Energy Correlator Conformal Blocks Demonstrate Positivity in Field Theory Operator Product Expansions

The fundamental behaviour of energy flow in quantum field theories underpins diverse areas of physics, from particle collisions to the very structure of consistent theoretical models. Bianka Meçaj from Los Alamos National Laboratory, Ian Moult from Yale University, and Matthew T. Walters from Heriot-Watt University, working with Yuan Xin and others, significantly advances our understanding of these energy flows by developing a detailed mathematical framework for analysing how energy is distributed within these theories. The team computes key components, known as conformal blocks, that describe energy flow between a source and a detector, considering both common and more unusual patterns of symmetry. By applying these calculations to known theoretical models, including the 3d Ising CFT, the researchers derive new and powerful constraints on the underlying rules governing energy behaviour, offering potential insights into the fundamental laws of nature and opening new avenues for theoretical exploration.

Two-point energy-energy correlators represent one of the simplest observables in quantum field theory and gravity, with diverse applications ranging from real-world collider physics to constraining the space of consistent theories. This work further develops the conformal block decomposition of energy-energy correlators in conformal field theories (CFTs), focusing on the source-detector operator product expansion (OPE). The researchers compute the general conformal blocks in this channel for traceless symmetric operators of arbitrary spin in any spacetime dimension, considering both parity-even and parity-odd contributions. Motivated by the availability of data from the conformal bootstrap, the team advances the understanding of these fundamental quantities and provides tools for analysing complex theoretical models.

Conformal Bootstrap and Holographic Exploration

This collection of papers represents a comprehensive investigation into conformal field theory (CFT), holography (AdS/CFT), the cosmological bootstrap, scattering amplitudes, and related topics. The research focuses on foundational techniques and applications of the conformal bootstrap, with early work solving for critical exponents, particularly for the 3D Ising model, establishing the basis for numerical bootstrap techniques. Key connections between the conformal bootstrap and holography have also been revealed, demonstrating how bootstrap bounds can be interpreted in terms of gravitational physics. Further refinements of bootstrap bounds, focusing on OPE coefficients and the Regge trajectory, push the precision of bootstrap calculations, while connections to bulk physics, specifically the phase shift in gravity, have been established.

Sharp boundaries for the swampland, the region of parameter space where consistent quantum gravity is impossible, have been explored using the bootstrap, and classic calculations in conformal invariant field theories lay groundwork for many later developments. This research also focuses on the application of CFT techniques to understand gravity in Anti-de Sitter (AdS) space, building upon the original AdS/CFT paper establishing the duality between gravity in AdS and a CFT on the boundary. Holographic calculations of gravity in arbitrary dimensions and calculations of 3-point functions in gravity using CFT have been achieved, alongside constraints on causality for corrections to the graviton 3-point coupling. Exploration of where string theory and M-theory fit within the space of scattering amplitudes using holographic techniques further expands the understanding of these complex systems.

The application of bootstrap techniques to cosmology, particularly inflation, represents another key area of investigation. A series of papers develop the cosmological bootstrap program, focusing on symmetries, factorization, and scalar seeds, with further development including spinning correlators. This research also focuses on the calculation and properties of scattering amplitudes, often using techniques from integrability, and the use of event shapes and other observables to study high-energy physics. Investigations into gravitational axial anomalies in 4D CFTs and hydrodynamic systems with triangle anomalies, alongside experimental signatures of these anomalies in Weyl semimetals, provide further insights into fundamental physics. Weight shifting operators and conformal blocks have also been explored, demonstrating a clear trend towards using the conformal bootstrap as a central tool for exploring the landscape of possible theories and making connections between different areas of physics.

Conformal Blocks Calculated For All Operator Spins

Scientists have achieved a comprehensive calculation of conformal blocks, essential components for understanding energy-energy correlators in conformal field theories (CFTs). This work computes these blocks for all traceless symmetric operators, regardless of spin, in any spacetime dimension, representing a crucial step towards calculating energy correlators in general CFTs. The results extend previous calculations of scalar event shape blocks, broadening the applicability of this approach to theories where the stress tensor is not directly related to a scalar operator, such as the 3d Ising CFT. Researchers demonstrated the utility of these conformal blocks by applying them to a tensor product theory, CFT1 ⊗ CFT2, where the energy-energy correlator factorizes, allowing for exact computation of necessary coefficients and providing a controlled environment to examine the convergence of the conformal block expansion.

Analysis of this system reveals that while the partial wave coefficients for the observable converge effectively, the convergence of the energy correlator distribution as a function of angle is poor, suggesting challenges in reconstructing the full distribution from local OPE data. Furthermore, the team leveraged the positivity of energy correlators, specifically the Average Null Energy Condition (ANEC), to derive novel bounds on OPE coefficients involving the stress-energy tensor. This work builds upon previous applications of ANEC positivity, extending its use to constrain renormalization group flows and exploring higher-point correlators, potentially offering stronger constraints through consideration of off-diagonal terms in linear combinations of operators. These advances motivate direct Lorentzian bootstrap approaches and further exploration of partial wave coefficients in phenomenological studies.

Conformal Blocks Detail Quantum Energy Propagation

This research advances the understanding of energy flow in quantum field theories, offering new tools for both theoretical exploration and potential connections to experimental observations. Scientists have developed a detailed analysis of energy-energy correlators, which describe how energy propagates within a system, focusing on the decomposition of these correlators into fundamental building blocks known as conformal blocks. This work extends the established framework to include operators with arbitrary spin and considers both parity-even and parity-odd contributions, providing a more complete picture of energy flow dynamics. While the analysis relies on specific approximations within the conformal framework, the authors acknowledge limitations related to the complexity of applying these techniques to non-conformal theories or systems far from equilibrium. Future research directions include extending these methods to explore more realistic physical scenarios and investigating the potential for applying these constraints to refine calculations in quantum chromodynamics, ultimately bridging the gap between theoretical predictions and experimental observations in particle physics.