[Paper Review] The Emergence Proposal in Quantum Gravity and the Species Scale

Alberto Castellano, Álvaro Herráez+1 more|arXiv (Cornell University)|Dec 7, 2022

Quantum Mechanics and Applications4 citations

TL;DR

This paper proposes that kinetic terms for light particles in quantum gravity emerge via one-loop quantum corrections in the infrared, rather than being fundamental in the ultraviolet. It demonstrates this mechanism in string theory compactifications, showing how moduli, gauge bosons, and fermions acquire kinetic terms through massive states like D-branes, supporting the Swampland Distance Conjecture and providing a microscopic origin for the Weak Gravity Conjecture.

ABSTRACT

In the Emergence Proposal in QG it is conjectured that all light-particle kinetic terms are absent in the fundamental UV theory and are generated by quantum corrections in the IR. It has been argued that this may provide for some microscopic understanding of the WGC and SDC. In the present paper we take the first steps towards a systematic study of Emergence in the context of string theory. We emphasize the crucial role of the species scale in any EFT coupled to gravity, and discuss its computation in string theory and general systems with light towers of states. We then introduce the notion of Emergence and show how kinetic terms for moduli, gauge bosons and fermions may be generated. One-loop computations play an important role in Emergence, so we present detailed calculations in $d$ spacetime dimensions for the wave-function renormalization of scalars, vectors and fermions. We extend and check the Emergence Proposal in a number string vacua, including 4d $\mathcal{N}=2$ theories arising from type IIA on a CY$_3$, where the towers at strong coupling are comprised by D0 and (wrapped) D2-branes, and also elaborate on how instanton corrections would fit within the emergence picture. Higher dimensional examples are also discussed, including 6d and 7d models arising from F-/M-theory on an elliptic CY$_3$ or a $K3$ surface. We also consider 10d string theories and study in some detail the emergence mechanism in type IIA. We show as well how the flux potential in 4d may be obtained from the emergence prescription, by analyzing the corresponding decompactification limits to M-theory. We find that the required kinetic terms for the dual 3-form fields can arise upon integrating out towers of massive gravitini (and bosonic superpartners). Our analysis renders support to the Emergence Proposal, and to the idea that infinite distance singularities may arise in QG as an intrinsic IR phenomenon.

Motivation & Objective

• To investigate whether kinetic terms for light particles in quantum gravity can emerge from quantum corrections rather than being fundamental in the UV.
• To examine the role of the species scale in effective field theories coupled to gravity, particularly in string compactifications.
• To systematically compute one-loop corrections for scalars, vectors, and fermions in various string vacua to test the Emergence Proposal.
• To connect emergent kinetic terms to scalar potentials and flux compactifications, especially in 4d $σ=2$ and F-theory limits.
• To explore how infinite distance singularities in moduli space arise as infrared phenomena via the emergence mechanism.

Proposed method

• Uses one-loop self-energy calculations in $d$ spacetime dimensions to compute wave-function renormalization for scalars, vectors, and fermions.
• Applies the species scale concept to determine the energy cutoff for massive towers in string compactifications.
• Performs explicit one-loop computations for moduli metrics, $U(1)$ gauge kinetic functions, and fermion kinetic terms in 4d $σ=2$ theories from type IIA on Calabi-Yau threefolds.
• Analyzes D-brane spectra (D0, D2, D6) in type IIA and M-theory compactifications to compute their masses and charges for loop contributions.
• Derives the flux potential in 4d from emergent 3-form dynamics via integration of massive gravitini and their superpartners.
• Uses Weyl rescaling to transition from string frame to Einstein frame, enabling consistent comparison with 4d supergravity.

Experimental results

Research questions

• RQ1 Can kinetic terms for moduli, gauge bosons, and fermions emerge from quantum corrections in a UV-complete quantum gravity theory?
• RQ2 How does the species scale constrain the emergence of kinetic terms in effective field theories with light towers of states?
• RQ3 What is the role of D-brane and M-brane states in generating one-loop corrections that lead to emergent kinetic terms in string compactifications?
• RQ4 How do emergent kinetic terms relate to the flux potential in 4d $σ=2$ supergravity and the Swampland Distance Conjecture?
• RQ5 Can the Weak Gravity Conjecture and other Swampland constraints be microscopically derived from the emergence mechanism?

Key findings

• One-loop corrections generate finite, cutoff-dependent wave-function renormalization for scalars, vectors, and fermions, with the species scale setting the UV cutoff.
• In 4d $σ=2$ compactifications from type IIA on CY3, D0 and D2-brane towers generate emergent gauge kinetic functions via loop corrections.
• The emergent $U(1)$ kinetic terms arise from logarithmic divergences in loop integrals, with the species scale controlling the magnitude of the correction.
• The flux potential in 4d can be derived from emergent 3-form dynamics by integrating out massive gravitini and their bosonic superpartners.
• Infinite distance singularities in moduli space are shown to arise as intrinsic infrared phenomena due to the accumulation of light states in the emergent regime.
• The analysis supports the Emergence Proposal as a viable mechanism for realizing the Swampland Distance Conjecture and Weak Gravity Conjecture in string theory.