Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1504.07985 · Physical Review Letters

Entanglement Entropy in Two-Dimensional String Theory

Sean A. Hartnoll, Edward A. Mazenc

Published Sep 16, 2015• 52 citations
arXivHTMLPDF

Abstract

To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two-dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large-N matrix quantum mechanics dual to two-dimensional string theory in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative "graininess" of space.

DOI
10.1103/physrevlett.115.121602

Related papers

Comments on entanglement entropy in the c = 1 string theory

Ben Craps, Marius Gerbershagen, Maxim Pavlov +1 more

A bstract We study entanglement entropy in the low-energy effective field theory of two-dimensional string theory as well as in the singlet sector of the dual c = 1 matrix quantum mechanics. From the target space perspective, we argue that a generic bulk subregion is expected to have an associated generalized entanglement entropy combining a dilaton-dependent gravitational term and a matter contribution coming from the tachyon, extending the construction from black hole horizons to arbitrary subregions. Motivated by the absence of the gravitational area-like term in previous analyses of entanglement entropy in the c = 1 model, we compute the effect on the entanglement entropy of the nonlocal transformation induced by the leg-pole factor that relates the target space tachyon and the matrix model collective excitations, finding that it cannot account for the area-like term. We offer preliminary comments on the possible origin of the area term in the non-singlet sectors of the theory.

Journal of High Energy Physics•Sep 1, 2026•0 citations

Area terms and entanglement entropy in the $c=1$ string theory

Ben Craps, Marius Gerbershagen, Maxim Pavlov +1 more

We study entanglement entropy in the low-energy effective field theory of two-dimensional string theory as well as in the singlet sector of the dual $c=1$ matrix quantum mechanics. From the target space perspective, we argue that a generic bulk subregion is expected to have an associated generalized entanglement entropy combining a dilaton-dependent gravitational term and a matter contribution coming from the tachyon. Given that the gravitational area-like term is absent in previous analyses of entanglement entropy in the $c=1$ model, we examine several possible mechanisms for its emergence. We show that the nonlocal transformation induced by the leg-pole factor that relates the target space tachyon and the matrix model collective excitations cannot account for the area-like term, and we comment on its possible origin in the non-singlet sectors of the theory.

arXiv:2602.02683•Feb 2, 2026•0 citations

Entanglement entropy and the large N expansion of two-dimensional Yang-Mills theory

William Donnelly, Sydney Timmerman, Nicolás Valdés-Meller

Abstract Two-dimensional Yang-Mills theory is a useful model of an exactly solvable gauge theory with a string theory dual at large N. We calculate entanglement entropy in the 1/N expansion by mapping the theory to a system of N fermions interacting via a repulsive entropic force. The entropy is a sum of two terms: the “Boltzmann entropy,” log dim(R) per point of the entangling surface, which counts the number of distinct microstates, and the “Shannon entropy,” − Σ p R log p R , which captures fluctuations of the macroscopic state. We find that the entropy scales as N 2 in the large N limit, and that at this order only the Boltzmann entropy contributes. We further show that the Shannon entropy scales linearly with N, and confirm this behaviour with numerical simulations. While the term of order N is surprising from the point of view of the string dual — in which only even powers of N appear in the partition function — we trace it to a breakdown of large N counting caused by the replica trick. This mechanism could lead to corrections to holographic entanglement entropy larger than expected from semiclassical field theory.

arXiv:1911.09302•Journal of High Energy Physics•Apr 1, 2020•18 citations

Entanglement in a two-dimensional string theory

William Donnelly, Gabriel Wong

What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large $N$. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. We derive the Modular hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an E-brane.

•Oct 6, 2016•0 citations

Remarks on entanglement entropy in string theory

Vijay Balasubramanian, Onkar Parrikar

Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the ``space of open string configurations.'' We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.

arXiv:1801.03517•Physical review. D/Physical review. D.•Mar 28, 2018•32 citations

Entanglement branes in a two-dimensional string theory

William Donnelly, Gabriel Wong

What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N . The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. We derive the modular Hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an entanglement brane, or E-brane.

arXiv:1610.01719•Journal of High Energy Physics•Sep 1, 2017•39 citations
To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two-dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large-N matrix quantum mechanics dual to two-dimensional string theory in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative "graininess" of space.
A bstract We study entanglement entropy in the low-energy effective field theory of two-dimensional string theory as well as in the singlet sector of the dual c = 1 matrix quantum mechanics. From the target space perspective, we argue that a generic bulk subregion is expected to have an associated generalized entanglement entropy combining a dilaton-dependent gravitational term and a matter contribution coming from the tachyon, extending the construction from black hole horizons to arbitrary subregions. Motivated by the absence of the gravitational area-like term in previous analyses of entanglement entropy in the c = 1 model, we compute the effect on the entanglement entropy of the nonlocal transformation induced by the leg-pole factor that relates the target space tachyon and the matrix model collective excitations, finding that it cannot account for the area-like term. We offer preliminary comments on the possible origin of the area term in the non-singlet sectors of the theory.
Area terms and entanglement entropy in the c=1c=1c=1 string theory
We study entanglement entropy in the low-energy effective field theory of two-dimensional string theory as well as in the singlet sector of the dual c=1c=1c=1 matrix quantum mechanics. From the target space perspective, we argue that a generic bulk subregion is expected to have an associated generalized entanglement entropy combining a dilaton-dependent gravitational term and a matter contribution coming from the tachyon. Given that the gravitational area-like term is absent in previous analyses of entanglement entropy in the c=1c=1c=1 model, we examine several possible mechanisms for its emergence. We show that the nonlocal transformation induced by the leg-pole factor that relates the target space tachyon and the matrix model collective excitations cannot account for the area-like term, and we comment on its possible origin in the non-singlet sectors of the theory.
Abstract Two-dimensional Yang-Mills theory is a useful model of an exactly solvable gauge theory with a string theory dual at large N. We calculate entanglement entropy in the 1/N expansion by mapping the theory to a system of N fermions interacting via a repulsive entropic force. The entropy is a sum of two terms: the “Boltzmann entropy,” log dim(R) per point of the entangling surface, which counts the number of distinct microstates, and the “Shannon entropy,” − Σ p R log p R , which captures fluctuations of the macroscopic state. We find that the entropy scales as N 2 in the large N limit, and that at this order only the Boltzmann entropy contributes. We further show that the Shannon entropy scales linearly with N, and confirm this behaviour with numerical simulations. While the term of order N is surprising from the point of view of the string dual — in which only even powers of N appear in the partition function — we trace it to a breakdown of large N counting caused by the replica trick. This mechanism could lead to corrections to holographic entanglement entropy larger than expected from semiclassical field theory.
What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large NNN. The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. We derive the Modular hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an E-brane.
Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature of strings. Here we propose a definition for bosonic open strings using the framework of string field theory. The key difference (compared to ordinary quantum field theory) is that the subregion is chosen inside a Cauchy surface in the ``space of open string configurations.'' We first present a simple calculation of this entanglement entropy in free light-cone string field theory, ignoring subtleties related to the factorization of the Hilbert space. We reproduce the answer expected from an effective field theory point of view, namely a sum over the one-loop entanglement entropies corresponding to all the particle-excitations of the string, and further show that the full string theory regulates ultraviolet divergences in the entanglement entropy. We then revisit the question of factorization of the Hilbert space by analyzing the covariant phase-space associated with a subregion in Witten's covariant string field theory. We show that the pure gauge (i.e., BRST exact) modes in the string field become dynamical at the entanglement cut. Thus, a proper definition of the entropy must involve an extended Hilbert space, with new stringy edge modes localized at the entanglement cut.
What is the meaning of entanglement in a theory of extended objects such as strings? To address this question we consider the spatial entanglement between two intervals in the Gross-Taylor model, the string theory dual to two-dimensional Yang-Mills theory at large N . The string diagrams that contribute to the entanglement entropy describe open strings with endpoints anchored to the entangling surface, as first argued by Susskind. We develop a canonical theory of these open strings, and describe how closed strings are divided into open strings at the level of the Hilbert space. We derive the modular Hamiltonian for the Hartle-Hawking state and show that the corresponding reduced density matrix describes a thermal ensemble of open strings ending on an object at the entangling surface that we call an entanglement brane, or E-brane.