arXiv subjects

Jacob M. Leedom

Publications and source records attributed to Jacob M. Leedom.

17 recordsLinked to original sources

arXiv2026

Automorphic Structures of Heterotic Vacua

We study moduli stabilization in 4D effective field theories with Sp(4,$\mathbb{Z}$) self-duality inspired by heterotic orbifold compactifications with Wilson lines. The target-space duality group of these theories is enhanced from SL$(2,\mathbb{Z})$ to Sp$(4,\mathbb{Z})$, making Siegel modular forms the appropriate language to formulate the effective supergravity action. We construct the corresponding effective theory including moduli-dependent threshold corrections to the gauge kinetic function and nonperturbative effects in the superpotential. The degeneration limit of the Wilson lines distinguishes different sectors and dictates which combination of cusp forms appears in threshold corrections. We compute the resulting scalar potential and prove several general statements about its extrema. In particular, we show that the fixed points of Sp$(4,\mathbb{Z})$ are extrema of the potential, and derive genus-2 analogues of no-go theorems for de Sitter vacua. Finally, we show how positive-energy metastable minima can arise once supersymmetry is broken in the dilaton direction by nonperturbative contributions to the Kähler potential.

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arXiv2025

Open Strings and Heterotic Instantons

Motivated by closed string perturbation theory arguments by S. Shenker, we consider non-perturbative effects of characteristic strength $\mathcal{O}(e^{-1/g_{s}})$, with $g_{s}$ the closed string coupling constant, in supersymmetric critical heterotic string theories. We argue that in 10D such effects arise from heterotic "D-instantons," i.e. heterotic disk diagrams, whose existence relies on a non-trivial interplay between worldsheet and spacetime degrees of freedom. In compactifications of the $\mathrm{SemiSpin}(32)$ heterotic string, we argue that similar effects can arise from wrapped Euclidean non-BPS "D-strings." Two general principles arise: The first is that the consistency of those heterotic branes on which the fundamental string can end relies on an inflow mechanism for spacetime degrees of freedom. The second is that Shenker's argument, taken to its logical conclusion, implies that all closed string theories must exhibit open strings as well.

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arXiv2025

Towards a Heterotic Axiverse

In this paper we initiate a broad study of some central properties of the string axiverse arising from Calabi-Yau compactifications of the perturbative heterotic $E_8\times E_8$ theory. Along this road toward a heterotic axiverse, we characterize the generic structure of the axion mass spectrum and the effective couplings of the non-QCD heterotic axions to Abelian and non-Abelian gauge fields and discuss their implications for cosmology, particle phenomenology, and the QCD axion quality problem. We also provide arguments that the heterotic axion masses are bounded from below much more strongly than, for example, the spectrum in type IIB compactifications.

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arXiv2025

Dark Matter Nuclear Magnetic Resonance is Sensitive to Dark Photons and the Axion-Photon Coupling

We demonstrate that nuclear magnetic resonance based searches for dark matter (DM) have intrinsic and powerful sensitivity to dark photons and the axion-photon coupling. The reason is conceptually straightforward. An instrument such as CASPEr-Gradient begins with a large sample of nuclear spins polarised in a background magnetic field. In the presence of axion DM coupled to nucleons, the spin ensemble feels an effective magnetic field $\mathbf{B} \propto \nabla a$ that tilts the spins, generating a potentially observable precession. If the magnetic field is real rather than effective, the system responds identically. A real field can be generated by a kinetically mixed dark photon within the shielded region the sample is placed or an axion coupled to photons through its interaction with the background magnetic field. We show that all three signals are detectable and distinguishable. If CASPEr-Gradient were to reach the QCD axion prediction of the axion-nucleon coupling, it would simultaneously be sensitive to kinetic mixings of $ε\simeq 3 \times 10^{-16}$ and axion-photon couplings of $g_{aγγ} \simeq 2 \times 10^{-16}\,{\rm GeV}^{-1}$ for $m \simeq 1\,μ{\rm eV}$.

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arXiv2025

Exact Results in Chiral Gauge Theories with Flavor

We present exact results in softly-broken supersymmetric $\text{SU}(N_C)$ chiral gauge theories with charged fermions in one antisymmetric, $N_F$ fundamental, and $N_C+N_F-4$ anti-fundamental representations. We achieve this by considering the supersymmetric version of these theories and utilizing anomaly mediated supersymmetry breaking at a scale $m \ll Λ$ to generate a vacuum. The connection to non-supersymmetric theories is then conjectured in the limit $m \rightarrow \infty$. For odd $N_C$, we determine the massless fermions and unbroken global symmetries in the infrared. For even $N_C$, we find global symmetries are non-anomalous and no massless fermions. In all cases, the symmetry breaking patterns differ from what the tumbling hypothesis would suggest.

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arXiv2025

Probing the UV with IR Axion Dark Matter Experiments

There is an ongoing and future experimental program searching for axions as both extensions of the Standard Model and as candidates for the observed dark matter. In this paper, we examine the feasibility of being able to pin down precise features of axions within the context of this program. We define a set of infrared data that can be probed by experiments and explain how it encodes the ultraviolet data defining particular models of the QCD axion. We then critically examine the extent to which these data can be determined. If the parameters are favorable, we will be able to determine the axion couplings to photons, electrons, nuclei, as well as the dark matter halo density. However, further experimental proposals are needed to fully flesh out the ultraviolet model of the axion.

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arXiv2024

Preheating Axions in String Cosmology

Certain inflationary models can feature periods of preheating - an era preceding reheating during which parametric resonance triggers an exponential production of bosons. This non-perturbative process can have significant impact on the history of our universe, with consequences ranging from altered reheating channels to overproduction of dark radiation to overclosure. In this work, we study parametric resonance production of axions in string models of inflation. We find that the kinetic couplings and moduli-dependent axion masses give rise to generalizations of the Mathieu equation. We study these generalizations and determine the strength of parametric resonance created by such couplings. We then apply this technology to fibre inflation models in Type IIB orientifold compactifications. We find that heavy axions can be copiously produced and avoidance of overclosure results in constraints on the typical fibre inflation parameter space.

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arXiv2024

Duality Origami: Emergent Ensemble Symmetries in Holography and Swampland

We discuss the interrelations between several ideas in quantum gravity -- holography, the Swampland, and the concept of ensemble averaging. To do so, we study ensemble averages of Narain-type theories associated with general even quadratic forms and their holographic duals. We establish the emergence of global symmetries and discuss their consistency with conjectures forbidding such symmetries. We also discuss how the spectral decomposition of Narain partition functions suggests a natural embedding of ensemble averaging within the low-energy limit of certain string compactifications, which in turn allows a connection with the Swampland program.

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arXiv2023

Gravitational Axiverse Spectroscopy: Seeing the Forest for the Axions

We consider inflationary models with multiple spectator axions coupled to dark gauge sectors via Chern-Simons (CS) terms. The energy injection into Abelian gauge fields from the axions engenders a multi-peak profile for scalar and tensor spectra. We highlight the constraining power of CMB spectral distortions on the scalar signal and discuss the conditions under which spectator sectors can account for the recently observed stochastic gravitational wave (GW) background in the nHz range. Given the tantalizing prospect of a multi-peak ``GW forest'' spanning several decades in frequency, we elaborate on possible ultraviolet origins of the spectator models from Type IIB orientifolds. String compactifications generically produce a multitude of axions, the ``Axiverse'', from dimensional reduction of p-form gauge fields. The CS coupling of such axions to dark gauge fields in the worldvolume theory of D7-branes can be tuned via multiple brane wrappings and/or quantized gauge field strengths. If string axions coupled to Abelian gauge fields undergo slow-roll during inflation, they produce GW signals with peaked frequency distribution whose magnitude depends on the details of the compactification. We discuss the restrictions on spectator models from consistency and control requirements of the string compactification and thereby motivate models that may live in the string landscape as opposed to the swampland.

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arXiv2023

Generalized Narain Theories Decoded: Discussions on Eisenstein series, Characteristics, Orbifolds, Discriminants and Ensembles in any Dimension

We study a class of newly-introduced CFTs associated with even quadratic forms of general signature, which we call generalized Narain theories. We first summarize the properties of these theories. We then consider orbifolds of these theories, thereby obtaining a large class of non-supersymmetric CFTs with exactly marginal deformations. We then discuss ensemble averages of such theories over their moduli space, and obtain a modular form associated with the quadratic form and an element of the discriminant group. The modular form can be written as a Poincare series, which contains novel invariants of lens spaces and suggests the interpretation of the holographic bulk as a theory of anyons.

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arXiv2023

On the Sensitivity of Spin-Precession Axion Experiments

A leading direction in the hunt for axion dark matter is to search for its influence on nuclear spins. The detection scheme involves polarizing a sample of nuclei within a strong static magnetic field and then looking for a spin precession induced by the oscillating axion field. We study the axion signal and background contributions that arise in such experiments (a prominent example being CASPEr), finding key differences with the existing literature. Most importantly, in the limit where the transverse spin-relaxation time of the material is the largest timescale of the problem, we show that the induced signal continues to grow even beyond the coherence time of the axion field. As a result, we find that spin-precession instruments are much more sensitive than what has been previously estimated in a sizable range of axion masses, with sensitivity improvement of up to a factor of 100 at an axion mass of 100 neV using a Xenon-129 sample. This improves the detection prospects for the QCD axion, and we estimate the experimental requirements to reach this motivated target. Our results apply to both the axion electric and magnetic dipole moment operators.

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arXiv2023

Heterotic de Sitter Beyond Modular Symmetry

We study the vacua of $4d$ heterotic toroidal orbifolds using effective theories consisting of an overall Kähler modulus, the dilaton, and non-perturbative corrections to both the superpotential and Kähler potential that respect modular invariance. We prove three de Sitter no-go theorems for several classes of vacua and thereby substantiate and extend previous conjectures. Additionally, we provide evidence that extrema of the scalar potential can occur inside the PSL$(2,\mathbb{Z})$ fundamental domain of the Kähler modulus, in contradiction of a separate conjecture. We also illustrate a loophole in the no-go theorems and determine criteria that allow for metastable de Sitter vacua. Finally, we identify inherently stringy non-perturbative effects in the dilaton sector that could exploit this loophole and potentially realize de Sitter vacua

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arXiv2021

Chern-Simons Invariants from Ensemble Averages

We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form $Q$. We provide evidence that the holographic dual after the ensemble average is the three-dimensional Abelian Chern-Simons theory with kinetic term determined by $Q$. The resulting partition function can be written as a modular form, expressed as a sum over the partition functions of Chern-Simons theories on lens spaces. For odd lattices, the dual bulk theory is a spin Chern-Simons theory, and we identify several novel phenomena in this case. We also discuss the holographic duality prior to averaging in terms of Maxwell-Chern-Simons theories.

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arXiv2021

Constraints on Dark Energy from Inflation and the Swampland Conjectures

We discuss the prospects of measuring deviations of the dark energy equation of state from w=-1 by using the swampland conjectures to relate inflationary models to quintessence scenarios. This note is based on work done by the author with H. Murayama and C. Chiang arXiv:1811.01987.

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arXiv2021

Cosmological Tension of Ultralight Axion Dark Matter and its Solutions

A number of proposed and ongoing experiments search for axion dark matter with a mass nearing the limit set by small scale structure (${\cal O} ( 10 ^{ - 21 } {\rm eV} ) $). We consider the late universe cosmology of these models, showing that requiring the axion to have a matter-power spectrum that matches that of cold dark matter constrains the magnitude of the axion couplings to the visible sector. Comparing these limits to current and future experimental efforts, we find that many searches require axions with an abnormally large coupling to Standard Model fields, independently of how the axion was populated in the early universe. We survey mechanisms that can alleviate the bounds, namely, the introduction of large charges, various forms of kinetic mixing, a clockwork structure, and imposing a discrete symmetry. We provide an explicit model for each case and explore their phenomenology and viability to produce detectable ultralight axion dark matter.

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arXiv2020

QCD Axion Dark Matter from a Late Time Phase Transition

We investigate the possibility that the Peccei-Quinn phase transition occurs at a temperature far below the symmetry breaking scale. Low phase transition temperatures are typical in supersymmetric theories, where symmetry breaking fields have small masses. We find that QCD axions are abundantly produced just after the phase transition. The observed dark matter abundance is reproduced even if the decay constant is much lower than $10^{11}$ GeV. The produced axions tend to be warm. For some range of the decay constant, the effect of the predicted warmness on structure formation can be confirmed by future observations of 21 cm lines. A portion of parameter space requires a mixing between the Peccei-Quinn symmetry breaking field and the Standard Model Higgs, and predicts an observable rate of rare Kaon decays.

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arXiv2018

What does Inflation say about Dark Energy given the Swampland Conjectures?

We discuss the relations between swampland conjectures and observational constraints on both inflation and dark energy. Using the requirement $|\nabla V|\geq c V$, with $c$ as a universal constant whose value can be derived from inflation, there may be no observable distinction between constant and non-constant models of dark energy. However, the latest modification of the above conjecture, which utilizes the second derivative of the potential, opens up the opportunity for observations to determine if the dark energy equation of state deviates from that of a cosmological constant. We also comment on the observability of tensor fluctuations despite the conjecture that field excursions are smaller than the Planck scale.

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