Classical and Quantum Stability in Putative Landscapes

TL;DR

This paper examines the constraints on large-field landscapes in string theory, emphasizing unitarity and perturbativity, and explores their implications for stability and the distribution of couplings in models with many fields.

Contribution

It highlights how unitarity and perturbativity constrain couplings in large-N landscapes, challenging the assumption of independent random distributions and analyzing stability in non-supersymmetric settings.

Findings

Couplings are bounded by order one numbers in certain string models.

Scaling of compactification radii with N is necessary for light fields and perturbativity.

Strong correlations among couplings may exist, questioning randomness assumptions.

Abstract

Landscape analyses often assume the existence of large numbers of fields, $N$, with all of the many couplings among these fields (subject to constraints such as local supersymmetry) selected independently and randomly from simple (say Gaussian) distributions. We point out that unitarity and perturbativity place significant constraints on behavior of couplings with $N$, eliminating otherwise puzzling results. In would-be flux compactifications of string theory, we point out that in order that there be large numbers of light fields, the compactification radii must scale as a positive power of $N$; scaling of the radii and couplings with $N$ may also be necessary for perturbativity. We show that in some simple string theory settings with large numbers of fields, for fixed $R$ and string coupling, one can bound certain sums of squares of couplings by order one numbers. This may argue for strong correlations, possibly calling into question the assumption of random distributions. We consider implications of these considerations for classical and quantum stability of states without supersymmetry, with low energy supersymmetry arising from tuning of parameters, and with dynamical breaking of supersymmetry.