TOPOLOGICAL STRING ENTANGLEMENT Mukund Rangamani QMAP & Dept of Physics, UC Davis It from Qubit School/Workshop Yukawa Institute for Theoretical Physics Kyoto Jun 20, 2019 Veronika Hubeny, Roji Pius, MR [1905.09890]
MOTIVATION Holographic entanglement proposals are well understood in the regime of planar, strongly coupled field theories, which translates to the hierarchy: en ` AdS � ` s � ` P , 1 Perturbation theory in inverse powers of coupling ◆ 4 ✓ ` AdS g 2 Y M N ∼ lead to geometric (though not extremal) surfaces ` s Quantum gravitational effects however lead to ◆ 4 ✓ ` AdS , N ∼ quantum entanglement across the bulk extremal surface ` P Effectively, our understanding of how between geometry arises from entanglement in field theory is limited to a small corner of parameter space. We should be asking for more…
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</latexit> MOTIVATION Explore the connection between entanglement and geometry in classical string theory, when . ` AdS ⇠ ` s � ` P For now, focus on topological context where lack of dynamics is compensated by the intrinsic tractability of the theories. Open/closed topological string duality provides a concrete context where we can explore what is the topological closed string quantity which captures Chern-Simons topological entanglement . More precisely, seek a topological analog of generalized gravitational entropy, and ask how the replica construction in Chern-Simons ports across to the closed topological string. We’ll argue for a natural replica construction in the closed topological string and the notion of an entangling brane in topological string theory.
Act I The topological open/closed string duality
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