Critical String Vacua from Noncritical Manifolds: A Novel Framework for String Compactification

TL;DR

This paper introduces a new framework for string compactification using noncritical manifolds, expanding the class of models beyond Calabi--Yau spaces and providing insights into their relation with exactly solvable models.

Contribution

It demonstrates that massless spectra of critical Calabi--Yau manifolds can be derived from higher-dimensional noncritical manifolds with quantized Ricci curvature, broadening the scope of string compactification models.

Findings

Higher-dimensional noncritical manifolds include spaces with no Kähler deformations.

These manifolds can serve as mirrors to rigid Calabi--Yau manifolds.

The framework links exactly solvable models to Calabi--Yau geometries.

Abstract

A new framework is found for the compactification of supersymmetric string theory. It is shown that the massless spectra of Calabi--Yau manifolds of complex dimension $D_{crit}$ can be derived from noncritical manifolds of complex dimension $2k + D_{crit}$, $k\geq 1$. These higher dimensional manifolds are spaces whose nonzero Ricci curvature is quantized in a particular way. This class is more general than that of Calabi--Yau manifolds because it contains spaces which correspond to critical string vacua with no K\"ahler deformations, i.e. no antigenerations, thus providing mirrors of rigid Calabi--Yau manifolds. The constructions introduced here lead to new insights into the relation between exactly solvable models and their mean field theories on the one hand and Calabi--Yau manifolds on the other. They also raise fundamental questions about the Kaluza--Klein concept of string compactification, in particular regarding the r\^{o}le played by the dimension of the internal theories.