About

Emanuel Katz is a professor in the Department of Physics at Boston University, with research interests centered on Quantum Field Theory (QFT). His work explores the non-perturbative regime of QFT, focusing on methods involving Conformal Field Theory (CFT) to describe many-body systems near phase transitions and to understand emergent behaviors in particle theories. His research aims to deepen understanding of high-energy multi-particle states, ergodicity, and the simulation of the Standard Model, which remains a challenge beyond perturbation theory. Professor Katz holds a B.S. in Physics and Theoretical Mathematics and a Ph.D. in Theoretical Physics, both from the Massachusetts Institute of Technology. His contributions to the field have been recognized through awards such as the NSF CAREER Award and the Sloan Research Fellowship. He is actively involved in advancing theoretical physics through his research, which includes exploring the applications of CFT in describing relativistic and scale-invariant systems, and investigating deformations of CFTs to explore novel regimes of particle theories.

Research topics

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

Selected publications

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

  Open MIND · 2026-02-04

  preprintSenior author

  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 accessSenior author

  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

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

  SciPost Physics · 2025-06-05 · 1 citations

  articleOpen access

  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

• Studying <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>QED</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> with radial quantization on the lattice: Free limit

  Physical review. D/Physical review. D. · 2025-12-10

  articleOpen access

  To investigate the three-dimensional quantum electrodynamics in the radial quantization on the lattice, the lattice action is constructed and the free limit is studied on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>S</a:mi> <a:mn>2</a:mn> </a:msup> <a:mo>×</a:mo> <a:mi mathvariant="double-struck">R</a:mi> </a:math> . With the overlap fermion, it is numerically verified that the important symmetries of the theory can be realized on the lattice. The analytic correlators are derived and compared to the lattice results, which agree including the overall normalization. The <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi>O</d:mi> <d:mo stretchy="false">(</d:mo> <d:msup> <d:mi>a</d:mi> <d:mn>2</d:mn> </d:msup> <d:mo stretchy="false">)</d:mo> </d:math> scaling is confirmed toward the analytic value in the continuum limit, and the number of reproduced excited states is estimated heuristically for the first few refinement levels. Our study helps us identify the features of the theory that we can study on the icosahedral lattice without fine-tuning.

  PublisherDOI

• 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

• Toolkit for general 2d scalar potential in LCT

  Journal of High Energy Physics · 2025-06-19

  articleOpen access

  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 accessSenior author

  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

• Giving Hamiltonian truncation a boost

  Journal of High Energy Physics · 2025-03-06 · 1 citations

  articleOpen access

  A bstract We study Hamiltonian truncation in boosted frames. We consider the thermal and magnetic field deformations of the 2d Ising model using TCSA at finite momentum. We find that even with moderate momenta, the spectrum and time-dependent correlation functions become significantly less dependent on the volume of the system. This allows for a more reliable determination of infinite volume observables.

  PublisherOA PDFDOI

• Chiral limit of 2d QCD revisited with lightcone conformal truncation

  Journal of High Energy Physics · 2024-01-31 · 5 citations

  articleOpen access

  A bstract We study the chiral limit of 2d QCD with a single quark flavor at finite N c using LCT. By modifying the LCT basis according to the quark mass in a manner motivated by ’t Hooft’s analysis, we are able to restore convergence for quark masses much smaller than the QCD strong coupling scale. For such small quark masses, the IR of the theory is expected to be well described by the Sine-Gordon model. We verify that LCT numerics are able to capture in detail the spectrum and correlation functions of the Sine-Gordon model. This opens up the possibility for studying deformations of various integrable CFTs using LCT by considering the chiral limit of QCD like theories.

  PublisherOA PDFDOI

• Constructing the Infrared Conformal Generators on the Fuzzy Sphere

  arXiv (Cornell University) · 2024-09-04 · 2 citations

  preprintOpen accessSenior author

  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 $\sim 5$ with $N=16$ 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

Recent grants

• CAREER: Electroweak and Strong Coupling Physics

  NSF · $400k · 2007–2013

Frequent coauthors

• A. Liam Fitzpatrick

  31 shared

• Matthew T. Walters

  École Polytechnique Fédérale de Lausanne

  18 shared

• Zuhair U. Khandker

  Boston University

  7 shared

• Y. L. Xin

  7 shared

• Yiming Xu

  7 shared

• Nikhil Anand

  McGill University

  7 shared

• Anders W. Sandvik

  6 shared

• Jared Kaplan

  6 shared

Awards & honors

• NSF CAREER Award
• Sloan Research Fellowship