TASI Lectures on Supergravity and String Vacua in Various Dimensions

TL;DR

This paper reviews the landscape of supergravity theories and string vacua across dimensions 10, 8, and 6, emphasizing quantum constraints, anomaly cancellation, and the development of F-theory techniques.

Contribution

It provides a systematic overview of supergravity and string vacua in various dimensions, including new insights into F-theory and the constraints on theories not realized in string theory.

Findings

Supersymmetry and anomaly cancellation strongly restrict consistent theories.

Expanding possibilities as space-time dimensionality decreases.

Developed foundational tools for describing diverse string vacua.

Abstract

These lectures aim to provide a global picture of the spaces of consistent quantum supergravity theories and string vacua in higher dimensions. The lectures focus on theories in the even dimensions 10, 8, and 6. Supersymmetry, along with with anomaly cancellation and other quantum constraints, places strong limitations on the set of physical theories which can be consistently coupled to gravity in higher-dimensional space-times. As the dimensionality of space-time decreases, the range of possible supergravity theories and the set of known string vacuum constructions expand. These lectures develop the basic technology for describing a variety of string vacua, including heterotic, intersecting brane, and F-theory compactifications. In particular, a systematic presentation is given of the basic elements of F-theory. In each dimension, we summarize the current state of knowledge regarding the extent to which supergravity theories not realized in string theory can be shown to be inconsistent.