Centro de Excelencia Severo Ochoa

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Speaker:

José Calderón Infante

Location&Place:

Orange Room / ICMAT

Abstract:

The goal of this thesis is to push the limits of the Swampland Distance Conjecture (SDC). This is one of the most relevant conjectures in the Swampland program, whose aim is to identify the criteria that an effective field theory must satisfy in order to be consistently coupled to quantum gravity. For this purpose, we study the SDC in two different contexts: Running solutions and AdS/CFT. After an introduction motivating the subject, we give a short review of the Swampland program. Special attention is given to the SDC and to the limitations that motivate this thesis.

We start by presenting a first example of running solution and its interplay with the SDC. It teaches us that the naive extension of the conjecture to this context fails. However, we argue that this is not a violation of the SDC in its usual formulation, but that it is protected in a non-trivial way. Motivated by these results, we propose that consistency of the SDC along the RG flow of the theory imposes constraints on the potentials that are attainable in quantum gravity. To characterize them, we consider the behaviour of the SDC along non-geodesic trajectories in field space. We first study some examples and then generalize the results by providing a geometric formulation of the SDC. It turns out to be equivalent to a convex hull condition, similar to the one appearing in a extension of the Weak Gravity Conjecture.

We then move to another type of running solutions, the so-called dynamical cobordisms. They receive this name for being the spacetime realization of cobordisms between different theories. Based on several examples in theories with dynamical tadpoles, we propose that the behaviour of scalars as one hits a cobordism wall allows for a distinction between two types of them: On one hand there are interpolating domain walls, in which scalars remain at finite field distance and after which spacetime continues. On the other hand, scalars explore infinite field distance as we approach a wall of nothing ending spacetime. For the latter case, we furthermore find some universal scaling relations between spacetime geometric quantities such as the distance to the wall or the scalar curvature and the field space distance. By performing a bottom-up effective field theory analysis of these kind of solutions, we moreover relate this universal scalings to the presence of exponential potentials at infinite field distance limits. These results suggest a relation between Cobordism, de Sitter (dS) and Distance conjectures.

Finally, we turn our attention to the SDC in the context of AdS/CFT. In all the examples we consider, infinite distance limits in the CFT turn out to be weak coupling points in which some sector decouples. The SDC tower of states from the CFT perspective is then formed by the higher-spin conserved currents that characterize these points. After reviewing the main entries of the AdS/CFT dictionary that are relevant for the conjecture, we warm up with the most well-known example of this duality in String Theory. We then perform some purely CFT analysis in the context of 4d $\mathcal{N}=2$ theories. For those with Einstein gravity dual, we are able to show that the exponential decay rate of the tower of states is at least order one. In addition, we take a closer look to an specific example with known bulk dual in String Theory. It exhibits interesting features such as infinite field distance limits induced by quantum corrections, parametrically large exponential decay rate for the tower and intriguing candidates for the stringy object that give rise to it.

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PhD José Calderón Infanta

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Pushing the Limits of the Swampland Distance Conjecture

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