A semi-classical symplectic two-form is defined as the sum of the gravitational symplectic form and the Berry curvature of the quantum matter state; it is shown to be independent of the Cauchy slice and to satisfy a quantum generalization of the Hollands-Iyer-Wald identity.
Modular Berry Connection
3 Pith papers cite this work, alongside 50 external citations. Polarity classification is still indexing.
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abstract
The Berry connection describes transformations induced by adiabatically varying Hamiltonians. We study how zero modes of the modular Hamiltonian are affected by varying the region that supplies the modular Hamiltonian. In the vacuum of a 2d CFT, global conformal symmetry singles out a unique modular Berry connection, which we compute directly and in the dual AdS$_3$ picture. In certain cases, Wilson loops of the modular Berry connection compute lengths of curves in AdS$_3$, reproducing the differential entropy formula. Modular Berry transformations can be measured by bulk observers moving with varying accelerations.
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Modular quantization of a single holographic CFT reproduces exact Hartle-Hawking correlators of smooth BTZ black holes in the semiclassical limit while yielding non-smooth stretched-horizon descriptions at finite GN.
Modular-flow generators for celestial CFT and Klein CFT are obtained as linear combinations of global SL(2,C)/SO(2,2) and supertranslation generators that preserve interval endpoints.
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Covariant phase space and the semi-classical Einstein equation
A semi-classical symplectic two-form is defined as the sum of the gravitational symplectic form and the Berry curvature of the quantum matter state; it is shown to be independent of the Cauchy slice and to satisfy a quantum generalization of the Hollands-Iyer-Wald identity.
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Modular quantization and black holes
Modular quantization of a single holographic CFT reproduces exact Hartle-Hawking correlators of smooth BTZ black holes in the semiclassical limit while yielding non-smooth stretched-horizon descriptions at finite GN.
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Modular Flow of Celestial Conformal Field Theory
Modular-flow generators for celestial CFT and Klein CFT are obtained as linear combinations of global SL(2,C)/SO(2,2) and supertranslation generators that preserve interval endpoints.