Motivated by the increasing connections between information theory and
high-energy physics, particularly in the context of the AdS/CFT correspondence,
we explore the information geometry associated to a variety of simple systems.
By studying their Fisher metrics, we derive some general lessons that may have
important implications for the application of information geometry in
holography. We begin by demonstrating that the symmetries of the physical
theory under study play a strong role in the resulting geometry, and that the
appearance of an AdS metric is a relatively general feature. We then
investigate what information the Fisher metric retains about the physics of the
underlying theory by studying the geometry for both the classical 2d Ising
model and the corresponding 1d free fermion theory, and find that the curvature
diverges precisely at the phase transition on both sides. We discuss the
differences that result from placing a metric on the space of theories vs.
states, using the example of coherent free fermion states. We also clarify some
misconceptions in the literature pertaining to different notions of flatness
associated to metric and non-metric connections, with implications for how one
interprets the curvature of the geometry. Our results indicate that in general,
caution is needed when connecting the AdS geometry arising from certain models
with the AdS/CFT correspondence, and seek to provide a useful collection of
guidelines for future progress in this exciting area.
Description
SciPost: SciPost Phys. 8, 073 (2020) - Information geometry in quantum field theory: lessons from simple examples
%0 Journal Article
%1 Erdmenger_2020
%A Erdmenger, Johanna
%A Grosvenor, Kevin
%A Jefferson, Ro
%D 2020
%I Stichting SciPost
%J SciPost Physics
%K a
%N 5
%P 073
%R 10.21468/scipostphys.8.5.073
%T Information geometry in quantum field theory: lessons from simple examples
%U https://scipost.org/10.21468/SciPostPhys.8.5.073
%V 8
%X Motivated by the increasing connections between information theory and
high-energy physics, particularly in the context of the AdS/CFT correspondence,
we explore the information geometry associated to a variety of simple systems.
By studying their Fisher metrics, we derive some general lessons that may have
important implications for the application of information geometry in
holography. We begin by demonstrating that the symmetries of the physical
theory under study play a strong role in the resulting geometry, and that the
appearance of an AdS metric is a relatively general feature. We then
investigate what information the Fisher metric retains about the physics of the
underlying theory by studying the geometry for both the classical 2d Ising
model and the corresponding 1d free fermion theory, and find that the curvature
diverges precisely at the phase transition on both sides. We discuss the
differences that result from placing a metric on the space of theories vs.
states, using the example of coherent free fermion states. We also clarify some
misconceptions in the literature pertaining to different notions of flatness
associated to metric and non-metric connections, with implications for how one
interprets the curvature of the geometry. Our results indicate that in general,
caution is needed when connecting the AdS geometry arising from certain models
with the AdS/CFT correspondence, and seek to provide a useful collection of
guidelines for future progress in this exciting area.
@article{Erdmenger_2020,
abstract = {Motivated by the increasing connections between information theory and
high-energy physics, particularly in the context of the AdS/CFT correspondence,
we explore the information geometry associated to a variety of simple systems.
By studying their Fisher metrics, we derive some general lessons that may have
important implications for the application of information geometry in
holography. We begin by demonstrating that the symmetries of the physical
theory under study play a strong role in the resulting geometry, and that the
appearance of an AdS metric is a relatively general feature. We then
investigate what information the Fisher metric retains about the physics of the
underlying theory by studying the geometry for both the classical 2d Ising
model and the corresponding 1d free fermion theory, and find that the curvature
diverges precisely at the phase transition on both sides. We discuss the
differences that result from placing a metric on the space of theories vs.
states, using the example of coherent free fermion states. We also clarify some
misconceptions in the literature pertaining to different notions of flatness
associated to metric and non-metric connections, with implications for how one
interprets the curvature of the geometry. Our results indicate that in general,
caution is needed when connecting the AdS geometry arising from certain models
with the AdS/CFT correspondence, and seek to provide a useful collection of
guidelines for future progress in this exciting area.},
added-at = {2020-10-22T16:00:25.000+0200},
author = {Erdmenger, Johanna and Grosvenor, Kevin and Jefferson, Ro},
biburl = {https://www.bibsonomy.org/bibtex/268069d245cfe0e54e6a6db48529765b3/ctqmat},
day = 6,
description = {SciPost: SciPost Phys. 8, 073 (2020) - Information geometry in quantum field theory: lessons from simple examples},
doi = {10.21468/scipostphys.8.5.073},
interhash = {4ef6a25deae3f3164c88779cde075ade},
intrahash = {68069d245cfe0e54e6a6db48529765b3},
journal = {SciPost Physics},
keywords = {a},
month = {5},
note = {cite arxiv:2001.02683Comment: 27 pages, 2 figures},
number = 5,
pages = 073,
publisher = {Stichting SciPost},
timestamp = {2023-01-16T14:49:29.000+0100},
title = {Information geometry in quantum field theory: lessons from simple examples},
url = {https://scipost.org/10.21468/SciPostPhys.8.5.073},
volume = 8,
year = 2020
}