[Paper Review] Cosmological Constant Seesaw in String/M-Theory

Michael McGuigan|ArXiv.org|Apr 14, 2006

Black Holes and Theoretical Physics47 references3 citations

TL;DR

This paper extends the cosmological constant seesaw mechanism to string/M-theory by leveraging large N duals to compute finite vacuum energies and enable transitions between vacua with different cosmological constants. It demonstrates that in 2d/3d string/M-theory, supersymmetry breaking via Wilson lines or dual gauge theories generates a large $M_{\text{Pl}}^4$ denominator, naturally yielding the observed small cosmological constant $\lambda_- \sim \lambda_1^2 / \lambda_2$.

ABSTRACT

In this paper we extend the Cosmological Constant Seesaw treatment of hep-th/0602112 to String/M-Theory where the cosmological constant is finite. We discuss how transitions between different $λ$, one of Planckian vacuum energy, can give rise to a large $M_{Pl}^4$ denominator in the Cosmological Constant Seesaw relation discussed by Banks, Motl and Carroll. We apply these ideas to 2d/3d String/M-Theory and show how the existence of a large N dual fermionic theory makes the demonstration of a transition between different $λ$ relatively straight forward. We also consider 2d/3d Heterotic String/M-Theory cosmology, a theory for which the large N dual is unknown. The minisuperspace associated to these models is 26/27 dimensional for the SO(24) theory and 10/11 dimensional for the $SO(8) imes E_8$ theory and consists of the $T$ fields as well as the dilaton and metric. 2d Heterotic String Quantum Cosmology is similar to critical string dynamics except for the inclusion of the 2d gauge fields. These 2d gauge fields have an important effect on the vacuum energy and on transitions between different $λ$ through the effects of Wilson lines. Finally we discuss the extension to existing higher dimensional string cosmologies possessing large N duals.

Motivation & Objective

• To resolve the hierarchy problem of the cosmological constant by embedding the seesaw mechanism within a UV-complete quantum gravity framework.
• To demonstrate that transitions between vacua with different cosmological constants ($\lambda_1$, $\lambda_2$) are dynamically possible in string/M-theory.
• To show that the large $M_{\text{Pl}}^4$ denominator in the seesaw relation arises naturally from finite, calculable vacuum energies in string/M-theory.
• To establish a mechanism for generating the observed $\sim 10^{-120} M_{\text{Pl}}^4$ cosmological constant via dual gauge theories with broken supersymmetry.
• To generalize the seesaw mechanism to higher-dimensional string cosmologies using holographic duals and light-cone formulations.

Proposed method

• Formulate the Wheeler-DeWitt (WDW) equation for 2d/3d string/M-theory compactifications, incorporating scale factor $a$, dilaton $\phi$, and metric degrees of freedom.
• Utilize large N duals—specifically 2d $\mathcal{N}=4$ SYM and 3d $\mathcal{N}=4$ SYM—for 2d/3d string theories to compute finite vacuum energies and enable transitions between $\lambda$ vacua.
• Model transitions between $\lambda$ vacua via Wilson lines in 2d heterotic string theory, which modify vacuum energy through gauge field holonomies.
• Apply the seesaw relation $\lambda_- = \lambda_1^2 / \lambda_2$ with $\lambda_1 \sim (2.4\,\text{TeV})^4$ and $\lambda_2 \sim \sigma^2 M_{\text{Pl}}^4$ to derive the observed small $\lambda_-$.
• Analyze light-cone cosmologies in M-theory with $ds^2 = -a^2(U) dU dV + b^2(U) dY^2$, where the holographic dual is a 2d large N gauge theory with time-dependent coupling.
• Construct $R \times S^1$ and $R \times H^4 \times S^5$ cosmologies with magnetic or five-form charge, showing that supersymmetry breaking leads to nonzero $\lambda$.

Experimental results

Research questions

• RQ1 Can the cosmological constant seesaw mechanism be realized in a UV-complete theory like string/M-theory?
• RQ2 How can transitions between vacua with different cosmological constants ($\lambda_1$, $\lambda_2$) be dynamically generated in string/M-theory?
• RQ3 What is the origin of the large $M_{\text{Pl}}^4$ denominator in the seesaw formula $\lambda_- = \lambda_1^2 / \lambda_2$ within string/M-theory?
• RQ4 Can finite, calculable vacuum energies in string theory replace the divergent effective field theory approach to the cosmological constant?
• RQ5 Do higher-dimensional string cosmologies with large N duals support the seesaw mechanism via supersymmetry breaking and vacuum energy transitions?

Key findings

• In 2d/3d string/M-theory, the cosmological constant seesaw mechanism is realizable via large N duals, with finite vacuum energies computed exactly from worldsheet sums.
• Transitions between vacua with $\lambda_1 \sim (2.4\,\text{TeV})^4$ and $\lambda_2 \sim M_{\text{Pl}}^4$ are enabled by Wilson lines in 2d heterotic string theory, modifying the vacuum energy dynamically.
• The large $M_{\text{Pl}}^4$ denominator in $\lambda_- = \lambda_1^2 / \lambda_2$ arises naturally from the dual gauge theory description, where $\lambda_2$ corresponds to a supersymmetry-breaking vacuum energy.
• Light-cone cosmologies in M-theory with $\phi(U) = -QU$ admit a 2d large N gauge theory dual, which breaks supersymmetry and generates a nonzero cosmological constant.
• In higher dimensions, $R \times S^2 \times S^1 \times K_6$ and $R \times H^4 \times S^5$ cosmologies with magnetic or five-form charge support transitions between $\lambda$ vacua via dual theories.
• The observed cosmological constant $\lambda_- \approx 10^{-120} M_{\text{Pl}}^4$ is consistent with the seesaw mechanism and lies within the anthropic window, suggesting a dynamical origin.