scholarly journals Entanglement entropy for logarithmic conformal field theory

2014 ◽  
Vol 89 (6) ◽  
Author(s):  
Mohsen Alishahiha ◽  
Amin Faraji Astaneh ◽  
M. Reza Mohammadi Mozaffar
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Entanglement Entropy ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
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.

scholarly journals Chern-Simons gravity dual of BCFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Tadashi Takayanagi ◽  
Takahiro Uetoko
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Entanglement Entropy ◽  
Einstein Gravity ◽  
Conformal Field ◽  
Holographic Entanglement Entropy ◽  
The World ◽  
Higher Spin ◽  
End Of The World ◽  
Chern Simons

Abstract In this paper we provide a Chern-Simons gravity dual of a two dimensional conformal field theory on a manifold with boundaries, so called boundary conformal field theory (BCFT). We determine the correct boundary action on the end of the world brane in the Chern-Simons gauge theory. This reproduces known results of the AdS/BCFT for the Einstein gravity. We also give a prescription of calculating holographic entanglement entropy by employing Wilson lines which extend from the AdS boundary to the end of the world brane. We also discuss a higher spin extension of our formulation.

scholarly journals Logarithmic conformal field theory: a lattice approach

2013 ◽  
Vol 46 (49) ◽  
pp. 494012 ◽  
Author(s):  
A M Gainutdinov ◽  
J L Jacobsen ◽  
N Read ◽  
H Saleur ◽  
R Vasseur
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory ◽  
Lattice Approach

scholarly journals Boundary logarithmic conformal field theory

2000 ◽  
Vol 486 (3-4) ◽  
pp. 353-361 ◽  
Author(s):  
Ian I. Kogan ◽  
John F. Wheater
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory

scholarly journals BITS AND PIECES IN LOGARITHMIC CONFORMAL FIELD THEORY

2003 ◽  
Vol 18 (25) ◽  
pp. 4497-4591 ◽  
Author(s):  
MICHAEL A. I. FLOHR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Quantum Hall ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory ◽  
Verlinde Formula

These are notes of my lectures held at the first School & Workshop on Logarithmic Conformal Field Theory and its Applications, September 2001 in Tehran, Iran. These notes cover only selected parts of the by now quite extensive knowledge on logarithmic conformal field theories. In particular, I discuss the proper generalization of null vectors towards the logarithmic case, and how these can be used to compute correlation functions. My other main topic is modular invariance, where I discuss the problem of the generalization of characters in the case of indecomposable representations, a proposal for a Verlinde formula for fusion rules and identities relating the partition functions of logarithmic conformal field theories to such of well known ordinary conformal field theories. The two main topics are complemented by some remarks on ghost systems, the Haldane-Rezayi fractional quantum Hall state, and the relation of these two to the logarithmic c=-2 theory.

scholarly journals HOLOGRAPHIC GEOMETRIC ENTROPY AT FINITE TEMPERATURE FROM BLACK HOLES IN GLOBAL ANTI-DE SITTER SPACES

2012 ◽  
Vol 27 (09) ◽  
pp. 1250048 ◽  
Author(s):  
IBRAHIMA BAH ◽  
LEOPOLDO A. PANDO ZAYAS ◽  
CÉSAR A. TERRERO-ESCALANTE
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Conformal Field Theory ◽  
Periodic Boundary ◽  
Entanglement Entropy ◽  
Periodic Boundary Conditions ◽  
Two Dimensional ◽  
De Sitter ◽  
Conformal Field ◽  
The Difference

Using a holographic proposal for the geometric entropy we study its behavior in the geometry of Schwarzschild black holes in global AdSp for p = 3, 4, 5. Holographically, the entropy is determined by a minimal surface. On the gravity side, due to the presence of a horizon on the background, generically there are two solutions to the surfaces determining the entanglement entropy. In the case of AdS3, the calculation reproduces precisely the geometric entropy of an interval of length l in a two-dimensional conformal field theory with periodic boundary conditions. We demonstrate that in the cases of AdS4 and AdS5 the sign of the difference of the geometric entropies changes, signaling a transition. Euclideanization implies that various embedding of the holographic surface are possible. We study some of them and find that the transitions are ubiquitous. In particular, our analysis renders a very intricate phase space, showing, for some ranges of the temperature, up to three branches. We observe a remarkable universality in the type of results we obtain from AdS4 and AdS5.

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