We use circle and orbicircle compactifications to illustrate generic features of string compactifications, including non-abelian gauge symmetry enhancement, Kac–Moody algebras and the Higgs effect. T-duality is introduced for both closed and open strings. Toroidal compactification are discussed in some detail, and two-tori are used as a proxi for Calabi–Yau compactifications and mirror symmetry. We discuss the vacuum selection problem and introduce the concepts of ‘landscape’ and ‘swampland’.

Three central questions that face a future philosophy of quantum gravity: Does quantum gravity eliminate spacetime as fundamental structure? How does quantum gravity explain the appearance of spacetime? What are the broader implications of quantum gravity for metaphysical (and other) accounts of the world? In this essay I begin to lay out a conceptual scheme for (1) analyzing dualities as cases of theoretical equivalence and (2) assessing when cases of theoretical equivalence are also cases of physical equivalence. The scheme is applied to gauge/gravity dualities. I expound what I argue to be their contribution to questions about (3) the nature of spacetime in quantum gravity and (4) broader philosophical and physical discussions of spacetime. Iapply this scheme to questions (3) and (4) for gauge/gravity dualities. I argue that the things that are physically relevant are those that stand in a bijective correspondence under duality: the common core of the two models. I therefore conclude that most of the mathematical and physical structures that we are familiar with, in these models (the dimension of spacetime, tensor fields, Lie groups), are largely, though crucially never entirely, not part of that common core. Thus, the interpretation of dualities for theories of quantum gravity compels us to rethink the roles that spacetime, and many other tools in theoretical physics, play in theories of spacetime.