arXiv subjects

Tom Rudelius

Publications and source records attributed to Tom Rudelius.

At least 19 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

Quantum Gravity Cutoff from Axions: A Type IIB Landscape Study

Extra-dimensional axions have coupling strength related to fundamental, ultraviolet physics. It has been proposed that the properties of such axions imply a bound on the quantum gravity cutoff: $\Lambda_\mathrm{QG} \lesssim 2\pi \sqrt{S} f$, where $f$ is the axion decay constant and $S$ is the instanton action. In the context of weakly-coupled string theory, we identify $\Lambda_\mathrm{QG}$ with the string scale $M_s$. In this paper, we carry out a quantitative study of this bound on the string scale in the context of Calabi-Yau compactifications of Type IIB string theory, considering both $C_2$ and $C_4$ axions. We show, both analytically and numerically, that the bound holds even near boundaries of the K\"ahler moduli space, including those where the co-scaling relationship for axion strings fails. This evidence bolsters previous arguments, based on naturalness and on unitarity, that the bound is a general feature of extra-dimensional axions in quantum gravity.

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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

Nonabelian Lattice Weak Gravity Conjecture and Monopole Confinement

Within the known landscape of quantum gravity, most theories satisfy the Lattice Weak Gravity Conjecture (LWGC), which requires a superextremal particle at every site in the electric charge lattice $\Gamma$. However, counterexamples to the LWGC exist, and it was recently hypothesized that such counterexamples necessarily feature fractionally charged confined monopoles. In this work, we verify this hypothesis in toroidal orbifold compactifications of the heterotic string, which notably feature LWGC violation in both the abelian and nonabelian gauge sectors. In all the cases we consider, there exists a discrete subgroup of the center of the gauge group $K \subseteq Z(G)$ such that superextremal particles exist at every site in the charge lattice of the quotient group $G/K$, while (confined) monopoles exist at all sites in the magnetic charge lattice of $G/K$. This suggests that LWGC violation cannot occur for gauge groups with trivial centers, and more generally the degree of LWGC violation in a nonabelian gauge theory is bounded in terms of the maximal order of the center.

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arXiv2025

On the Field Excursion Bound

In a recent work, Herderschee and Wall (HW) proved a bound on scalar field excursions in spatially flat FRW cosmologies. In this note, we give an alternate proof of their bound using the Friedmann equations, and we prove that it can be saturated only in universes with vanishing acceleration, $\ddot a =0$. We argue that in a realistic (eternal) inflation scenario, the bound is robust against quantum corrections and spacetime curvature, and it can be violated by higher-derivative corrections only at the expense of a superluminal speed of sound. We further speculate on possible connections between the swampland program and the vacuum estimates given in the work of HW.

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arXiv2025

Co-Scaling and Alignment of Electric and Magnetic Towers

Towers of electrically and magnetically charged states in quantum gravity often exhibit two important properties. First, the ratio of the mass (or tension) of electrically charged states to magnetically charged states is of order $e^2/(4\pi)$, which we refer to as "co-scaling." Second, in theories of multiple gauge fields, the towers of states that exhibit co-scaling have charges that point in approximately the same direction in charge space as measured by the gauge kinetic matrix, which we refer to as "alignment." After motivating these ideas with some heuristic arguments, we examine the spectrum of BPS states in the 5d supergravity landscape arising from M-theory on a Calabi-Yau threefold. In this setting, every tower of magnetically charged strings is paired with a corresponding tower of electrically charged particles that exhibits co-scaling and rapid alignment. In particular, this motivates a sharp mathematical characterization of the magnetic infinity cone in Calabi-Yau geometry. We propose a universal conjecture about quantum gravity: towers of charged states which, in some limit in moduli space, have maximally divergent charge-to-mass ratios always have corresponding magnetic partner states exhibiting co-scaling and alignment. Co-scaling is not a general feature of extremal black hole solutions in theories of gauge fields and scalars, suggesting that it is a principle of UV complete quantum gravity. We briefly remark on possible phenomenological applications, including to axion physics.

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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

An Introduction to the Weak Gravity Conjecture

The Weak Gravity Conjecture holds that gravity must be the weakest force. This is true of the familiar forces in our own universe -- electromagnetism, for instance, is many orders of magnitude stronger than gravity. But the bold claim of the Weak Gravity Conjecture is that this statement is true, not only for electromagnetism in our universe, but for any similar force in any consistent universe governed by quantum mechanics. In this brief introduction, aimed at advanced undergraduates or beginning graduate students, we elaborate on the precise definition of the Weak Gravity Conjecture, the evidence for it, and some of the remarkable implications of it. We explain how the Weak Gravity Conjecture may play a role in bridging the gulf between the formal mathematics of string theory and the real-world observations of particle physics and cosmology.

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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 $T\sim \exp(-\alpha\Delta)$ with the moduli space distance $\Delta$ at a rate of at least $\alpha\geq 1/\sqrt{d-p_\text{max}-1}$. 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 $(-\vec{\nabla}\log\Lambda_{\text{QG}})$ 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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arXiv2024

A Symmetry-centric Perspective on the Geometry of the String Landscape and the Swampland

As famously observed by Ooguri and Vafa nearly twenty years ago, scalar field moduli spaces in quantum gravity appear to exhibit various universal features. For instance, they seem to be infinite in diameter, have trivial fundamental group, and feature towers of massive particles that become light in their asymptotic limits. In this essay, we explain how these features can be reformulated in more modern language using generalized notions of global symmetries. Such symmetries are ubiquitous in non-gravitational quantum field theories, but it is widely believed that they must be either gauged or broken in quantum gravity. In what follows, we will see that the observations of Ooguri and Vafa can be understood as consequences of such gauging or breaking.

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arXiv2023

Persistence of the Pattern in the Interior of 5d Moduli Spaces

Castellano, Ruiz, and Valenzuela recently observed a remarkable "pattern" in infinite-distance limits of moduli spaces in quantum gravity, which relates the field space variation of the mass of the lightest tower of particles to the field space variation of the species scale. In this work, we show how a version of this pattern can be proven to hold for BPS particles and strings throughout the vector multiplet moduli space of a 5d supergravity theory, even in regions where the particle masses and string tensions are substantially modified relative to their asymptotic behavior in the infinite-distance limits. This suggests that a suitably defined version of the pattern may hold not merely in the asymptotic limits of moduli space, but in the interior as well.

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arXiv2023

Gopakumar-Vafa Invariants and the Emergent String Conjecture

The Emergent String Conjecture of Lee, Lerche, and Weigand holds that every infinite-distance limit in the moduli space of a quantum gravity represents either a decompactification limit or an emergent string limit in some duality frame. Within the context of 5d supergravities coming from M-theory compactifications on Calabi-Yau threefolds, we find evidence for this conjecture by studying (a) the gauge couplings and (b) the BPS spectrum, which is encoded in the Gopakumar-Vafa invariants of the threefold. In the process, we disuss a testable geometric consequence of the Emergent String Conjecture, and we verify that it is satisfied in all complete intersection Calabi-Yau threefolds in products of projective spaces (CICYs).

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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 $\alpha \ge \frac{1}{\sqrt{d-2}}$ 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

Revisiting the Refined Distance Conjecture

The Distance Conjecture of Ooguri and Vafa holds that any infinite-distance limit in the moduli space of a quantum gravity theory must be accompanied by a tower of exponentially light particles, which places tight constraints on the low-energy effective field theories in these limits. One attempt to extend these constraints to the interior of moduli space is the refined Distance Conjecture, which holds that the towers of light particles predicted by the Distance Conjecture must appear any time a modulus makes a super-Planckian excursion in moduli space. In this note, however, we point out that a tower which satisfies the Distance Conjecture in an infinite-distance limit of moduli space may be parametrically heavier than the Planck scale for an arbitrarily long geodesic distance. This means that the refined Distance Conjecture, in its most naive form, does not place meaningful constraints on low-energy effective field theory. This motivates alternative refinements of the Distance Conjecture, which place an absolute upper bound on the tower mass scale in the interior of moduli space. We explore two possibilities, providing evidence for them and briefly discussing their implications.

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arXiv2022

Moduli Space Reconstruction and Weak Gravity

We present a method to construct the extended K\"ahler cone of any Calabi-Yau threefold by using Gopakumar-Vafa invariants to identify all geometric phases that are related by flops or Weyl reflections. In this way we obtain the K\"ahler moduli spaces of all favorable Calabi-Yau threefold hypersurfaces with $h^{1,1} \le 4$, including toric and non-toric phases. In this setting we perform an explicit test of the Weak Gravity Conjecture by using the Gopakumar-Vafa invariants to count BPS states. All of our examples satisfy the tower/sublattice WGC, and in fact they even satisfy the stronger lattice WGC.

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arXiv2022

TF08 Snowmass Report: BSM Model Building

We summarize the state of Beyond the Standard Model (BSM) model building in particle physics for Snowmass 2021, focusing mainly on several whitepaper contributions to BSM model building (TF08) and closely related areas.

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arXiv2022

Asymptotic Scalar Field Cosmology in String Theory

Asymptotic (late-time) cosmology depends on the asymptotic (infinite-distance) limits of scalar field space in string theory. Such limits feature an exponentially decaying potential $V \sim \exp(- c \phi)$ with corresponding Hubble scale $H \sim \sqrt{\dot \phi^2 + 2 V} \sim \exp(- \lambda_H \phi)$, and at least one tower of particles whose masses scale as $m \sim \exp( - \lambda \phi)$, as required by the Distance Conjecture. In this paper, we provide evidence that these coefficients satisfy the inequalities $\sqrt{(d-1)/(d-2)} \geq \lambda_H \geq \lambda_{\text{lightest}} \geq 1/\sqrt{d-2}$ in $d$ spacetime dimensions, where $\lambda_{\text{lightest}}$ is the $\lambda$ coefficient of the lightest tower. This means that at late times, as the scalar field rolls to $\phi \rightarrow \infty$, the low-energy theory remains a $d$-dimensional FRW cosmology with decelerated expansion, the light towers of particles predicted by the Distance Conjecture remain at or above the Hubble scale, and both the strong energy condition and the dominant energy condition are satisfied.

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