About

Andrew Liam Fitzpatrick is an Associate Professor of Physics at Boston University. His research focuses on Quantum Field Theory, a framework capable of describing a wide range of systems that may seem unrelated at first glance. He is particularly interested in the concepts of emergence and universality, which explain how systems can behave differently on larger scales compared to their individual components, and how most detailed properties become irrelevant at large scales. Fitzpatrick specializes in effective field theories that simplify and unify various models by focusing on large-scale behavior. His work emphasizes the significance of scale-invariant theories, which maintain their properties even as the observation scale increases, and their role in modern physics. He is especially interested in the ability of these theories to describe quantum gravity through non-trivial dualities, where different theoretical descriptions are shown to be equivalent. Fitzpatrick holds a B.S. in Physics and Mathematics from the University of Chicago and a Ph.D. in Physics from Harvard University. He is recognized as a Sloan Research Fellow and is actively involved in research, teaching, and outreach within the Department of Physics at Boston University.

Research topics

• Physics
• Quantum mechanics
• Mathematical physics
• Theoretical physics
• Mathematics
• Mathematical analysis
• Geometry
• Statistical physics
• Quantum electrodynamics
• Classical mechanics
• Statistics

Selected publications

• Improving 3d Ising OPE Coefficients with Fuzzy Sphere Conformal Generators

  Open MIND · 2026-02-04

  preprint

  We use the $K$ special conformal generator in the Fuzzy sphere setup of the Ising CFT to determine primary states. For $Δ\lesssim 8$, we recover the known primaries and find several new ones, including in the parity-odd sector. We then use these primaries to compute OPE coefficients. We find that using primaries constructed from special-$K$ allows for better extrapolation of OPE coefficients to the CFT limit, because of the existence of an $O(1)$ gap between primaries and descendants in the spectrum of eigenvalues of $|K|^2$ which protects the primaries from strongly mixing with descendants. We compare the CFT data we obtain with the Eigenstate Thermalization Hypothesis.

  DOI

• Improving 3d Ising OPE Coefficients with Fuzzy Sphere Conformal Generators

  ArXiv.org · 2026-02-04

  articleOpen access

  We use the $K$ special conformal generator in the Fuzzy sphere setup of the Ising CFT to determine primary states. For $Δ\lesssim 8$, we recover the known primaries and find several new ones, including in the parity-odd sector. We then use these primaries to compute OPE coefficients. We find that using primaries constructed from special-$K$ allows for better extrapolation of OPE coefficients to the CFT limit, because of the existence of an $O(1)$ gap between primaries and descendants in the spectrum of eigenvalues of $|K|^2$ which protects the primaries from strongly mixing with descendants. We compare the CFT data we obtain with the Eigenstate Thermalization Hypothesis.

  PublisherOA PDF

• Descending into the Modular Bootstrap

  ArXiv.org · 2026-04-01

  articleOpen access

  In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus partition function of a 2d CFT is fixed by the spectrum of its primary operators and its chiral algebra, which we take to be the Virasoro algebra with $c>1$. We translate the requirement that this partition function is modular invariant into a loss function, which we then minimize to identify possible primary spectra. Our approach involves two technical innovations that facilitate finding reliable candidate CFTs. The first is a strategy to estimate the uncertainty associated with truncating the spectrum to the lowest dimension operators. The second is the use of a new singular-value-based optimizer (Sven) that is more effective than gradient descent at navigating the hierarchical structure of the loss landscape. We numerically construct candidate truncated CFT partition functions with central charges between 1 and $\frac{8}{7}$, a range devoid of known examples, and argue that these candidates likely come from a continuous space of modular bootstrap solutions. We also provide evidence for a more stringent constraint on the spectral gap near $c = 1$ than the existing bound of $Δ_{\rm gap} \le \frac{c}{6} + \frac{1}{3}$.

  PublisherOA PDF

• Descending into the Modular Bootstrap

  HAL (Le Centre pour la Communication Scientifique Directe) · 2026-04-01

  preprintOpen access

  In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus partition function of a 2d CFT is fixed by the spectrum of its primary operators and its chiral algebra, which we take to be the Virasoro algebra with $c>1$. We translate the requirement that this partition function is modular invariant into a loss function, which we then minimize to identify possible primary spectra. Our approach involves two technical innovations that facilitate finding reliable candidate CFTs. The first is a strategy to estimate the uncertainty associated with truncating the spectrum to the lowest dimension operators. The second is the use of a new singular-value-based optimizer (Sven) that is more effective than gradient descent at navigating the hierarchical structure of the loss landscape. We numerically construct candidate truncated CFT partition functions with central charges between 1 and $\frac{8}{7}$, a range devoid of known examples, and argue that these candidates likely come from a continuous space of modular bootstrap solutions. We also provide evidence for a more stringent constraint on the spectral gap near $c = 1$ than the existing bound of $Δ_{\rm gap} \le \frac{c}{6} + \frac{1}{3}$.

  PublisherOA PDFDOI

• Large momentum EFT and lightcone quantization

  Journal of High Energy Physics · 2025-07-01

  articleOpen access

  A bstract We develop methods for computing the effective action at infinite momentum for 1 + 1 d QFTs at finite volume which do not rely on the theory having a Lagrangian description. We do this by taking the infinite momentum limit of equal-time quantization and integrating out all except for the chiral modes of the theory. Our main application of this method is to the Ising Field Theory (IFT), with an energy and magnetic deformation, where we compute the effective lightcone Hamiltonian numerically and check it against results from TCSA. Remarkably, in the low-temperature phase, the Lorentz invariant effective Hamiltonian at infinite momentum takes a very compact form and depends on the volume only through the finite volume vacuum expectation value of ⟨ σ ⟩, the spin operator.

  PublisherOA PDFDOI

• Lightcone Hamiltonian for Ising field theory I: $T < T_c$

  SciPost Physics · 2025-06-05 · 1 citations

  articleOpen access1st authorCorresponding

  We study 2d Ising Field Theory (IFT) in the low-temperature phase in lightcone quantization, and show that integrating out zero modes generates a very compact form for the effective lightcone interaction that depends on the finite volume vacuum expectation value of the \sigma <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>σ</mml:mi> </mml:math> operator. This form is most naturally understood in a conformal basis for the lightcone Hilbert space. We further verify that this simple form reproduces to high accuracy results for the spectra, the c <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>c</mml:mi> </mml:math> -function, and the form-factors from integrability methods for the magnetic deformation of IFT. For generic non-integrable values of parameters we also compute the above observables and compare our numeric results to those of equal-time truncation. In particular, we report on new measurements of various bound-state form-factors as well as the stress-tensor spectral density. We find that the stress tensor spectral density provides additional evidence that certain resonances of IFT are surprisingly narrow, even at generic strong coupling. Explicit example code for constructing the effective Hamiltonian is included in an appendix.

  PublisherOA PDFDOI

• Toolkit for general 2d scalar potential in LCT

  Journal of High Energy Physics · 2025-06-19

  articleOpen access1st author

  A bstract We present efficient algorithms for obtaining the Hamiltonian in Lightcone Conformal Truncation (LCT) for a 2d scalar field with a generic potential. We apply this method to the sine-Gordon and sinh-Gordon models in 1 +1 d , and find precise agreement with integrability results when the scaling dimension ∆ of the deforming cosine/cosinh potential is in the range ∆ ≤ 1. The agreement provides additional evidence for a recent conjecture for how to compute the effective lightcone Hamiltonian in this class of models. In addition, to high precision, we provide the first direct confirmation for the conjectured self-duality of the sinh-Gordon model (∆ &lt; 0), which relates ∆ ↔ 4/∆. As the dimension approaches the upper limit ∆ = 1 from below, we show analytically that the Hamiltonian matrix elements exactly reproduce those of a free Majorana fermion, demonstrating how bosonization is manifested in the LCT basis. We comment on the possible extension of the approach to ∆ &gt; 1.

  PublisherOA PDFDOI

• Constructing the infrared conformal generators on the fuzzy sphere

  SciPost Physics · 2025-03-10 · 12 citations

  articleOpen access

  We investigate the conformal algebra on the fuzzy sphere, and in particular the generators of translations and special conformal transformations which are emergent symmetries in the infinite IR but are broken along the RG flow. We show how to extract these generators using the energy momentum tensor, which is complicated by the fact that one does not have a priori access to the energy momentum tensor of the CFT limit but rather must construct it numerically. We discuss and quantitatively analyze the main sources of corrections to the conformal generators due to the breaking of scale-invariance at finite energy, and develop efficient methods for removing these corrections. The resulting generators have matrix elements that match CFT predictions with accuracy varying from sub-percent level for the lowest-lying states up to several percent accuracy for states with dimension \sim 5 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> with N=16 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>16</mml:mn> </mml:mrow> </mml:math> fermions. We show that the generators can be used to accurately identify primary operators vs descendant operators in energy ranges where the spectrum is too dense to do the identification solely based on the approximate integer spacing within conformal multiplets.

  PublisherOA PDFDOI

• Leakage of Light and its Relation to the Stiles-Crawford Effect

  2025-01-01

  article1st authorCorresponding

  Many hypotheses fail to provide complete explanations of the Stiles-Crawford effects of the first and second kind. Here, using a macroscopic model, we describe absorption in the photoreceptors in terms of leakage and cross-talk.

  PublisherDOI

• Properties of scalar partition functions of 2d CFTs

  Journal of High Energy Physics · 2025-09-03

  articleOpen access

  A bstract We study the spectrum of scalar primary operators in any two-dimensional conformal field theory. We show that the scalars alone obey a nontrivial crossing equation. This extends previous work that derived a similar equation for Narain conformal field theories. Additionally, we show that at high temperature, the difference between the true scalar partition function and the one predicted from a semiclassical gravity calculation is controlled by: the modular integral of the partition function, the light states of the theory, and an infinite series terms directly related to the nontrivial zeros of the Riemann zeta function. We give several numerical examples and compute their modular integrals.

  PublisherOA PDFDOI

Frequent coauthors

• Jared Kaplan

  59 shared

• Emanuel Katz

  Boston University

  31 shared

• Shamit Kachru

  30 shared

• S. Raghu

  Stanford University

  26 shared

• Matthew T. Walters

  École Polytechnique Fédérale de Lausanne

  18 shared

• Gonzalo Torroba

  16 shared

• Daliang Li

  11 shared

• Nikhil Anand

  McGill University

  11 shared

Awards & honors

• Sloan Research Fellow