About

Nathaniel Craig is a Professor at the Department of Physics at UC Santa Barbara, specializing in High Energy Physics, Particle Phenomenology, and Cosmology. His research focuses on theoretical aspects of fundamental particles and their interactions, exploring the underlying principles that govern the universe at the smallest scales. As a faculty member, he contributes to advancing the understanding of particle physics beyond the Standard Model, addressing key questions in cosmology and high energy theory.

Research topics

• Particle physics
• Physics
• Computer Science
• Nuclear physics
• Political Science
• Artificial Intelligence
• Applied mathematics
• Mathematics
• Database
• Theoretical physics
• Quantum mechanics
• Engineering

Selected publications

• The FERMIACC: Agents for Particle Theory

  arXiv (Cornell University) · 2026-03-23

  articleOpen access

  We present the FERMIACC, a scaffolded reasoning model built on OpenAI agents designed to autonomously generate and quantitatively validate theory hypotheses for high energy physics data at scale.

  PublisherOA PDF

• Generalized symmetries and emergence in axion effective field theories

  ArXiv.org · 2026-04-13

  articleOpen accessSenior author

  We study the phenomenological consequences of higher symmetry structures in axion effective field theories. Higher-group and non-invertible symmetries impose parametric constraints on the energy scales at which different symmetries can emerge in the infrared, providing a guide to the ultraviolet physics. We clarify and analyze these emergence constraints in axion EFTs coupled to abelian and non-abelian gauge bosons, with and without charged matter. We show that emergence constraints are universally saturated by anomaly inflow onto topological defects, while in perturbative UV completions they are supererogatory owing to the parametric separation of scales.

  PublisherOA PDF

• The FERMIACC: Agents for Particle Theory

  arXiv (Cornell University) · 2026-03-23

  preprintOpen access

  We present the FERMIACC, a scaffolded reasoning model built on OpenAI agents designed to autonomously generate and quantitatively validate theory hypotheses for high energy physics data at scale.

  PublisherDOI

• Fermi geometry of the Higgs sector

  Journal of High Energy Physics · 2026-02-03 · 1 citations

  preprintOpen access1st author

  A bstract We develop the field space geometry of scalar-fermion effective field theories as a vector bundle supermanifold. We further establish a Fermi normal coordinate system on the bundle that clarifies the geometric content in scattering amplitudes, particularly the imprints of field space non-analyticities. Specializing to the Standard Model Higgs sector, we examine the geometric consequences of custodial symmetry violation, including implications for the physical Higgs field as a distinguished scalar axis and deformations in the fermionic sector. Our results enable a systematic and realistic geometric interpretation of Higgs sector phenomenology.

  PublisherOA PDFDOI

• Optimal Transport for $e/π^0$ Particle Classification in LArTPC Neutrino Experiments

  arXiv (Cornell University) · 2025-06-10

  preprintOpen access

  The efficient classification of electromagnetic activity from $π^0$ and electrons remains an open problem in the reconstruction of neutrino interactions in Liquid Argon Time Projection Chamber (LArTPC) detectors. We address this problem using the mathematical framework of Optimal Transport (OT), which has been successfully employed for event classification in other HEP contexts and is ideally suited to the high-resolution calorimetry of LArTPCs. Using a publicly available simulated dataset from the MicroBooNE collaboration, we show that OT methods achieve state-of-the-art reconstruction performance in $e/π^0$ classification. The success of this first application indicates the broader promise of OT methods for LArTPC-based neutrino experiments.

  PublisherOA PDFDOI

• Multiscale optimal transport for complete collider events

  Physical review. D/Physical review. D. · 2025-07-08 · 1 citations

  articleOpen access

  Building upon the success of optimal transport metrics defined for single collinear jets, we develop a multiscale framework that models entire collider events as distributions on the manifold of their constituent jets, which are themselves distributions on the ground space of the calorimeter. This hierarchical structure of optimal transport effectively captures relevant physics at different scales. We demonstrate the versatility of our method in two event classification tasks, which respectively emphasize intrajet substructure and interjet spatial correlations. Our results highlight the importance of a nested structure of manifolds in the treatment of full collider events, broadening the applicability of optimal transport methods in collider analyses.

  PublisherOA PDFDOI

• Weakly supervised anomaly detection with event-level variables

  Physical review. D/Physical review. D. · 2025-09-26

  articleOpen accessSenior author

  We introduce a new topology for weakly supervised anomaly detection searches, diobject plus X. In this topology, one looks for a resonance decaying to two standard model particles produced in association with other anomalous event activity (X). This additional activity is used for classification. We demonstrate how anomaly detection techniques which have been developed for dijet searches focusing on jet substructure anomalies can be applied to event-level anomaly detection in this topology. To robustly capture event-level features of multiparticle kinematics, we employ new physically motivated variables derived from the geometric structure of a collision’s phase space manifold. As a proof of concept, we explore the application of this approach to several benchmark signals in the di-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>τ</a:mi></a:math> and di-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>μ</c:mi></c:math> plus X final states. We demonstrate that our anomaly detection approach can reach discovery-level significances for signals that would be missed in a conventional bump-hunt approach.

  PublisherDOI

• Multi-scale Optimal Transport for Complete Collider Events

  ArXiv.org · 2025-01-18

  preprintOpen access

  Building upon the success of optimal transport metrics defined for single collinear jets, we develop a multi-scale framework that models entire collider events as distributions on the manifold of their constituent jets, which are themselves distributions on the ground space of the calorimeter. This hierarchical structure of optimal transport effectively captures relevant physics at different scales. We demonstrate the versatility of our method in two event classification tasks, which respectively emphasize intra-jet substructure and inter-jet spatial correlations. Our results highlight the relevance of a nested structure of manifolds in the treatment of full collider events, broadening the applicability of optimal transport methods in collider analyses.

  PublisherOA PDFDOI

• High-quality axions from higher-form symmetries in extra dimensions

  Physical review. D/Physical review. D. · 2025-01-30 · 15 citations

  articleOpen access1st authorCorresponding

  The extradimensional axion solves the strong <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>C</a:mi><a:mi>P</a:mi></a:mrow></a:math> problem while largely circumventing the quality problem that plagues its four-dimensional counterparts. Such high quality can be clearly understood in terms of the generalized global symmetries of the higher-dimensional theory. We emphasize that an electric one-form symmetry is entirely responsible for protecting the potential of axions arising from 5D gauge theories and use this to systematically characterize the extradimensional axion quality problem. We identify three ways of breaking this one-form symmetry to generate an axion potential: adding electrically charged matter, gauging a magnetic higher-form symmetry, and turning on an Adler-Bell-Jackiw anomaly. In the latter case, we identify new ways of generating an axion potential via extradimensional magnetic monopoles. We also discuss how the axion is modified if the protective electric one-form symmetry is itself gauged. Finally, we relate these effects to gravitational expectations for the quality problem via generalized weak gravity conjectures. The clarity that generalized symmetries bring to the extradimensional axion quality problem highlights their relevance to particle phenomenology.

  PublisherDOI

• Physics Briefing Book: Input for the 2026 update of the European Strategy for Particle Physics

  Desy publication database (The Deutsches Elektronen-Synchrotron) · 2025-01-01 · 7 citations

  preprintOpen access

  The European Strategy for Particle Physics (ESPP) reflects the vision and presents concrete plans of the European particle physics community for advancing human knowledge in fundamental physics. The ESPP is updated every five-to-six years through a community-driven process. It commences with the submission of specific proposals and other input from the community at large, outlining projects envisioned for the near-, mid-, and long-term future. All submitted contributions are evaluated by the Physics Preparatory Group (PPG), and a preliminary analysis is presented at a Symposium meant to foster a broad community discussion on the scientific value and feasibility of the various ideas proposed. The outcomes of the analysis and the deliberations at the Symposium are synthesized in the current Briefing Book, which provides an important input in the deliberations of the Strategy recommendations by the European Strategy Group (ESG).

  PublisherDOI

Frequent coauthors

• Kyoungchul Kong

  University of Kansas

  40 shared

• Patrick Draper

  39 shared

• Zhen Liu

  Nanjing University

  35 shared

• Dave Sutherland

  University of Glasgow

  32 shared

• D. Whiteson

  31 shared

• Timothy Cohen

  University of Oregon

  30 shared

• Tao Han

  Shanghai Artificial Intelligence Laboratory

  29 shared

• Alfredo Glioti

  Centre National de la Recherche Scientifique

  26 shared

Labs

• Nathaniel Craig LabPI

Education

• Ph.D, Physics

  Stanford University

  2010

• A.B., Physics

  Harvard University

  2005