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AGPhil: Arbeitsgruppe Philosophie der Physik

AGPhil 2: Quantum and Classical Gravity 2

AGPhil 2.1: Invited Talk

Monday, March 18, 2024, 11:30–12:15, PTB SR AvHB

The AdS/CFT correspondence: Status and new relations between information and geometry — •Johanna Erdmenger — Lehrstuhl für Theoretische Physik 3, Julius-Maximilians-Universität Würzburg

Based on string theory, the AdS/CFT correspondence conjectures a duality between a quantum gravity theory and a quantum field theory without gravity. A central conceptual element is the holographic principle, according to which a gravity theory in a given volume has the same amount of degrees of freedom as the theory on its boundary. This is reminiscent of the Bekenstein-Hawking formula, according to which the entropy of a black hole scales with its horizon area.

Within AdS/CFT, information-theoretic measures are mapped to geometry. Examples include entanglement entropy (mapped to a minimal surface by the Ryu-Takayanagi formula) and computational complexity. Recent developments allow for the evaluation of the Page curve describing the evolution of von Neumann entropy under black hole evaporation. Moreover, operator algebras of algebraic quantum field theory are used to address the `factorization puzzle' of AdS/CFT.

I will give an overview over these recent developments, and briefly mention own work that uses the topological concept of geometric phases for characterizing the factorization properties of the operator algebra associated to the AdS eternal black hole [1].

[1] S. Banerjee, M. Dorband, J. Erdmenger, A.-L. Weigel, `Geometric phases characterise operator algebras and missing information', JHEP 10 (2023) 026.

Keywords: AdS/CFT correspondence; quantum gravity; quantum information and geometry