Entanglement as a probe of confinement

By I. Klebanov, D. Kutasov, A. Murugan. 2007

533 citations recorded by the source corpus.

Abstract We investigate the entanglement entropy in gravity duals of confining large N c gauge theories using the proposal of [S. Ryu, T. Takayanagi, Phys. Rev. Lett. 96 (2006) 181602, hep-th/0603001 ; S. Ryu, T. Takayanagi, JHEP 0608 (2006) 045, hep-th/0605073 ]. Dividing one of the directions of space into a line segment of length l and its complement, the entanglement entropy between the two subspaces is given by the classical action of the minimal bulk hypersurface which approaches the endpoints of the line segment at the boundary. We find that in confining backgrounds there are generally two such surfaces. One consists of two disconnected components localized at the endpoints of the line segment. The other contains a tube connecting the two components. The disconnected surface dominates the entropy for l above a certain critical value l crit while the connected one dominates below that value. The change of behavior at l = l crit is reminiscent of the finite temperature deconfinement transition: for l l crit the entropy scales as N c 2 , while for l > l crit as N c 0 . We argue that a similar transition should occur in any field theory with a Hagedorn spectrum of non-interacting bound states. The requirement that the entanglement entropy has a phase transition may be useful in constraining gravity duals of confining theories.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/aa80a05625463184b39e21763a067bf44eb1cd0a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. T. Takayanagi
2. R. Myers
3. T. Nishioka
4. T. Faulkner
5. V. Hubeny
6. William Donnelly
7. S. Ryu
8. D. Harlow

In Atomic and Molecular Physics, and Optics

1. T. Takayanagi
2. R. Myers
3. T. Nishioka
4. Aitor Lewkowycz
5. T. Faulkner
6. D. Harlow
7. S. Ryu
8. M. Headrick

In Nuclear and High Energy Physics

1. R. Myers
2. T. Takayanagi
3. T. Nishioka
4. T. Faulkner
5. D. Harlow
6. V. Hubeny
7. Aitor Lewkowycz
8. J. Maldacena

Citations in the corpus

• Holographic entanglement entropy in Lovelock gravities (2011, unknown): “Computing the EE for a slab in this background and generalizing the results of [76] may help to clarify the meaning of γ(a, c).”
• Decomposition of entanglement entropy in lattice gauge theory (2011, background): “In gauge theories, entanglement entropy may be useful in studying the deconfining phase transition [9, 10].”
• Holographic superconductor/insulator transition at zero temperature (2009, background): “It may also be intriguing to calculate the entanglement entropy via the AdS/CFT [34] to understand better the phase transition between the insulator and superconductor phase because this quantity is non-vanishing even at zero temperature (for the confinement/deconfinement phase transition, this was ”
• Exact results for five-dimensional superconformal field theories with gravity duals (2012, methodology): “This prescription was generalized in [32] to gravity duals with non-trivial dilaton profile.”
• Bit Threads and Holographic Entanglement (2016, background): “First, the minimal surface can jump under continuous deformations of A [4–7], suggesting that the bits strangely jump from one place to another.”
• Holographic entanglement entropy: an overview (2009, methodology): “Our holographic formula has also been successfully applied to the explanation of black hole and de-Sitter entropy [22, 23, 25, 41] (see also [80, 81] for earlier pioneering ideas on the entanglement entropy in AdS/CFT with event horizon; see also [82]), and to an order parameter of a confinement/dec”
• Entanglement Entropy of Black Holes (2011, background): “Different choices may correspond to different phases in the boundary theory [157].”
• Entanglement entropy, trace anomalies and holography ✩ (2008, background): “Using the aforementioned holographic representation for massive d = 4 theories in [5] information about the phase structure of these theories was obtained.”
• Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy (2009, methodology): “In the absence of D7-branes, this is interpreted as the confinement/deconfinement transition as the smaller size of A probes more UV region of the gauge theory [42, 43].”
• Entanglement entropy from a holographic viewpoint (2012, background): “• If we consider the holographic entanglement entropy in gravity duals of confining gauge theories such as the AdS soliton [76] and Klebanov-Strassler solutions [77], we find that the derivative of SA with respect to the size of A gets discontinuous at some point [78, 79, 80, 81, 82, 83, 84].”
• Unquenched Flavor in the Gauge/Gravity Correspondence (2010, background): “(9)The monotonicity of H(u) also plays a crucial role in holographic computations of the entanglement entropy, see [89].”
• Near extremal black hole entropy as entanglement entropy via AdS 2 / CFT 1 (2007, methodology): “(4)This holographic method has also been applied to the analysis of the confining gauge theories [12, 13].”
• On volumes of subregions in holography and complexity (2016, background): “These transitions were first studied in [17, 18] (see also [58, 60]), and were interpreted as a probe of the confinementdeconfinement transition.”
• Comments on holographic entanglement entropy and RG flows (2012, background): “A similar phase transition was also found in considering the holographic entanglement entropy of the strip geometry for a bulk background corresponding to a confining phase of the boundary theory [93, 94].”