Lessons from the landscape of six-dimensional supergravity theories

Abstract

Comparing the set of supergravity theories allowed by low-energy consistency conditions with the set of string vacua provides useful insights into quantum gravity and string theory. In fact, such a "landscape analysis" for ten-dimensional supergravity theories was at the core of the exciting series of developments that is now referred to as the first superstring revolution. In this thesis, we discuss the lessons we learn about quantum supergravity and string theory by carrying out such an analysis for the space of six-dimensional supergravity theories with minimal supersymmetry. We first review six-dimensional supergravity theories and explain why the space of these theories is an ideal place to carry out the landscape analysis. We then describe how anomaly constraints bound the space of consistent theories, i.e., we map the space of theories T that satisfy known low-energy consistency conditions. We then go on to describe string constructions that give six-dimensional string vacua with minimal supersymmetry, i.e., we map the space of theories S c T that come from string vacua. Finally, we compare the space of theories T and S and explore its implications. We first find that there is a large discrepancy between T and S. Among the set T - S, we identify some theories that are potentially new string vacua, but also identify many theories that cannot be embedded in any known string vacua. These theories may potentially be ruled out by yet undiscovered low energy constraints. Understanding these theories is an important step in addressing the question of string universality in six dimensions. We also find some surprising equalities that hold for Calabi-Yau threefolds that follow from demanding that F-theory string vacua should be consistent.