A Gentle Hike Through the Swampland

At first sight, it might seem that any quantum field theory, regarded as a low-energy effectve field theory (EFT), can be coupled to Einsteinian gravity. Over the past few years, a large body of work has challenged this view, arguing that not every EFT arises as the IR of a consistent theory of quantum gravity. EFT’s that do not descend from quantum gravity are said to be in the “Swampland”. This chapter provides a bird’s eye view over some of the recent efforts in delineating the boundaries of the Swampland, collectively known as the “Swampland Program”. We focus on recent progress that may not have been covered in existing reviews. We first give an introduction to the oldest Swampland Conjecture, the absence of global symmetries, but from a modern point of view of topological symmetry operators and its generalization to non-invertible symmetries. We then introduce a certain extension of the absence of global symmetries, known as the Cobordimsm Conjecture, and discuss its applications to constrain the Landscape of minimal supergravity in more than six dimensions. These better-established conjectures are connected to other conjectured properties of quantum gravity which we cover in this chapter. These include the Weak Gravity Conjecture, its phenomenological implications and generalizations to de Sitter space (Festina Lente), the Distance Conjecture, ranging from recent connections to EFT strings to the Emergent String Conjecture and implications for potentials, and conjectures involving the vacuum energy.