Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape

Abstract

Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that the defining data of such theories, as well as the landscape of effective field theories that are valid at least up to a fixed cutoff, admit descriptions with a uniform bound on complexity. To make this precise, we use tame geometry and work in sharply o-minimal structures, in which tame sets and functions come with two integer parameters that quantify their information content; we call this pair their tame complexity. Our Finite Complexity Conjectures are supported by controlled examples in which an infinite Wilsonian expansion nevertheless admits an equivalent finite-complexity description, typically through hidden rigidity conditions such as differential or recursion relations. We further assemble evidence from string compactifications, highlighting the constraining role of moduli space geometry and the importance of dualities. This perspective also yields mathematically well-defined notions of counting and volume measures on the space of effective theories, formulated in terms of effective field theory domains and coverings, whose finiteness is naturally enforced by the conjectures.

arXiv comment50 pages, 7 figures; v3: minor corrections

References in corpus (43)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Exact evolution equation for the effective potential
• Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric QCD
• On the Geometry of the String Landscape and the Swampland
• Nonperturbative Evolution Equation for Quantum Gravity
• The Swampland: Introduction and Review
• An SL(2,Z) Multiplet of Type IIB Superstrings
• Black Holes and Large N Species Solution to the Hierarchy Problem
• Instantons and recursion relations in N=2 Susy gauge theory
• Lectures on the Swampland Program in String Compactifications
• New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls
• Infinite Distances in Field Space and Massless Towers of States
• Introduction to S-Duality in N=2 Supersymmetric Gauge Theory. (A pedagogical review of the work of Seiberg and Witten)
• Some Relationships Between Dualities in String Theory
• Nonperturbative Effective Actions of N=2 Supersymmetric Gauge Theories
• Global aspects of the space of 6D N = 1 supergravities
• Matter and singularities
• Introduction to Seiberg-Witten Theory and its Stringy Origin
• Quantum Information and Gravity Cutoff in Theories with Species
• Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry
• The Emergence Proposal in Quantum Gravity and the Species Scale
• IR/UV Mixing, Towers of Species and Swampland Conjectures
• A bound on 6D N=1 supergravities
• The effectiveness of the local potential approximation in the Wegner-Houghton renormalization group
• Four Dimensional $\mathcal{N}=4$ SYM and the Swampland
• Finiteness and the Swampland
• Moduli-dependent Species Scale
• Structure in 6D and 4D N=1 supergravity theories from F-theory
• Swampland Constraints on 5d $\mathcal{N}=1$ Supergravity
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Fine Tuning, Sequestering, and the Swampland
• Taming the Landscape of Effective Theories
• Quantum Gravity Bounds on N=1 Effective Theories in Four Dimensions
• Effective Field Theories on the Jet Bundle
• Finiteness for self-dual classes in integral variations of Hodge structure
• Finiteness and the Emergence of Dualities
• On Measuring Distances in the Quantum Gravity Landscape
• Effective Field Theories as Lagrange Spaces
• Boundedness of elliptic Calabi-Yau varieties with a rational section
• Connecting flux vacua through scalar field excursions
• EFT & Species Scale: Friends or foes?
• Finite Landscape of 6d N=(1,0) Supergravity
• Boundedness of elliptic Calabi-Yau threefolds