Thermodynamics of Noncritical M-Theory and the Topological A-Model

TL;DR

This paper investigates noncritical M-theory at finite temperature, deriving its free energy, revealing a high-temperature effective description, and proposing a duality with the topological A-model on a Calabi-Yau, linking temperature and string coupling.

Contribution

It provides the first exact free energy expression for noncritical M-theory at finite temperature and establishes a duality with the topological A-model, connecting temperature and string coupling.

Findings

High-temperature behavior described by an M-theory solution with T^3 scaling.

Noncritical M-theory is dual to the topological A-model on a Calabi-Yau.

T-duality in M-theory implies S-duality in the A-model.

Abstract

In hep-th/0508024, noncritical M-theory for two-dimensional Type 0A and 0B strings was defined in terms of a double-scaled theory of nonrelativistic fermions in 2+1 dimensions. Here we study this noncritical M-theory at finite temperature. We derive the exact expression for the free energy of its vacuum solution, as a function of a coupling constant $g_M$ and the radius $R$ of the thermal circle. We show that at high temperature, the theory is effectively described by another M-theory solution, whose effective loop-counting coupling scales in a novel way characteristic of M-theory, as $T^3$. Our calculations further suggest that noncritical M-theory is dual to the closed string theory of the topological A-model on a Calabi-Yau, with the radius $R$ of the Euclidean time circle in M-theory playing the role of the string coupling constant of the A-model. In this correspondence, T-duality on the Euclidean time circle of noncritical M-theory implies an S-duality for the topological A-model.