scholarly journals Batalin-Vilkovisky formality for Chern-Simons theory

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Ezra Getzler
Keyword(s):  
Field Theory ◽  
Lie Algebra ◽  
Simons Theory ◽  
Semisimple Lie Algebra ◽  
General Field ◽  
Graded Lie Algebra ◽  
Variational Complex ◽  
Differential Graded Lie Algebra ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We prove that the differential graded Lie algebra of functionals associated to the Chern-Simons theory of a semisimple Lie algebra is homotopy abelian. For a general field theory, we show that the variational complex in the Batalin-Vilkovisky formalism is a differential graded Lie algebra.

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 BATALIN–VILKOVISKY YANG–MILLS THEORY AS A HOMOTOPY CHERN–SIMONS THEORY VIA STRING FIELD THEORY

2009 ◽  
Vol 24 (07) ◽  
pp. 1309-1331 ◽  
Author(s):  
ANTON M. ZEITLIN
Keyword(s):  
Field Theory ◽  
String Field Theory ◽  
Simons Theory ◽  
Yang Mills ◽  
Algebraic Constructions ◽  
Chern Simons ◽  
Chern Simons Theory

We show explicitly how Batalin–Vilkovisky Yang–Mills action emerges as a homotopy generalization of Chern–Simons theory from the algebraic constructions arising from string field theory.

scholarly journals Explicit Connection Between Conformal Field Theory and 2+1 Chern–Simons Theory

1997 ◽  
Vol 12 (23) ◽  
pp. 1687-1697
Author(s):  
Daniel C. Cabra ◽  
Gerardo L. Rossini
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Wilson Loop ◽  
Simons Theory ◽  
Gauge Invariant ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

We give explicit field theoretical representations for the observables of (2+1)-dimensional Chern–Simons theory in terms of gauge-invariant composites of 2-D WZW fields. To test our identification we compute some basic Wilson loop correlators and re-obtain the known results.

COHERENT STATE QUANTIZATION OF CHERN-SIMONS THEORY

1990 ◽  
Vol 05 (05) ◽  
pp. 959-988 ◽  
Author(s):  
MICHIEL BOS ◽  
V.P. NAIR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Coherent State ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Three-dimensional Chern-Simons gauge theories are quantized in a functional coherent state formalism. The connection with two-dimensional conformal field theory is found to emerge naturally. The normalized wave functionals are identified as generating functionals for the chiral blocks of two-dimensional current algebra.

ANYONS AND GAUSSIAN CONFORMAL FIELD THEORIES

1991 ◽  
Vol 06 (04) ◽  
pp. 289-294 ◽  
Author(s):  
DILEEP P. JATKAR ◽  
SUMATHI RAO
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Mass Parameter ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Conformal Blocks ◽  
Conformal Field ◽  
A Charge ◽  
Chern Simons ◽  
Chern Simons Theory

We identify the spin of the anyons with the holomorphic dimension of the primary fields of a Gaussian conformal field theory. The angular momentum addition rules for anyons go over to the fusion rules for the primary fields and the r↔1/2r duality of the Gaussian CFT is reproduced by a charge-flux duality of the anyons. For a U(1) Chern-Simons theory with topological mass parameter k=2n, N-anyon states on the torus have 2n components, which correspond to the 2n conformal blocks of an N-point function in the Gaussian conformal field theory.

scholarly journals PERTURBATIVE CHERN-SIMONS THEORY

1995 ◽  
Vol 04 (04) ◽  
pp. 503-547 ◽  
Author(s):  
DROR BAR-NATAN
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Integral Formula ◽  
Simons Theory ◽  
Gauge Field Theory ◽  
Complete Agreement ◽  
Knot Invariants ◽  
Arf Invariant ◽  
Chern Simons ◽  
Chern Simons Theory

We present the perturbation theory of the Chern-Simons gauge field theory and prove that to second order it indeed gives knot invariants. We identify these invariants and show that in fact we get a previously unknown integral formula for the Arf invariant of a knot, in complete agreement with earlier non-perturbative results of Witten. We outline our expectations for the behavior of the theory beyond two loops.

scholarly journals CHERN–SIMONS APPROACH TO THREE-MANIFOLD INVARIANTS

1995 ◽  
Vol 10 (06) ◽  
pp. 487-493
Author(s):  
BOGUSŁAW BRODA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lie Group ◽  
Three Dimensional ◽  
Simons Theory ◽  
Quantum Field ◽  
Topological Quantum ◽  
Chern Simons ◽  
Direct Implementation ◽  
Chern Simons Theory

A new, formal, noncombinatorial approach to invariants of three-dimensional manifolds of Reshetikhin, Turaev and Witten in the framework of nonperturbative topological quantum Chern–Simons theory, corresponding to an arbitrary compact simple Lie group, is presented. A direct implementation of surgery instructions in the context of quantum field theory is proposed. An explicit form of the specialization of the invariant to the group SU(2) is shown.

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