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David Poland

Publications and source records attributed to David Poland.

At least 19 recordsLinked to original sources
arXiv2026

Maximally heavy dynamics in the causal diamond

Correlation functions of CFT operators with infinite scaling dimension are rich, multifaceted objects that describe physics ranging across classical holography, black hole dynamics, and flat-space scattering amplitudes. In this work, we provide a rigorous framework for characterizing the space of four-point functions of identical operators with infinite dimension in terms of well-defined ``maximally heavy observables,'' which are akin to intrinsic quantities describing statistical systems in the thermodynamic limit. These observables are highly constrained by crossing symmetry and unitarity, and give novel insights into the locality of bulk states through the emergence of dynamical phase transitions. In certain cases, these results connect directly to the more familiar picture of torus partition functions at large central charge. We apply our framework to a number of illustrative examples including generalized free fields, chiral product correlators, and maximal giant gravitons in planar $\mathcal{N}=4$ SYM.

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arXiv2026

Moments in the CFT Landscape

We develop a novel numerical bootstrap for unitary, crossing-symmetric conformal field theories, focusing on moment observables defined as weighted averages over conformal data. Providing a global and coarse-grained probe of the operator spectrum, this framework yields numerically rigorous bounds on the operator distribution using standard semidefinite programming techniques. In the heavy correlator regime, these bounds remain robust and converge rapidly towards analytically-derived power laws. At finite external dimensions, low-lying moments capture corrections to analytic heavy limit results, while reproducing familiar bootstrap solutions such as Ising-model kinks on the boundary of moment space. Most importantly, the moment bootstrap reveals new features in previously unexplored regions of the bootstrap landscape. The lower bounds on moment variables exhibit two continuous families of kinks persisting across $2 < d < 6$, reflecting nontrivial spectral reorganizations connected to underlying operator decoupling phenomena. These results demonstrate that moment variables uncover bootstrap solutions and collective structures that are difficult to access within traditional numerical approaches.

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arXiv2025

Classifying GNY-like models

We perform a systematic classification of (2+1)d Gross--Neveu--Yukawa-like models built out of one or more 4-component Dirac fermions and $M$ scalar fields, which preserve an O($M$) symmetry rotating the scalars. We then identify the perturbative fixed points of these models in the $4-\epsilon$ expansion. Our classification highlights several targets for the conformal bootstrap and reveals a new fixed point with $M=3$, which we call the "orthogonal Heisenberg" CFT.

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arXiv2025

Accurate bootstrap bounds from optimal interpolation

We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should minimize a certain error norm related to the asymptotics of dispersive functionals. This error norm can be made small using interpolation nodes with an appropriate optimal density. The optimal density turns out to satisfy a kind of force-balance equation for charges in one dimension, which can be solved using standard techniques from large-N matrix models. We also describe how to use optimal density interpolation nodes to improve condition numbers inside the semidefinite program solver SDPB. Altogether, our new approximation scheme and improvements to condition numbers lead to more accurate bootstrap bounds with fewer computational resources. They were crucial in the recent bootstrap study of stress tensors in the 3d Ising CFT.

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arXiv2025

Mixed five-point correlators in the 3d Ising model

We study five-point correlators of the $\sigma$, $\epsilon$, and $\epsilon'$ operators in the critical 3d Ising model. We consider the $\sigma \times \sigma$ and $\sigma \times \epsilon$ operator product expansions (OPEs) and truncate them by including a finite set of exchanged operators. We approximate the truncated operators by the corresponding contributions in appropriate disconnected five-point correlators. We compute a number of OPE coefficients that were previously unknown and show that these are consistent with predictions obtained using the fuzzy sphere regularization of the critical 3d Ising model.

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arXiv2024

Moments and saddles of heavy CFT correlators

We study the operator product expansion (OPE) of identical scalars in a conformal four-point correlator as a Stieltjes moment problem, and use Riemann-Liouville type fractional differential operators to generate classical moments from the correlation function. We use crossing symmetry to derive leading and subleading relations between moments in $\Delta$ and $J_2 \equiv \ell(\ell+d-2)$ in the ``heavy" limit of large external scaling dimension, and combine them with constraints from unitarity to derive two-sided bounds on moment sequences in $\Delta$ and the covariance between $\Delta$ and $J_2$. The moment sequences which saturate these bounds produce ``saddle point" solutions to the crossing equations which we identify as particular limits of correlators in a generalized free field (GFF) theory. This motivates us to study perturbations of heavy GFF four-point correlators by way of saddle point analysis, and we show that saddles in the OPE arise from contributions of fixed-length operator families encoded by a decomposition into higher-spin conformal blocks. To apply our techniques, we consider holographic correlators of four identical single scalar fields perturbed by a bulk interaction, and use their first few moments to derive Gaussian weight-interpolating functions that predict the OPE coefficients of interacting double-twist operators in the heavy limit.

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arXiv2024

Bootstrapping the 3d Ising Stress Tensor

We compute observables of the critical 3d Ising model to high precision by applying the numerical conformal bootstrap to mixed correlators of the leading scalar operators $\sigma$ and $\epsilon$, and the stress tensor $T_{\mu\nu}$. We obtain new precise determinations of scaling dimensions $(\Delta_\sigma, \Delta_\epsilon) = (0.518148806(24), 1.41262528(29))$ as well as OPE coefficients involving $\sigma$, $\epsilon$, and $T_{\mu\nu}$. We also describe several improvements made along the way to algorithms and software tools for the numerical bootstrap.

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arXiv2024

Bounding irrelevant operators in the 3d Gross-Neveu-Yukawa CFTs

We perform a numerical bootstrap study of scalar operators in the critical 3d Gross-Neveu-Yukawa models, a family of conformal field theories containing N Majorana fermions in the fundamental representation of an O(N) global symmetry. We compute rigorous bounds on the scaling dimensions of the next-to-lowest parity-even and parity-odd singlet scalars at N = 2, 4, and 8. All of these dimensions have lower bounds greater than 3, implying that there are only two relevant singlet scalars and placing constraints on the RG flow structure of these theories.

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arXiv2023

Improving the five-point bootstrap

We present a new algorithm for the numerical evaluation of five-point conformal blocks in $d$-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Pad\'e approximant to accelerate its convergence. We then study the $\langle\sigma\sigma\epsilon\sigma\sigma\rangle$ correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff $\Delta\leqslant \Delta_{\rm cutoff}$. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

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arXiv2023

The Gross-Neveu-Yukawa Archipelago

We perform a bootstrap analysis of a mixed system of four-point functions of bosonic and fermionic operators in parity-preserving 3d CFTs with O(N) global symmetry. Our results provide rigorous bounds on the scaling dimensions of the O(N)-symmetric Gross-Neveu-Yukawa (GNY) fixed points, constraining these theories to live in isolated islands in the space of CFT data. We focus on the cases N = 1, 2, 4, 8, which have applications to phase transitions in condensed matter systems, and compare our bounds to previous analytical and numerical results.

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arXiv2023

The five-point bootstrap

We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators $\langle \sigma \sigma \epsilon \sigma \sigma \rangle$ in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff $\Delta \leqslant \Delta_{\rm cutoff}$. We then compute several OPE coefficients involving $\epsilon$ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.

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arXiv2023

Snowmass Topical Summary: Formal QFT

We attempt to give a broad conceptual overview of modern quantum field theory, highlighting important recent developments. This report serves as the TF03 topical group summary for Snowmass 2021.

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arXiv2022

Recursion relations for 5-point conformal blocks

We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.

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arXiv2022

Bootstrapping $N_f=4$ conformal QED$_3$

We present the results of a conformal bootstrap study of the presumed unitary IR fixed point of quantum electrodynamics in three dimensions (QED$_3$) coupled to $N_f=4$ two-component Dirac fermions. Specifically, we study the four-point correlators of the $SU(4)$ adjoint fermion bilinear $r$ and the monopole of lowest topological charge $\mathcal{M}_{1/2}$. Most notably, the scaling dimensions of the fermion bilinear $r$ and the monopole $\mathcal{M}_{1/2}$ are found to be constrained into a closed island with a combination of spectrum assumptions inspired by the $1/N_f$ perturbative results as well as a novel interval positivity constraint on the next-lowest-charge monopole $\mathcal{M}_1$. Bounds in this island on the $SU(4)$ and topological $U(1)_t$ conserved current central charges $c_J$, $c_J^t$, as well as on the stress tensor central charge $c_T$, are comfortably consistent with the perturbative results. Together with the scaling dimensions, this suggests that a part of estimates from the $1/N_f$ expansion -- even at $N_f=4$ -- provide a self-consistent solution to the bootstrap crossing relations, despite some of our assumptions not being strictly justified.

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arXiv2022

Precision Bootstrap for the $\mathcal{N}=1$ Super-Ising Model

In this note we report an improved determination of the scaling dimensions and OPE coefficients of the minimal supersymmetric extension of the 3d Ising model using the conformal bootstrap. We also show how this data can be used as input to the Lorentzian inversion formula, finding good agreement between analytic calculations and numerical extremal spectra once mixing effects are resolved.

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arXiv2021

Bootstrapping Heisenberg Magnets and their Cubic Instability

We study the critical $O(3)$ model using the numerical conformal bootstrap. In particular, we use a recently developed cutting-surface algorithm to efficiently map out the allowed space of CFT data from correlators involving the leading $O(3)$ singlet $s$, vector $ϕ$, and rank-2 symmetric tensor $t$. We determine their scaling dimensions to be $(Δ_{s}, Δ_ϕ, Δ_{t}) = (0.518942(51), 1.59489(59), 1.20954(23))$, and also bound various OPE coefficients. We additionally introduce a new "tip-finding" algorithm to compute an upper bound on the leading rank-4 symmetric tensor $t_4$, which we find to be relevant with $Δ_{t_4} < 2.99056$. The conformal bootstrap thus provides a numerical proof that systems described by the critical $O(3)$ model, such as classical Heisenberg ferromagnets at the Curie transition, are unstable to cubic anisotropy.

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arXiv2021

Searching for gauge theories with the conformal bootstrap

Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can potentially be solved with the conformal bootstrap. We start by considering the bootstrap for $SO(N)$ vector 4-point functions in general dimension $D$. In the large $N$ limit, upper bounds on the scaling dimensions of the lowest $SO(N)$ singlet and traceless symmetric scalars interpolate between two solutions at $Δ=D/2-1$ and $Δ=D-1$ via generalized free field theory. In 3D the critical $O(N)$ vector models are known to saturate the bootstrap bounds and correspond to the kinks approaching $Δ=1/2$ at large $N$. We show that the bootstrap bounds also admit another infinite family of kinks ${\cal T}_D$, which at large $N$ approach solutions containing free fermion bilinears at $Δ=D-1$ from below. The kinks ${\cal T}_D$ appear in general dimensions with a $D$-dependent critical $N^*$ below which the kink disappears. We also study relations between the bounds obtained from the bootstrap with $SO(N)$ vectors, $SU(N)$ fundamentals, and $SU(N)\times SU(N)$ bi-fundamentals. We provide a proof for the coincidence between bootstrap bounds with different global symmetries. We show evidence that the proper symmetries of the underlying theories of ${\cal T}_D$ are subgroups of $SO(N)$, and we speculate that the kinks ${\cal T}_D$ relate to the fixed points of gauge theories coupled to fermions.

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