Noncritical M-theory and the Gross-Neveu model in 2+1 dimensions

TL;DR

This paper uncovers a deep connection between noncritical M-theory and the Gross-Neveu model in 2+1 dimensions, relating their vacuum energies and cosmological constants through analytic continuation and large-N limits.

Contribution

It establishes a novel link between noncritical M-theory and the Gross-Neveu model, providing insights into their vacuum energies and cosmological constants at critical points.

Findings

Vacuum energy of noncritical M-theory matches large-N free-energy of Gross-Neveu model.

Critical point values are 4/5 and 2/5 of infinite string coupling values.

Analytic continuation relates M-theory subtraction point to Liouville volume.

Abstract

We point out a non-trivial connection between the model proposed by Horava and Keeler as a candidate for noncritical M-theory and the Gross-Neveu model with fermionic fields obeying periodic boundary conditions in 2+1 dimensions. Specifically, the vacuum energy of the former is identified with the large-N free-energy of the latter up to an overall constant. This identification involves an appropriate analytic continuation of the subtraction point in noncritical M-theory, which is related to the volume of the Liouville dimension. We show how the world-sheet cosmological constant may be obtained from the Gross-Neveu model. At its critical point, which is given in terms of the golden mean, the values of the vacuum energy and of the cosmological constant are 4/5 and 2/5 of the corresponding values at infinite string coupling constant.