arXiv subjects

Rajeev S. Erramilli

Publications and source records attributed to Rajeev S. Erramilli.

9 recordsLinked to original sources

arXiv2026

Bootstrapping currents and stress tensors in 3d CFTs

We perform a numerical conformal bootstrap study of the mixed system of correlation functions involving a spin-1 $\mathrm{U}(1)$ current $J$ and the stress-energy tensor $T$ in parity-preserving 3d CFTs. We find universal bounds on the stress-tensor two-point function $c_T$, which numerically reproduce the conformal collider bounds on $\langle JJT\rangle$ and $\langle TTT\rangle$, as well as bounds on the leading parity-even and parity-odd scalar operator dimensions. Under mild assumptions, we determine the values of the $\langle JJT\rangle$ and $\langle TTT\rangle$ three-point functions in the $\mathrm{O}(2)$ vector model. The $\langle TTT\rangle$ result is new and $\langle JJT\rangle$ is consistent with a previous result in the literature.

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arXiv2026

Upgrading Extremal Flows in the Space of Derivatives

The method of extremal flows has presented an alluring alternative approach to numerically solving bootstrap constraints. Here I present the development and adaptation of that approach to a more general class of flows with apparent discontinuities. I focus on upgrading solutions of gap maximization for the spinning modular bootstrap from low to high numerical order, though the methodology is generic to a broader class of bootstrap constraints and flows. This methodology presents various nontrivialities and nuances which reflect a richness of the space of bootstrap solutions. The result is a prototype which successfully upgrades solutions in a simple test case at small scale.

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arXiv2026

Towards 3D CFT Cartography with the Stress Tensor Bootstrap

We present new numerical results on the space of local, unitary, parity-preserving conformal field theories (CFTs) in three dimensions from the stress tensor bootstrap. In bounds maximizing certain OPE coefficients, we find a plethora of sharp features, such as kinks and ridges, as a function of scaling dimensions. We show that some of these features correspond to known theories, but there are many others that are equally strong but do not match known CFTs. We argue that these features are robust to raising numerical order and could then correspond to numerous as yet unknown CFTs. We conclude in proposing a program of "CFT cartography": the systematic exploration of the landscape of CFTs without individual theory targets in mind.

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arXiv2025

Do null defects dream of conformal symmetry?

We initiate the study of null line defects in Lorentzian conformal field theories in various dimensions. We show that null lines geometrically preserve a larger set of conformal isometries than their timelike and spacelike counterparts, explain a connection to non-relativistic systems, and constrain correlation functions using conformal Ward identities. We argue that having conformal symmetry, and especially maximal conformal symmetry, is extremely constraining -- nearly trivializing systems. We consider the (3+1)d scalar pinning field and null Wilson line examples in depth, compare their results to ultraboosted limits of timelike and spacelike systems, and argue that shockwave-type solutions are generic. A number of physical consistency conditions compel us to consider defect correlators as distributions on a restricted subspace of Schwartz test functions. Consequently, we provide a resolution to the longstanding problem of ultraboosted limits of gauge potentials in classical electromagnetism. We briefly analyze semi-infinite sources for the scalar in ($4-ε$)-dimensions, consider solutions on the Lorentzian cylinder, and introduce the ''perfect null polygon'' which emerges for compatibility between Gauss' law and ultraboosted limits.

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arXiv2025

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 $σ$ and $ε$, and the stress tensor $T_{μν}$. We obtain new precise determinations of scaling dimensions $(Δ_σ, Δ_ε) = (0.518148806(24), 1.41262528(29))$ as well as OPE coefficients involving $σ$, $ε$, and $T_{μν}$. We also describe several improvements made along the way to algorithms and software tools for the numerical bootstrap.

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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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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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arXiv2020

blocks_3d: Software for general 3d conformal blocks

We introduce the software blocks_3d for computing four-point conformal blocks of operators with arbitrary Lorentz representations in 3d CFTs. It uses Zamolodchikov-like recursion relations to numerically compute derivatives of blocks around a crossing-symmetric configuration. It is implemented as a heavily optimized, multithreaded, C++ application. We give performance benchmarks for correlators containing scalars, fermions, and stress tensors. As an example application, we recompute bootstrap bounds on four-point functions of fermions and study whether a previously observed sharp jump can be explained using the "fake primary" effect. We conclude that the fake primary effect cannot fully explain the jump and the possible existence of a "dead-end" CFT near the jump merits further study.

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arXiv2019

Recursion relation for general 3d blocks

We derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional conformal field theory. This result opens a path to efficient automatic generation of conformal block tables, which has immediate applications in numerical conformal bootstrap program. Our derivation is based on an understanding of null states and conformally-invariant differential operators in momentum space, combined with a careful choice of the relevant tensor structures bases. This derivation generalizes straightforwardly to higher spacetime dimensions d, provided the relevant Clebsch-Gordan coefficients of Spin(d) are known.

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