zbMATH — the first resource for mathematics

Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups. (English) Zbl 1387.58029
Summary: We study the entanglement for a state on linked torus boundaries in \(3d\) Chern-Simons theory with a generic gauge group and present the asymptotic bounds of Rényi entropy at two different limits: (i) large Chern-Simons coupling \(k\), and (ii) large rank \(r\) of the gauge group. These results show that the Rényi entropies cannot diverge faster than ln \(k\) and ln \(r\), respectively. We focus on torus links \(T(2, 2n)\) with topological linking number \(n\). The Rényi entropy for these links shows a periodic structure in \(n\) and vanishes whenever \(n\) = 0 (mod p), where the integer p is a function of coupling \(k\) and rank \(r\). We highlight that the refined Chern-Simons link invariants can remove such a periodic structure in \(n\).

58J28 Eta-invariants, Chern-Simons invariants
81T45 Topological field theories in quantum mechanics
81P40 Quantum coherence, entanglement, quantum correlations
Full Text: DOI
[1] Ryu, S.; Takayanagi, T., Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett., 96, 181602, (2006) · Zbl 1228.83110
[2] Hubeny, VE; Rangamani, M.; Takayanagi, T., A covariant holographic entanglement entropy proposal, JHEP, 07, 062, (2007)
[3] Lewkowycz, A.; Maldacena, J., Generalized gravitational entropy, JHEP, 08, 090, (2013) · Zbl 1342.83185
[4] Bianchi, E.; Myers, RC, On the architecture of spacetime geometry, Class. Quant. Grav., 31, 214002, (2014) · Zbl 1303.83010
[5] Balasubramanian, V.; Czech, B.; Chowdhury, BD; Boer, J., The entropy of a hole in spacetime, JHEP, 10, 220, (2013) · Zbl 1342.83226
[6] Balasubramanian, V.; Chowdhury, BD; Czech, B.; Boer, J.; Heller, MP, Bulk curves from boundary data in holography, Phys. Rev., D 89, (2014)
[7] Myers, RC; Rao, J.; Sugishita, S., Holographic holes in higher dimensions, JHEP, 06, 044, (2014)
[8] Swingle, B., Entanglement renormalization and holography, Phys. Rev., D 86, (2012)
[9] Nozaki, M.; Numasawa, T.; Prudenziati, A.; Takayanagi, T., Dynamics of entanglement entropy from Einstein equation, Phys. Rev., D 88, (2013)
[10] Lashkari, N.; McDermott, MB; Raamsdonk, M., Gravitational dynamics from entanglement ‘thermodynamics’, JHEP, 04, 195, (2014)
[11] Faulkner, T.; Guica, M.; Hartman, T.; Myers, RC; Raamsdonk, M., Gravitation from entanglement in holographic cfts, JHEP, 03, 051, (2014) · Zbl 1333.83141
[12] B. Swingle and M. Van Raamsdonk, Universality of gravity from entanglement, arXiv:1405.2933 [INSPIRE]. · Zbl 1348.81389
[13] Calabrese, P.; Cardy, JL, Entanglement entropy and quantum field theory, J. Stat. Mech., 0406, (2004) · Zbl 1082.82002
[14] Calabrese, P.; Cardy, J., Entanglement entropy and conformal field theory, J. Phys., A 42, 504005, (2009) · Zbl 1179.81026
[15] Klebanov, IR; Pufu, SS; Sachdev, S.; Safdi, BR, Rényi entropies for free field theories, JHEP, 04, 074, (2012) · Zbl 1348.81140
[16] Casini, H.; Huerta, M., Entanglement entropy in free quantum field theory, J. Phys., A 42, 504007, (2009) · Zbl 1186.81017
[17] Fursaev, DV, Entanglement Rényi entropies in conformal field theories and holography, JHEP, 05, 080, (2012) · Zbl 1348.81389
[18] Witten, E., Quantum field theory and the Jones polynomial, Commun. Math. Phys., 121, 351, (1989) · Zbl 0667.57005
[19] Levin, M.; Wen, X-G, Detecting topological order in a ground state wave function, Phys. Rev. Lett., 96, 110405, (2006)
[20] Dong, S.; Fradkin, E.; Leigh, RG; Nowling, S., Topological entanglement entropy in Chern-Simons theories and quantum Hall fluids, JHEP, 05, 016, (2008)
[21] Kitaev, A.; Preskill, J., Topological entanglement entropy, Phys. Rev. Lett., 96, 110404, (2006)
[22] Balasubramanian, V.; Hayden, P.; Maloney, A.; Marolf, D.; Ross, SF, Multiboundary wormholes and holographic entanglement, Class. Quant. Grav., 31, 185015, (2014) · Zbl 1300.81067
[23] Marolf, D.; Maxfield, H.; Peach, A.; Ross, SF, Hot multiboundary wormholes from bipartite entanglement, Class. Quant. Grav., 32, 215006, (2015) · Zbl 1329.83063
[24] Salton, G.; Swingle, B.; Walter, M., Entanglement from topology in Chern-Simons theory, Phys. Rev., D 95, 105007, (2017)
[25] Balasubramanian, V.; Fliss, JR; Leigh, RG; Parrikar, O., Multi-boundary entanglement in Chern-Simons theory and link invariants, JHEP, 04, 061, (2017) · Zbl 1378.81061
[26] Aganagic, M.; Shakirov, S., Knot homology and refined Chern-Simons index, Commun. Math. Phys., 333, 187, (2015) · Zbl 1322.81069
[27] W. Fulton and J. Harris, Representation theory: a first course, Springer Science & Business Media 129, Springer, New York U.S.A., (2013). · Zbl 0744.22001
[28] Eliahou, S.; Kauffman, LH; Thistlethwaite, MB, Infinite families of links with trivial Jones polynomial, Topology, 42, 155, (2003) · Zbl 1013.57005
[29] Morton, HR; Cromwell, PR, Distinguishing mutants by knot polynomials, J. Knot Theor. Ramifications, 5, 225, (1996) · Zbl 0866.57002
[30] Nawata, S.; Ramadevi, P.; Singh, VK, Colored HOMFLY-PT polynomials that distinguish mutant knots, J. Knot Theor. Ramifications, 26, 1750096, (2017) · Zbl 1405.57017
[31] Mironov, A.; Morozov, A.; Morozov, A.; Ramadevi, P.; Singh, VK, Colored HOMFLY polynomials of knots presented as double fat diagrams, JHEP, 07, 109, (2015) · Zbl 1388.57010
[32] Mlawer, EJ; Naculich, SG; Riggs, HA; Schnitzer, HJ, Group level duality of WZW fusion coefficients and Chern-Simons link observables, Nucl. Phys., B 352, 863, (1991)
[33] P. Di Francesco, P. Mathieu and D. Sénéchal, Conformal field theory, Springer Science & Business Media, Springer, New York U.S.A., (2012) [INSPIRE]. · Zbl 0869.53052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.