Full Eigenstate Thermalization in Quantum Field Theory: Free Cumulants and Gravitational Scrambling
Abstract
Using thermal analyticity, we derive directional large-frequency bounds on the smooth functions entering full eigenstate thermalization in continuum quantum field theory. The strongest directions reproduce the scales previously identified for lattice systems, while the complete analyticity domain reveals a broader asymmetric multifrequency structure. In thermal two-dimensional conformal field theory, exact two- and three-point functions saturate the corresponding bounds. At fourth order, where genuine dynamical information first appears, we show that the holographic CFTs studied here saturate the strongest full-ETH bounds. These results establish a direct connection between full ETH, free cumulants, and gravitational scrambling, and are consistent with the emergence of asymptotic freeness realized by the gravitational scrambling algebra.
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BibTeX
@misc{espindola2026full,
title = {{Full Eigenstate Thermalization in Quantum Field Theory: Free Cumulants and Gravitational Scrambling}},
author = {Ricardo Espíndola and Viktor Jahnke},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17669},
eprint = {2609.17669},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17669},
}
RIS
TY - UNPB
TI - Full Eigenstate Thermalization in Quantum Field Theory: Free Cumulants and Gravitational Scrambling
AU - Ricardo Espíndola
AU - Viktor Jahnke
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17669
UR - https://arxiv.org/abs/2609.17669
AB - Using thermal analyticity, we derive directional large-frequency bounds on the smooth functions entering full eigenstate thermalization in continuum quantum field theory. The strongest directions reproduce the scales previously identified for lattice systems, while the complete analyticity domain reveals a broader asymmetric multifrequency structure. In thermal two-dimensional conformal field theory, exact two- and three-point functions saturate the corresponding bounds. At fourth order, where genuine dynamical information first appears, we show that the holographic CFTs studied here saturate the strongest full-ETH bounds. These results establish a direct connection between full ETH, free cumulants, and gravitational scrambling, and are consistent with the emergence of asymptotic freeness realized by the gravitational scrambling algebra.
ER -