All-Order Volume Conjecture for Closed 3-Manifolds from Complex Chern–Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

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Four-dimension aspect of the perturbative renormalization in three-dimensional Chern-Simons theory

Nuclear Physics B ◽

10.1016/0550-3213(91)90130-p ◽

1991 ◽

Vol 352 (1) ◽

pp. 87-112 ◽

Cited By ~ 24

Author(s):

M.A. Shifman

Keyword(s):

Three Dimensional ◽

Simons Theory ◽

Perturbative Renormalization ◽

Chern Simons ◽

Chern Simons Theory

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Infrared finiteness of the two-loop correction to the Chern–Simons term in the Yang–Mills–Chern–Simons theory

Canadian Journal of Physics ◽

10.1139/p95-048 ◽

1995 ◽

Vol 73 (5-6) ◽

pp. 344-348 ◽

Cited By ~ 2

Author(s):

Yeong-Chuan Kao ◽

Hsiang-Nan Li

Keyword(s):

Effective Action ◽

Background Field ◽

Landau Gauge ◽

Quantum Corrections ◽

Simons Theory ◽

Loop Correction ◽

Loop Contribution ◽

Yang Mills ◽

Chern Simons ◽

Chern Simons Theory

We show that the two-loop contribution to the coefficient of the Chern–Simons term in the effective action of the Yang–Mills–Chern–Simons theory is infrared finite in the background field Landau gauge. We also discuss the difficulties in verifying the conjecture, due to topological considerations, that there are no more quantum corrections to the Chern–Simons term other than the well-known one-loop shift of the coefficient.

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Is there a phase transition in Maxwell-Chern-Simons theory?

Physical Review D ◽

10.1103/physrevd.48.1808 ◽

1993 ◽

Vol 48 (4) ◽

pp. 1808-1820 ◽

Cited By ~ 6

Author(s):

Mark Burgess ◽

David J. Toms ◽

Nils Tveten

Keyword(s):

Phase Transition ◽

Simons Theory ◽

Chern Simons ◽

Chern Simons Theory

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Poincaré series, 3d gravity and averages of rational CFT

Journal of High Energy Physics ◽

10.1007/jhep04(2021)267 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Viraj Meruliya ◽

Sunil Mukhi ◽

Palash Singh

Keyword(s):

Poincaré Series ◽

Simons Theory ◽

Partition Functions ◽

Moody Algebra ◽

Modular Invariant ◽

Poincare Series ◽

Single Genus ◽

3D Gravity ◽

Chern Simons ◽

Chern Simons Theory

Abstract We investigate the Poincaré series approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)k WZW models provide unitary examples for which the Poincaré series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT’s sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and all relevant values of k. We then study other WZW models, notably SU(N)1 and SU(3)k, and find that each class presents rather different features. Finally we consider multiple genus-1 boundaries, where we find a class of seed functions for the Poincaré sum that reproduces both disconnected and connected contributions — the latter corresponding to analogues of 3-manifold “wormholes” — such that the expected average is correctly reproduced.

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Tunable dynamical magnetoelectric effect in antiferromagnetic topological insulator MnBi2Te4 films

npj Computational Materials ◽

10.1038/s41524-021-00589-3 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Tongshuai Zhu ◽

Huaiqiang Wang ◽

Haijun Zhang ◽

Dingyu Xing

Keyword(s):

Topological Insulator ◽

Condensed Matter ◽

Simons Theory ◽

Spin Wave Excitations ◽

Axion Field ◽

Chern Simons ◽

Related Compounds ◽

The Universe ◽

Crystalline Symmetry ◽

Chern Simons Theory

AbstractAxion was postulated as an elementary particle to solve the strong charge conjugation and parity puzzle, and later axion was also considered to be a possible component of dark matter in the universe. However, the existence of axions in nature has not been confirmed. Interestingly, axions arise out of pseudoscalar fields derived from the Chern–Simons theory in condensed matter physics. In antiferromagnetic insulators, the axion field can become dynamical due to spin-wave excitations and exhibits rich exotic phenomena, such as axion polariton. However, antiferromagnetic dynamical axion insulator has yet been experimentally identified in realistic materials. Very recently, MnBi2Te4 was discovered to be an antiferromagnetic topological insulator with a quantized static axion field protected by inversion symmetry $${\mathcal{P}}$$ P and magnetic-crystalline symmetry $${\mathcal{S}}$$ S . Here, we studied MnBi2Te4 films in which both the $${\mathcal{P}}$$ P and $${\mathcal{S}}$$ S symmetries are spontaneously broken and found that substantially enhanced dynamical magnetoelectric effects could be realized through tuning the thickness of MnBi2Te4 films, temperature, or element substitutions. Our results show that thin films of MnBi2Te4 and related compounds could provide a promising material platform to experimentally study axion electrodynamics.

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ON CANONICAL QUANTIZATION OF THE GAUGED WZW MODEL WITH PERMUTATION BRANES

International Journal of Modern Physics A ◽

10.1142/s0217751x11054668 ◽

2011 ◽

Vol 26 (26) ◽

pp. 4647-4660

Author(s):

GOR SARKISSIAN

Keyword(s):

Riemann Surface ◽

Phase Space ◽

Boundary Conditions ◽

Canonical Quantization ◽

Simons Theory ◽

Gauge Fields ◽

Time Line ◽

Chern Simons ◽

Special Case ◽

Chern Simons Theory

In this paper we perform canonical quantization of the product of the gauged WZW models on a strip with boundary conditions specified by permutation branes. We show that the phase space of the N-fold product of the gauged WZW model G/H on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of the double Chern–Simons theory on a sphere with N holes times the time-line with G and H gauge fields both coupled to two Wilson lines. For the special case of the topological coset G/G we arrive at the conclusion that the phase space of the N-fold product of the topological coset G/G on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of Chern–Simons theory on a Riemann surface of the genus N-1 times the time-line with four Wilson lines.

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