-dimensional vacuum energy through an exponential warp-factor suppression. Intriguingly the required suppression scale relates directly to the GUT scale. We demonstrate the mechanism explicitly in a 5-dimensional brane-world setup with warped geometry. Upon lifting the setup to 10-dimensional IIB string-theory, the relevance of the GUT scale becomes clear as the IIB string-theory description, which is based on D3-brane stacks, gives rise to a spontaneously broken SU(5) supersymmetric GUT theory with low-energy MSSM spectrum and Higgs doublet-triplet splitting.

Figures (9)

• Figure 1: The double 3-brane setup with interbrane separation $2l$. To obtain a critical vacuum energy one has to set $2l\approx 1/M_{\text{GUT}}$.
• Figure 2: The function $A(x^5)$ which determines the warp-factor along the non-compact fifth dimension.
• Figure 3: The two 3-branes resolved as stacks of D3-branes in the microscopic IIB string-theory picture.
• Figure 4: The relevant open strings of the D3-brane setup. The state ${\bf (n,m)}_z$ transforms as $\bf{n}$ under SU(3), as $\bf{m}$ under SU(2) and bears U(1) charge $z$. For better visibility we magnify the small split into $2+1$ branes of the second D3-brane stack. Note that the fundamental 2 of SU(2) is pseudoreal.
• Figure 5: Open strings and their SU(3)$\times$SU(2)$\times$U(1) transformations. Those which start and end on the same D3-brane stack will give rise to SM gauge fields and part of the Higgs bosons filling the $\bf 24$ adjoint Higgs multiplet of a supersymmetric SU(5) GUT. Those open strings which stretch between different D3-branes will provide the $\bf 5$ and $\bf\bar{5}$ SU(5) Higgs multiplets. Gauge fields originate from open strings vibrating in the non-compact directions with Neumann boundary conditions at their ends while Higgs fields originate from open strings vibrating in the internal directions satisfying Dirichlet boundary conditions on the D3-branes. The geometry directly implies a mass hierarchy between color triplet and weak doublet Higgs fields.