Exploring the Landscape of effective field theories

TL;DR

This thesis develops new tools within four-dimensional supergravity theories derived from string and M-theory to explore the landscape of possible effective field theories, emphasizing the role of gauge forms and extended objects.

Contribution

It introduces a hierarchy of gauge forms and extended objects to systematically analyze flux backgrounds, tadpole conditions, and domain wall transitions in the string theory landscape.

Findings

Gauge forms generate flux-induced superpotentials and impose background constraints.

Extended objects like strings, membranes, and 3-branes expand the landscape of solutions.

Membrane-mediated transitions influence scalar field flows between vacua.

Abstract

In this thesis we provide new tools to determine and explore the Landscape of four-dimensional effective field theories originating from string and M-theory. The main aim is to introduce, within four-dimensional effective descriptions, elements that are predicted from string theory. To this end, a hierarchy of forms is introduced within the four-dimensional $\mathcal{N}=1$ supergravity theories. The inclusion of gauge three-forms delivers a dynamical way to generate flux-induced superpotentials. Instead, gauge two-forms, dual descriptions of axions, may be eventually gauged by three-forms to generate a superpotential coupling between the different chiral multiplet sectors of the theory. The mutual constraints among the background fluxes, such as tadpole cancellations, are imposed by gauge four-forms. A hierarchy of objects, to which the gauge forms couple, is then introduced: four-dimensional BPS-strings, membranes and 3-branes enlarge the Landscape, allowing the background fluxes to consistently change transversing different spacetime regions. The Freed-Witten anomaly cancellations and the changing of tadpole cancellation conditions due to background sources are neatly expressed by BPS-junctions of membranes ending on strings and 3-branes ending on membranes. Membrane-mediated domain wall transitions are studied, which determine how the scalar fields flow connecting a vacuum to another of the Landscape. According to the perturbative regime that is scanned only some transitions are allowed, with a dramatic influence on the spectrum of objects that can be consistently incorporated in the four-dimensional description.