Johanna Erdmenger, Kevin T. Grosvenor, Ro Jefferson
SciPost Phys. 8, 073 (2020) ·
published 6 May 2020

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Motivated by the increasing connections between information theory and highenergy 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 compare the latter to the metric on the space of coherent free boson states and show that in both cases the metric is determined by the symmetries of the corresponding density matrix. We also clarify some misconceptions in the literature pertaining to different notions of flatness associated to metric and nonmetric 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.
SciPost Phys. 6, 042 (2019) ·
published 5 April 2019

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We show how the traversable wormhole induced by a doubletrace deformation of
the thermofield double state can be understood as a modular inclusion of the
algebras of exterior operators. The effect of this deformation is the creation
of a new region of spacetime deep in the bulk, corresponding to a nontrivial
center between the left and right algebras. This setup provides a precise
framework for investigating how black hole interiors are encoded in the CFT. In
particular, we use modular theory to demonstrate that state dependence is an
inevitable feature of any attempt to represent operators behind the horizon.
Building on this geometrical structure, we propose that modular inclusions may
provide a more precise means of investigating the nascent relationship between
entanglement and geometry in the context of the emergent spacetime paradigm.
Shira Chapman, Jens Eisert, Lucas Hackl, Michal P. Heller, Ro Jefferson, Hugo Marrochio, Robert C. Myers
SciPost Phys. 6, 034 (2019) ·
published 15 March 2019

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Motivated by holographic complexity proposals as novel probes of black hole
spacetimes, we explore circuit complexity for thermofield double (TFD) states
in free scalar quantum field theories using the Nielsen approach. For TFD
states at t = 0, we show that the complexity of formation is proportional to
the thermodynamic entropy, in qualitative agreement with holographic complexity
proposals. For TFD states at t > 0, we demonstrate that the complexity evolves
in time and saturates after a time of the order of the inverse temperature. The
latter feature, which is in contrast with the results of holographic proposals,
is due to the Gaussian nature of the TFD state of the free bosonic QFT. A novel
technical aspect of our work is framing complexity calculations in the language
of covariance matrices and the associated symplectic transformations, which
provide a natural language for dealing with Gaussian states. Furthermore, for
free QFTs in 1+1 dimension, we compare the dynamics of circuit complexity with
the time dependence of the entanglement entropy for simple bipartitions of
TFDs. We relate our results for the entanglement entropy to previous studies on
nonequilibrium entanglement evolution following quenches. We also present a
new analytic derivation of a logarithmic contribution due to the zero momentum
mode in the limit of vanishing mass for a subsystem containing a single degree
of freedom on each side of the TFD and argue why a similar logarithmic growth
should be present for larger subsystems.
Dr Jefferson: "We wish to thank the referee f..."
in Report on Information geometry in quantum field theory: lessons from simple examples