[Paper Review] Exploring the Landscape of effective field theories

Stefano Lanza|arXiv (Cornell University)|Dec 18, 2019

Cosmology and Gravitation Theories4 citations

TL;DR

This thesis develops a systematic framework to explore the landscape of four-dimensional effective field theories (EFTs) derived from string and M-theory, introducing a hierarchy of gauge forms—three-forms, two-forms, and four-forms—that dynamically generate flux-induced superpotentials and mediate transitions between vacua. The key contribution is a unified description of flux compactifications incorporating BPS branes, domain walls, and anomaly cancellations via higher-form gauge symmetries, revealing constraints on allowed vacuum transitions and consistent EFTs.

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.

Motivation & Objective

• To develop a systematic framework for constructing and analyzing four-dimensional N=1 supergravity theories derived from string and M-theory compactifications.
• To understand the constraints on flux vacua by incorporating higher-rank gauge forms and extended objects such as membranes and 3-branes.
• To clarify the conditions under which vacuum transitions—via domain walls or junctions—are dynamically allowed within perturbative EFTs.
• To identify the consistency conditions (e.g., tadpole cancellation, Freed-Witten anomalies) that determine which flux configurations and brane sources can coexist in a consistent EFT.
• To connect abstract EFT structures with concrete string-theoretic realizations, particularly through gauged two- and three-forms and their role in generating superpotentials.

Proposed method

• Introduces a hierarchy of gauge forms (three-forms, two-forms, four-forms) in global and supergravity settings to dynamically generate flux-induced superpotentials.
• Uses three-form multiplets to realize linear and nonlinear superpotentials via coupling to chiral multiplets and gauge symmetry enhancements.
• Applies dualities between two-forms (axions) and three-forms to construct gaugings that couple different chiral multiplet sectors.
• Imposes consistency conditions—tadpole cancellation and Freed-Witten anomaly cancellation—via gauge four-forms and BPS junctions of membranes and branes.
• Constructs domain wall solutions interpolating between vacua, analyzing their stability and compatibility with perturbative control.
• Reformulates string/M-theory compactifications in terms of effective 4D N=1 supergravity with extended objects, ensuring consistency with quantum gravity constraints.

Experimental results

Research questions

• RQ1 How can higher-rank gauge forms (three-, two-, four-forms) be systematically incorporated into 4D N=1 supergravity to generate flux-induced superpotentials?
• RQ2 What are the dynamical and consistency conditions that determine which vacuum transitions between flux vacua are allowed in perturbative EFTs?
• RQ3 How do BPS junctions of membranes ending on strings or 3-branes ending on membranes encode Freed-Witten anomaly cancellations and changing tadpole conditions?
• RQ4 In what way do gauged two-forms (axions) and three-forms mediate couplings between chiral multiplet sectors and influence the structure of the superpotential?
• RQ5 What constraints do the Swampland program and quantum gravity consistency conditions impose on the inclusion of extended objects and fluxes in 4D EFTs?

Key findings

• The inclusion of gauge three-forms provides a dynamical mechanism to generate flux-induced superpotentials in 4D N=1 supergravity, extending the standard flux-compactification paradigm.
• Gauged two-forms (dual to axions) can couple to three-forms to generate nontrivial superpotential terms between chiral multiplet sectors, enriching the vacuum structure.
• Tadpole cancellation and Freed-Witten anomaly cancellation are naturally encoded in the dynamics of gauge four-forms and BPS junctions of membranes and branes.
• Domain wall solutions interpolating between vacua are constrained by the perturbative regime; only a subset of transitions are dynamically allowed, significantly restricting the viable landscape.
• The framework reveals that consistent EFTs must include specific combinations of fluxes, branes, and higher-form symmetries to avoid quantum anomalies and maintain stability.
• The landscape of vacua is not merely a set of isolated points but is connected by physical processes mediated by extended objects, with transitions governed by the interplay of gauge symmetries and superpotential structure.