arXiv subjects

Muldrow Etheredge

Publications and source records attributed to Muldrow Etheredge.

16 recordsLinked to original sources

arXiv2026

Taxonomy of Potentials in Asymptotic Limits

In infinite-distance limits of scalar field moduli spaces in quantum gravity, particle masses, brane tensions, and scalar field potentials scale exponentially with geodesic distance. Previous work has shown that the exponential decay rates of particle masses and brane tensions admit a discrete classification. In this work, we extend this classification to the case of scalar field potentials. We find that leading contributions to the potential typically scale with tensions of codimension-1 branes as $V \sim T_{d-1}^2$ or codimension-0 branes as $V \sim T_d$, and these relations hold formally even when the associated branes are absent from the spectrum. As a result, the taxonomy rules for potentials are intimately connected to the brane taxonomy rules. More generally, potential contributions can be labeled by a collection of integers, which correspond physically to their transformation properties under Weyl rescalings and their order in the string loop expansion. This implies that the vector $\vec v = - \vec \nabla \log V$ is lattice-valued, and indeed it lies in precisely the same lattice as the analogous vectors $\vec \alpha = - \vec \nabla \log T_d$ for codimension-0 branes of tension $T_d$. We verify our taxonomy rules in various examples in string theory. We show that these rules imply that sums of positive potential terms satisfy the Strong Asymptotic de Sitter Conjecture, which requires $|\vec \nabla \log V| \geq 2/\sqrt{d-2}$ in asymptotic regimes of scalar field moduli space, and they imply that higher-derivative gravitational corrections are suppressed by powers of the species scale.

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arXiv2026

Integral Scaling for EFT Strings from the Bottom-Up

Near the core of an EFT string in a 4d $\mathcal{N}=1$ theory, the scalars are dynamically driven to infinite field distance and a tower of states becomes light, with mass scaling with the string tension in Planck units as $m^2\sim \mathcal{T}^{\,w}$. According to the Integral Scaling Conjecture, $w$ takes only values 1, 2 and 3. In this paper, we examine how this conjecture can follow from the brane-taxonomy rules associated with the Emergent String Conjecture. In this context, we classify the relevant types of duality frames into 74 classes, identify which lattice sites can be relevant EFT candidates, and exhaustively test integral scaling for all of these candidates. We find that it holds with $w\leq 3$ for all the leading towers and also for the subleading towers below the species scale (up to half-integral subtleties that also appear in top-down examples). We further find evidence that the oscillator modes of EFT string candidates generate the lattices of particles and strings. Moreover, $w=1$ implies a perturbative string limit, but the converse is not true. We compare our classification with concrete type IIA, F-theory and M-theory compactifications.

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arXiv2026

Moduli-Space Laplacians, Asymptotic Geometry, and the Emergent String Conjecture

At asymptotic limits of moduli spaces of quantum gravity vacua, we argue that the masses of the lightest particle towers are eigenfunctions of the moduli-space Laplacian. The associated eigenvalues are quantized by the Emergent String Conjecture and determine the exponential decay rates of axionic directions in these limits. We also connect the quantization of Laplacian eigenvalues to the spectrum of instantons for the theory. We support our claims with diverse examples that preserve between 4 and 32 supercharges.

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arXiv2026

Sharpening the Supersymmetric Axion Weak Gravity Conjecture

The Axion Weak Gravity Conjecture provides one of the most effective quantum gravity tools for constraining particle physics and cosmology, but it has long been thought of as a slightly fuzzy statement: given an axion with decay constant $f$ there should exist an instanton of charge $n$ and action $S$ with $fS/|n|$ at most an order-one number in Planck units. Recent work related to axion wormholes motivated a specific order-one coefficient, $\frac{fS}{|n|} \leq \frac{\pi}{2 \kappa_d} \sqrt{\frac{d-1}{d-2}}$. In this work, we verify this bound in various axion sectors across the string landscape using three complementary approaches. In the process, we derive even tighter bounds on instantons in such sectors. For example, we argue that supersymmetric instantons in 4d satisfy the stronger bound of $\frac{fS}{|n|}\leq \frac 1{\kappa_4}\sqrt{\frac{7}{2}}$.

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arXiv2026

Moduli Space Quantum Mechanics

In this paper, continuing the discussion about Species Quantum Mechanics, we investigate quantum mechanics in moduli spaces using a mini-superspace approach. From this perspective, moduli-dependent functions can be viewed as operators, and we explore how the taxonomic relations from the Emergent String Conjecture can constrain the non-commutativity between these operators. Next, we study wave functions on moduli spaces, and we find that the geometry of moduli space plays an important role and leads to excited wave functions localised in the bulks of moduli spaces, and with positive energy eigenvalues. For cases when potentials are present, these effects result in moduli localised away from classical minima, and often result in excited, positive energy states.

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arXiv2025

Taxonomy of branes in infinite distance limits

I consider flat slices of moduli spaces where the $(-\nabla \log T)$-vectors of particle-towers and branes are constant, and I show that the Emergent String Conjecture constrains these vectors to reside on lattices. In asymptotic limits, this results in exponentially separated, discretized hierarchies of energy scales. I further identify conditions that determine whether a given lattice site must be populated, and I show that only a finite set of configurations satisfies these conditions. I classify all such configurations for 0d, 1d, and 2d moduli spaces in theories with 3 to 11 spacetime dimensions, and I argue that 11d is the maximal spacetime dimension compatible with my assumptions. Remarkably, this classification reproduces the detailed particle and brane content of various string theory examples with 32, 16, and 8 supercharges. It also describes some examples where the assumptions I use are violated, suggesting that my assumptions can be relaxed and the scope of this classification can be expanded. It might also predict new branes. For instance, if heterotic string theory is described by this classification, then it must possess non-BPS branes with D-brane-like tensions. Similarly, if this classification applies to the Dark Dimension Scenario with an extra modulus, then it requires the existence of strings with tensions related to the cosmological constant by $T\lesssim Λ^{1/6}$ in 4d Planck units.

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arXiv2025

Confined monopoles and failure of the Lattice Weak Gravity Conjecture

Almost all known theories of quantum gravity satisfy the Lattice Weak Gravity Conjecture (LWGC), which posits that a consistent theory of quantum gravity must have a superextremal particle at every site in the charge lattice. However, a number of theories have been observed to violate the LWGC; such theories exhibit only a (finite index) sublattice of superextremal particles. This paper aims to identify universal features and patterns associated with LWGC violation across numerous examples in effective field theory, string theory, and M-theory. Some of these examples have appeared previously in the literature, while others are novel. In all such examples, we observe that LWGC failure is accompanied by the existence of fractionally charged monopoles confined by flux tubes, where superextremal particles exist everywhere in the sublattice dual to the superlattice of fractional confined monopole charges. The confining flux tubes become light when the failure of the LWGC becomes more extreme, so monopoles deconfine in the limit where LWGC-violating particles become infinitely massive. We also identify similarities between these confined monopoles, non-invertible symmetries, and the Hanany-Witten effect.

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arXiv2024

A Distance Conjecture for Branes

We use branes to generalize the Distance Conjecture. We conjecture that in any infinite-distance limit in the moduli space of a $d$-dimensional quantum gravity theory, among the set of particle towers and fundamental branes with at most $p_\text{max}\leq d-2$ spacetime dimensions, at least one has mass/tension decreasing exponentially $T\sim \exp(-αΔ)$ with the moduli space distance $Δ$ at a rate of at least $α\geq 1/\sqrt{d-p_\text{max}-1}$. Since $p_\text{max}$ can vary, this represents multiple conditions, where the Sharpened Distance Conjecture is the $p_\text{max}=1$ case. This conjecture is a necessary condition imposed on higher-dimensional theories in order for the Sharpened Distance Conjecture to hold in lower-dimensional theories. We test our conjecture in theories with maximal and half-maximal supersymmetry in diverse dimensions, finding that it is satisfied and often saturated. In some cases where it is saturated -- most notably, heterotic string theory in 10 dimensions -- we argue that novel, low-tension non-supersymmetric branes must exist. We also identify patterns relating the rates at which various brane tensions vary in infinite-distance limits and relate these tensions to the species scale.

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arXiv2024

Taxonomy of Infinite Distance Limits

The Emergent String Conjecture constrains the possible types of light towers in infinite-distance limits in quantum gravity moduli spaces. In this paper, we use these constraints to restrict the geometry of the scalar charge-to-mass vectors $(-\vec{\nabla}\log m)$ of the light towers and the analogous vector $(-\vec{\nabla}\logΛ_{\text{QG}})$ of the species scale. We derive taxonomic rules that these vectors must satisfy in each duality frame. Under certain assumptions, this allows us to classify the ways in which different duality frames can fit together globally in the moduli space in terms of a finite list of polytopes. Many of these polytopes arise in known string theory compactifications, while others suggest either undiscovered corners of the landscape or new swampland constraints.

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arXiv2023

Geodesic Gradient Flows in Moduli Space

Geodesics in moduli spaces of string vacua are important objects in string phenomenology. In this paper, we highlight a simple condition that connects brane tensions, including particle masses, with geodesics in moduli spaces. Namely, when a brane's scalar charge-to-tension ratio vector $-\nabla \log T$ has a fixed length, then the gradient flow induced by the logarithm of the brane's tension is a geodesic. We show that this condition is satisfied in many examples in the string landscape.

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arXiv2023

Constrained Spin Systems and KNdS Black Holes

Kerr-Newman de Sitter (KNdS) spacetimes have a rich thermodynamic structure that involves multiple horizons, and so differs in key respects from asymptotically flat or AdS black holes. In this paper, we show that certain features of KNdS spacetimes can be reproduced by a constrained system of $N$ non-interacting spins in a magnetic field. Both the KNdS and spin systems have bounded energy and entropy, a maximum of the entropy in the interior of the energy range, and a symmetry that maps lower energy states to higher energy states with the same entropy. Consequently, both systems have a temperature that can be positive or negative, where the gravitational temperature is defined analogously to that of the spins. We find that the number of spins $N$ corresponds to $1/Λ$ for black holes with very small charge $q$ and rotation parameter $a$, and scales like $\sqrt{(a^2+q^2)/Λ}$ for larger values of $a$ and $q$. By studying constrained spin systems, we provide insight into the thermodynamics of KNdS spacetimes and its quantum mechanical description.

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arXiv2023

Dense Geodesics, Tower Alignment, and the Sharpened Distance Conjecture

The Sharpened Distance Conjecture and Tower Scalar Weak Gravity Conjecture are closely related but distinct conjectures, neither one implying the other. Motivated by examples, I propose that both are consequences of two new conjectures: 1. The infinite distance geodesics passing through an arbitrary point $ϕ$ in the moduli space populate a dense set of directions in the tangent space at $ϕ$. 2. Along any infinite distance geodesic, there exists a tower of particles whose scalar-charge-to-mass ratio ($-\nabla \log m$) projection everywhere along the geodesic is greater than or equal to $1/\sqrt{d-2}$. I perform several nontrivial tests of these new conjectures in maximal and half-maximal supergravity examples. I also use the Tower Scalar Weak Gravity Conjecture to conjecture a sharp bound on exponentially heavy towers that accompany infinite distance limits.

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arXiv2023

Running Decompactification, Sliding Towers, and the Distance Conjecture

We study towers of light particles that appear in infinite-distance limits of moduli spaces of 9-dimensional $\mathcal{N}=1$ string theories, some of which notably feature decompactification limits with running string coupling. The lightest tower in such decompactification limits consists of the non-BPS Kaluza-Klein modes of Type I$'$ string theory, whose masses depend nontrivially on the moduli of the theory. We work out the moduli-dependence by explicit computation, finding that despite the running decompactification the Distance Conjecture remains satisfied with an exponential decay rate $α\ge \frac{1}{\sqrt{d-2}}$ in accordance with the sharpened Distance Conjecture. The related sharpened Convex Hull Scalar Weak Gravity Conjecture also passes stringent tests. Our results non-trivially test the Emergent String Conjecture, while highlighting the important subtlety that decompactification can lead to a running solution rather than to a higher-dimensional vacuum.

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arXiv2023

Branes and symmetries for $\mathcal N=3$ S-folds

We describe the higher-form and non-invertible symmetries of 4d $\mathcal N= 3$ S-folds using the brane dynamics of their holographic duals. In cases with enhancement to $\mathcal N=4$ supersymmetry, our analysis reproduces the known field theory results of Aharony, Seiberg and Tachikawa, and is compatible with the effective action recently given by Bergman and Hirano. Likewise, for two specific $\mathcal N=3$ theories for which Zafrir has conjectured $\mathcal N=1$ Lagrangians our results agree with those implied by the Lagrangian description. In all other cases, our results imply novel predictions about the symmetries of the corresponding $\mathcal N=3$ field theories.

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arXiv2022

Derivative Corrections to Extremal Black Holes with Moduli

We derive formulas for the leading mass, entropy, and long-range self-force corrections to extremal black holes due to higher-derivative operators. These formulas hold for black holes with arbitrary couplings to gauge fields and moduli, provided that the leading-order solutions are static, spherically-symmetric, extremal, and have nonzero horizon area. To use these formulas, both the leading-order black hole solution and the higher-derivative effective action must be known, but there is no need to solve the derivative-corrected equations of motion. We demonstrate that the mass, entropy and self-force corrections involve linearly-independent combinations of the higher-derivative couplings at any given point in the moduli space, and comment on their relations to various swampland conjectures.

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arXiv2022

Sharpening the Distance Conjecture in Diverse Dimensions

The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field distance $\Vertϕ\Vert$ as $m \sim \exp(- λ\Vertϕ\Vert)$, where $λ$ is order-one in Planck units. While the evidence for this conjecture is formidable, there is at present no consensus on which values of $λ$ are allowed. In this paper, we propose a sharp lower bound for the lightest tower in a given infinite-distance limit in $d$ dimensions: $λ\geq 1/\sqrt{d-2}$. In support of this proposal, we show that (1) it is exactly preserved under dimensional reduction, (2) it is saturated in many examples of string/M-theory compactifications, including maximal supergravity in $d= \text{4 - 10}$ dimensions, and (3) it is saturated in many examples of minimal supergravity in $d= \text{4 - 10}$ dimensions, assuming appropriate versions of the Weak Gravity Conjecture. We argue that towers with $λ< 1/\sqrt{d-2}$ discussed previously in the literature are always accompanied by even lighter towers with $λ\geq 1/\sqrt{d-2}$, thereby satisfying our proposed bound. We discuss connections with and implications for the Emergent String Conjecture, the Scalar Weak Gravity Conjecture, the Repulsive Force Conjecture, large-field inflation, and scalar field potentials in quantum gravity. In particular, we argue that if our proposed bound applies beyond massless moduli spaces to scalar fields with potentials, then accelerated cosmological expansion cannot occur in asymptotic regimes of scalar field space in quantum gravity.

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