Constraints on Low-Dimensional String Compactifications

TL;DR

This paper investigates the constraints on string, M-theory, and F-theory compactifications in low dimensions, focusing on tadpole cancellation conditions and their implications for supersymmetric vacua and nonperturbative effects.

Contribution

It provides a detailed analysis of tadpole cancellation constraints in low-dimensional compactifications and explores their relation to supersymmetry and nonperturbative superpotentials.

Findings

Sufficient branes can cancel tadpoles in many supersymmetric vacua.

Some tadpoles cannot be canceled due to fractional values or sign issues.

Membranes and three-branes relate to the nonperturbative superpotential.

Abstract

We study the restrictions imposed by cancellation of the tadpoles for two, three, and four-form gauge fields in string theory, M-theory and F-theory compactified to two, three and four dimensions, respectively. For a large class of supersymmetric vacua, turning on a sufficient number of strings, membranes and three-branes, respectively, can cancel the tadpoles, and preserve supersymmetry. However, there are cases where the tadpole cannot be removed in this way, either because the tadpole is fractional, or because of its sign. For M-theory and F-theory compactifications, we also explore the relation of the membranes and three-branes to the nonperturbative space-time superpotential.