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Title:
Entanglement, large N, and strings in two dimensions
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Abstract:
Entanglement plays a fundamental role in gauge/gravity duality, yet spacetime entanglement entropy remains poorly understood from the perspective of the underlying string theory. As a model of this problem, we consider entanglement entropy in two-dimensional Yang-Mills theory, which has a dual description as a theory of strings in a two-dimensional target spacetime. On the string side of the duality, we find that entanglement entropy counts states of open strings ending on a pointlike object we call an entanglement brane. In the large N limit an analog of the Ryu-Takayanagi formula holds, where the leading term in the entanglement entropy is the expectation value of a local operator of order N^2. Intriguingly, the subleading corrections to the entropy are of order N, indicating a breakdown of the genus expansion when analytically continuing through different replica topologies.
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