High Energy Theory Seminar

In this talk I will discuss recent developments on the Swampland Distance Conjecture (SDC). This conjecture is at the core of the Swampland program, which aims to determine the constraints that any EFT must satisfy to be consistent with quantum gravity. First, we will study the SDC in the context of AdS/CFT, which translates to a relation between the geometry of conformal manifolds and the spectrum of local operators. Interestingly, it seems that a stronger and more universal version of the conjecture is valid for conformal field theories in d > 2 spacetime dimensions; namely, that all theories at infinite distance in the Zamolodchikov metric possess an emergent higher-spin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Interpreted gravitationally, it implies that approaching infinite distance in moduli space at fixed AdS radius, a tower of higher-spin fields becomes massless at an exponential rate that is bounded from below in Planck units. This relates to recent developments of the SDC in N=1 4d supergravity theories, where the SDC can be derived from the universal presence of an axionic BPS string at every infinite field distance limit. This allows us to identify the infinite distance limits with RG flow endpoints of BPS strings, and also give a lower bound on the exponential rate. I will show that if the string satisfies the Weak Gravity Conjecture, then the SDC follows automatically, uncovering a new relation between the swampland conjectures.

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