Effective actions for F-theory compactifications and tensor theories

In this thesis we study the low-energy effective dynamics emerging
from a class of F-theory compactifications in four and six
dimensions. We also investigate six-dimensional supersymmetric
quantum field theories with self-dual tensors, motivated by the
problem of describing the long-wavelength regime of a stack of
M5-branes in M-theory. These setups share interesting common
features. They both constitute examples of intrinsically
non-perturbative physics. On the one hand, in the context of
F-theory the non-perturbative character is encoded in the geometric
formulation of this class of string vacua, which allows the
complexified string coupling to vary in space. On the other hand,
the dynamics of a stack of multiple M5-branes flows in the infrared
to a novel kind of superconformal field theories in six dimensions
- commonly referred to as (2,0) theories - that are expected to
possess no perturbative weakly coupled regime and have resisted a
complete understanding so far. In particular, no Lagrangian
description is known for these models. The strategy we employ to
address these two problems is also analogous. A recurring Leitmotif
of our work is a transdimensional treatment of the system under
examination: in order to extract information about dynamics in $d$
dimensions we consider a (d-1)-dimensional setup. As far as
F-theory compactifications are concerned, this is a consequence of
the duality between M-theory and F-theory, which constitutes our
main tool in the derivation of the effective action of F-theory
compactifications. We apply it to six-dimensional F-theory vacua,
obtained by taking the internal space to be an elliptically fibered
Calabi-Yau threefold, but we also employ it to explore a novel kind
of F-theory constructions in four dimensions based on manifolds
with Spin(7) holonomy. With reference to six-dimensional (2,0)
theories, the transdimensional character of our approach relies in
the idea of studying these theories in five dimensions. Indeed, we
propose a Lagrangian that is formulated in five dimensions but has
the potential to capture the six-dimensional interactions of (2,0)
theories. This investigation leads us to explore in closer detail
the relation between physics in five and in six dimensions. One of
the outcomes of our exploration is a general result for one-loop
corrections to Chern-Simons couplings in five dimensions.