arXiv subjects

James Halverson

Publications and source records attributed to James Halverson.

At least 55 records · Page 3Linked to original sources

arXiv2019

A Quadrillion Standard Models from F-theory

We present an explicit construction of ${\cal O}(10^{15})$ globally consistent string compactifications that realize the exact chiral spectrum of the Standard Model of particle physics with gauge coupling unification in the context of F-theory. Utilizing the power of algebraic geometry, all global consistency conditions can be reduced to a single criterion on the base of the underlying elliptically fibered Calabi--Yau fourfolds. For toric bases, this criterion only depends on an associated polytope and is satisfied for at least ${\cal O}(10^{15})$ bases, each of which defines a distinct compactification.

hep-th↗

arXiv2019

On String Theory Expectations for Photon Couplings to Axion-Like Particles

ALP-photon couplings are modeled in large ensembles of string vacua and random matrix theories. In all cases, the effective coupling increases polynomially in the number of ALPs, of which hundreds or thousands are expected in the string ensembles, many of which are ultralight. The expected value of the couplings $g_{aγγ}\simeq 10^{-12}\text{GeV}^{-1} - 10^{-10}\text{GeV}^{-1}$ provide viable targets for future x-ray telescopes and axion helioscopes, and in some cases are already in tension with existing data.

hep-th↗

arXiv2019

Branes with Brains: Exploring String Vacua with Deep Reinforcement Learning

We propose deep reinforcement learning as a model-free method for exploring the landscape of string vacua. As a concrete application, we utilize an artificial intelligence agent known as an asynchronous advantage actor-critic to explore type IIA compactifications with intersecting D6-branes. As different string background configurations are explored by changing D6-brane configurations, the agent receives rewards and punishments related to string consistency conditions and proximity to Standard Model vacua. These are in turn utilized to update the agent's policy and value neural networks to improve its behavior. By reinforcement learning, the agent's performance in both tasks is significantly improved, and for some tasks it finds a factor of O(200) more solutions than a random walker. In one case, we demonstrate that the agent learns a human-derived strategy for finding consistent string models. In another case, where no human-derived strategy exists, the agent learns a genuinely new strategy that achieves the same goal twice as efficiently per unit time. Our results demonstrate that the agent learns to solve various string theory consistency conditions simultaneously, which are phrased in terms of non-linear, coupled Diophantine equations.

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arXiv2019

On Axion Reheating in the String Landscape

We demonstrate that asymmetric reheating arises in a large ensemble of string compactifications with many axions and gauged dark sectors. This phenomenon may help avoid numerous cosmological problems that may arise if the sectors were reheated democratically. Distributions of couplings are presented for two classes of axion reheatons, both of which exhibit very small couplings to most of the gauge sectors. In one class, ratios of reheating couplings and also preferred gauge groups are frequently determined by local regions in the string geometry.

hep-th↗

arXiv2018

Estimating Calabi-Yau Hypersurface and Triangulation Counts with Equation Learners

We provide the first estimate of the number of fine, regular, star triangulations of the four-dimensional reflexive polytopes, as classified by Kreuzer and Skarke (KS). This provides an upper bound on the number of Calabi-Yau threefold hypersurfaces in toric varieties. The estimate is performed with deep learning, specifically the novel equation learner (EQL) architecture. We demonstrate that EQL networks accurately predict numbers of triangulations far beyond the $h^{1,1}$ training region, allowing for reliable extrapolation. We estimate that number of triangulations in the KS dataset is $10^{10,505}$, dominated by the polytope with the highest $h^{1,1}$ value.

hep-th↗

arXiv2018

Vacuum Selection from Cosmology on Networks of String Geometries

We introduce network science as a framework for studying the string landscape. Two large networks of string geometries are constructed, where nodes are extra-dimensional six-manifolds and edges represent topological transitions between them. We show that a standard bubble cosmology model on the networks has late-time behavior determined by the largest eigenvector of $-(\mathbf{L} + \mathbf{D})$, where $\mathbf{L}$ and $\mathbf{D}$ are the Laplacian and degree matrices of the networks, which provides a dynamical mechanism for vacuum selection in the string landscape.

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arXiv2018

Dark Glueballs and their Ultralight Axions

Dark gauge sectors and axions are well-motivated in string theory. We demonstrate that if a confining gauge sector gives rise to dark glueballs that are a fraction of the dark matter, and the associated axion has a decay constant near the string scale, then this axion is ultralight and naturally realizes the fuzzy dark matter scenario with a modest tuning of a temperature ratio. Astrophysical observations constrain the size of the glueball component relative to the axionic component, while electric dipole moments constrain mixing with the QCD axion.

hep-ph↗

arXiv2018

Non-simply-laced Symmetry Algebras in F-theory on Singular Spaces

We demonstrate how non-simply-laced gauge and flavor symmetries arise in F-theory on spaces with non-isolated singularities. The breaking from a simply-laced symmetry to one that is non-simply-laced is induced by Calabi-Yau complex structure deformation. In all examples the deformation maintains non-isolated singularities but is accompanied by a splitting of an I1 seven-brane that opens new loops in the geometry near a non-abelian seven-brane. The splitting also arises in the moduli space of a probe D3-brane, which upon traversing the new loop experiences a monodromy that acts on 3-7 string junctions on the singular space. The monodromy reduces the symmetry algebra, which is the flavor symmetry of the D3-brane and the gauge symmetry of the seven-brane, to one that is non-simply-laced. A collision of the D3-brane with the seven-brane gives rise to a 4d N = 1 SCFT with a non-simply-laced flavor symmetry.

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arXiv2018

Infinitely Many M2-instanton Corrections to M-theory on $G_2$-manifolds

We consider the non-perturbative superpotential for a class of four-dimensional $\mathcal N=1$ vacua obtained from M-theory on seven-manifolds with holonomy $G_2$. The class of $G_2$-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over $S^3$. We show that the non-perturbative superpotential of M-theory on a class of TCS geometries receives infinitely many inequivalent M2-instanton contributions from infinitely many three-spheres, which we conjecture are supersymmetric (and thus associative) cycles. The rationale for our construction is provided by the duality chain of arXiv:1708.07215, which relates M-theory on TCS $G_2$-manifolds to $E_8\times E_8$ heterotic backgrounds on the Schoen Calabi-Yau threefold, as well as to F-theory on a K3-fibered Calabi-Yau fourfold. The latter are known to have an infinite number of instanton corrections to the superpotential and it is these contributions that we trace through the duality chain back to the $G_2$-compactification.

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arXiv2018

TASI Lectures on Remnants from the String Landscape

Superstring theories are very promising theoretically, but the enormous landscape of string vacua and the (likely) very large underlying string scale imply that they may never be tested directly. Nevertheless, concrete constructions consistent with the observed world frequently lead to observable remnants, i.e., new particles or features that are apparently accidental consequences of the ultraviolet theory and that are typically not motivated by specific shortcomings of the standard models of particle physics or cosmology. For example, moduli, axions, large extended gauge sectors, additional $Z'$ gauge bosons, extended Higgs/Higgsino sectors, and quasi-chiral exotics are extremely common. They motivate alternative cosmological paradigms and could lead to observable signatures at the LHC. Similar features can emerge in other standard model extensions, but in the stringy case they are more likely to occur in isolation and not as part of a more complete TeV-scale structure. Conversely, some common aspects of the infinite "landscape" of field theories, such as large representations, are expected to be very rare in the string landscape, and observation of features definitively in the swampland could lead to falsification. In this article, common stringy remnants and their phenomenology are surveyed, and implications for indirectly supporting or casting doubt on string theory are discussed.

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arXiv2017

Exact Geodesic Distances in FLRW Spacetimes

Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3+1)-dimensional Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

gr-qc↗

arXiv2017

On the Scarcity of Weak Coupling in the String Landscape

We study the geometric requirements on a threefold base for the corresponding F-theory compactification to admit a weakly-coupled type IIB limit. We examine both the standard Sen limit and a more restrictive limit, and determine conditions sufficient for their non-existence for both toric bases and more general algebraic bases. In a large ensemble of geometries generated by base changing resolutions we derive an upper bound on the frequency with which a weak-coupling limit may occur, and find that such limits are extremely rare. Our results sharply quantify the widely held notion that the vast number of weakly-coupled IIB vacua is but a tiny fraction of the landscape.

hep-th↗

arXiv2017

Machine Learning in the String Landscape

We utilize machine learning to study the string landscape. Deep data dives and conjecture generation are proposed as useful frameworks for utilizing machine learning in the landscape, and examples of each are presented. A decision tree accurately predicts the number of weak Fano toric threefolds arising from reflexive polytopes, each of which determines a smooth F-theory compactification, and linear regression generates a previously proven conjecture for the gauge group rank in an ensemble of $\frac43 \times 2.96 \times 10^{755}$ F-theory compactifications. Logistic regression generates a new conjecture for when $E_6$ arises in the large ensemble of F-theory compactifications, which is then rigorously proven. This result may be relevant for the appearance of visible sectors in the ensemble. Through conjecture generation, machine learning is useful not only for numerics, but also for rigorous results.

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arXiv2017

On Algorithmic Universality in F-theory Compactifications

We study universality of geometric gauge sectors in the string landscape in the context of F-theory compactifications. A finite time construction algorithm is presented for $\frac43 \times 2.96 \times 10^{755}$ F-theory geometries that are connected by a network of topological transitions in a connected moduli space. High probability geometric assumptions uncover universal structures in the ensemble without explicitly constructing it. For example, non-Higgsable clusters of seven-branes with intricate gauge sectors occur with probability above $1-1.01\times 10^{-755}$, and the geometric gauge group rank is above $160$ with probability $.999995$. In the latter case there are at least $10$ $E_8$ factors, the structure of which fixes the gauge groups on certain nearby seven-branes. Visible sectors may arise from $E_6$ or $SU(3)$ seven-branes, which occur in certain random samples with probability $\simeq 1/200$.

hep-th↗

arXiv2017

Strong Coupling in F-theory and Geometrically Non-Higgsable Seven-branes

Geometrically non-Higgsable seven-branes carry gauge sectors that cannot be broken by complex structure deformation, and there is growing evidence that such configurations are typical in F-theory. We study strongly coupled physics associated with these branes. Axiodilaton profiles are computed using Ramanujan's theories of elliptic functions to alternative bases, showing explicitly that the string coupling is order one in the vicinity of the brane; that it sources nilpotent $SL(2,\mathbb{Z})$ monodromy and therefore the associated brane charges are modular; and that essentially all F-theory compactifications have regions with order one string coupling. It is shown that non-perturbative $SU(3)$ and $SU(2)$ seven-branes are related to weakly coupled counterparts with D7-branes via deformation-induced Hanany-Witten moves on $(p,q)$ string junctions that turn them into fundamental open strings; only the former may exist for generic complex structure. D3-brane near these and the Kodaira type II seven-branes probe Argyres-Douglas theories. The BPS states of slightly deformed theories are shown to be dyonic string junctions.

hep-th↗

arXiv2017

An Ultralight Axion in Supersymmetry and Strings and Cosmology at Small Scales

Dynamical mechanisms to generate an ultralight axion of mass $\sim 10^{-21}-10^{-22}$ eV in supergravity and strings are discussed. An ultralight particle of this mass provides a candidate for dark matter that may play a role for cosmology at scales $10\, {\rm kpc}$ or less. An effective operator approach for the axion mass provides a general framework for models of ultralight axions, and in one case recovers the scale $10^{-21}-10^{-22}$ eV as the electroweak scale times the square of the hierarchy with an $O(1)$ Wilson coefficient. We discuss several classes of models realizing this framework where an ultralight axion of the necessary size can be generated. In one class of supersymmetric models an ultralight axion is generated by instanton like effects. In the second class higher dimensional operators involving couplings of Higgs, standard model singlets, and axion fields naturally lead to an ultralight axion. Further, for the class of models considered the hierarchy between the ultralight scale and the weak scale is maintained. We also discuss the generation of an ultralight scale within string based models. Here it is shown that in the single modulus KKLT moduli stabilization scheme an ultralight axion would require an ultra-low weak scale. However, within the Large Volume Scenario, the desired hierarchy between the axion scale and the weak scale is achieved. A general analysis of couplings of Higgs fields to instantons within the string framework is discussed and it is shown that the condition necessary for achieving such couplings is the existence of vector-like zero modes of the instanton. Some of the phenomenological aspects of these models are also discussed.

hep-ph↗

arXiv2016

Dualities of Deformed $\mathcal{N=2}$ SCFTs from Link Monodromy on D3-brane States

We study D3-brane theories that are dually described as deformations of two different $\mathcal{N}=2$ superconformal theories with massless monopoles and dyons. These arise at the self-intersection of a seven-brane in F-theory, which cuts out a link on a small three-sphere surrounding the self-intersection. The spectrum is studied by taking small loops in the three-sphere, yielding a link-induced monodromy action on string junction D3-brane states, and subsequently quotienting by the monodromy. This reduces the differing flavor algebras of the $\mathcal{N}=2$ theories to the same flavor algebra, as required by duality, and projects out charged states, yielding an $\mathcal{N}=1$ superconformal theory on the D3-brane. In one, a deformation of a rank one Argyres-Douglas theory retains its $SU(2)$ flavor symmetry and exhibits a charge neutral flavor triplet that is comprised of electron, dyon, and monopole string junctions. From duality we argue that the monodromy projection should also be imposed away from the conformal point, in which case the D3-brane field theory appears to exhibit confinement of electrons, dyons, and monopoles. We will address the mathematical counterparts in a companion paper.

hep-th↗

arXiv2016

The Cost of Seven-brane Gauge Symmetry in a Quadrillion F-theory Compactifications

We study seven-branes in $O(10^{15})$ four-dimensional F-theory compactifications where seven-brane moduli must be tuned in order to achieve non-abelian gauge symmetry. The associated compact spaces $B$ are the set of all smooth weak Fano toric threefolds. By a study of fine star regular triangulations of three dimensional reflexive polytopes, the number of such spaces is estimated to be $5.8\times 10^{14}\lesssim N_\text{bases}\lesssim 1.8\times 10^{17}$. Typically hundreds or thousands of moduli must be tuned to achieve symmetry for $h^{11}(B)<10$, but the average number drops sharply into the range $O(25)$-$O(200)$ as $h^{11}(B)$ increases. For some low rank groups, such as $SU(2)$ and $SU(3)$, there exist examples where only a few moduli must be tuned in order to achieve seven-brane gauge symmetry.

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