Aspects of scalar dynamics and vacuum energy in the string swampland program

I will discuss properties of scalar dynamics and vacuum energy in the context of string theory compactifications, and investigate their connection with some swampland conjectures.

In the first part of the talk, I will consider warped throats with locally AdS geometry, and study their stability. Motivated by considering the near horizon limit of systems of fractional branes at singularities, I will argue that such backgrounds cannot be stable in the absence of supersymmetry, thus generalizing the swampland criterion that forbids stable non supersymmetric AdS vacua. This will shed new light on already known instabilities, and unveil a novel decay mechanism associated with the presence N=2 fractional branes. 
Then I will focus on the asymptotic Klebanov–Tseytlin solution, regarded as a compactification to five dimensions in which an axion runs in the radial direction of the locally AdS spacetime. This will be reinterpreted as a fully backreacted solution of transplanckian axion monodromy, thus providing an existence proof of transplanckian field excursions in string theory.

In the second part I will propose a refinement of certain swampland conjectures in the presence of discrete gauge symmetries. I will consider theories with both discrete and continuous gauge symmetries, and use a black hole argument based on the weak gravity conjecture together with the species bound to relate the gauge coupling of the continuous symmetry with the order of the discrete symmetry. I will also study discrete symmetries associated with domain walls, and use them to justify the presence of separation of scales in an infinite family of AdS_4 flux vacua of type IIA string theory.

In the last part I will focus on running solutions sourced by tadpoles for dynamical fields, and analyse their properties in large classes of string theory models. I will show that these solutions can only extend up to a finite distance in spacetime, scaling inversely with the strength of the tadpole, and are capped off by cobordism walls of nothing in a dynamical realization of the cobordism conjecture. I will also discuss domain walls interpolating between different (but
cobordant) theories, and explain which is the criterion to distinguish between the two kinds of walls. This will be related to the distance in field space, thus suggesting a connection with the distance conjecture.