String theory is the most promising candidate for a consistent quantum theory of gravitationally interacting matter fields. The theory is defined in 10 or 11 space-time dimensions, which means we need to compactify the extra dimensions (for example, by curling them up into tiny circles) so as to be consistent with our four-dimensional Universe. Different compactification scenarios produce different low-energy four-dimensional quantum field theories, which together form the so-called “string landscape” (Fig. 1). Somewhere within this string-consistent region is the standard model QFT. But how big is the landscape? Does it contain all possible QFTs? If the answer were yes, then string theory would not offer much insight into how to go beyond the standard model. However, as it turns out there is growing evidence that we cannot get all QFTs as low-energy limits of string compactifications [1, 2], and in fact the overwhelming majority of QFTs belong to the swampland that is outside of the landscape (Fig. 2).

APS/ Alan Stonebraker Figure 2: A Venn diagram showing how the swampland encompasses the landscape. The standard model is located within the landscape.

APS/ Alan Stonebraker Figure 2: A Venn diagram showing how the swampland encompasses the landscape. The standard model is located within the landscape. ×

Determining the criteria that distinguish landscape QFTs from swampland QFTs is one of the active areas of research in string theory today. Since we do not know the full list of consistent compactifications of string theory, we cannot be sure about the exact conditions delimiting the boundaries between these two regions. But we can take an empirical approach by examining the large class of reliable compactifications that decades of string theory research have provided and see if there are common features among the resulting low-energy QFTs. From this, we can come up with universal criteria for deciding which QFTs reside in the swampland or the landscape. An example of such criteria is the weak gravity conjecture, which says that gravity is always the weakest force in any string-consistent QFT [3]. Some evidence for this conjecture comes from studies of black hole physics and their thermodynamical properties. And, recently, additional support for the weak gravity conjecture has emerged from numerical simulations that show how gravity’s relative weakness to other forces can prevent naked singularities from occurring [4].

Besides the weak gravity conjecture, the swampland approach has led to conjectures about the maximum number of low-mass particles allowed [5], which agrees well with the fact that the standard model has just a handful of fundamental particles. Another conjecture—called the swampland distance conjecture—concerns what happens when one of the compactified dimensions begins to change in extreme ways, such as grow in size. For example, the diameter of a curled-up dimension could become larger, allowing several low-mass particles in this dimension to populate our Universe [6]. This set of new particles, referred to as a “tower of light states,” could have implications in several situations. For example, if such a tower of light states existed in the very early Universe, it would impact inflation—a predicted epoch of exponential expansion at the very beginning of cosmic time. The swampland distance conjecture, therefore, could place interesting constraints on inflation models [7].