scholarly journals Averaging over moduli in deformed WZW models

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Junkai Dong ◽  
Thomas Hartman ◽  
Yikun Jiang
Keyword(s):  
Moduli Space ◽  
Central Charge ◽  
Principal Result ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Chern Simons ◽  
Conserved Currents ◽  
Matter Fields ◽  
Chern Simons Theory

Abstract WZW models live on a moduli space parameterized by current-current deformations. The moduli space defines an ensemble of conformal field theories, which generically have N abelian conserved currents and central charge c > N. We calculate the average partition function and show that it can be interpreted as a sum over 3-manifolds. This suggests that the ensemble-averaged theory has a holographic dual, generalizing recent results on Narain CFTs. The bulk theory, at the perturbative level, is identified as U(1)2N Chern-Simons theory coupled to additional matter fields. From a mathematical perspective, our principal result is a Siegel-Weil formula for the characters of an affine Lie 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 REPRESENTATIONS OF COMPOSITE BRAIDS AND INVARIANTS FOR MUTANT KNOTS AND LINKS IN CHERN-SIMONS FIELD THEORIES

1995 ◽  
Vol 10 (22) ◽  
pp. 1635-1658 ◽  
Author(s):  
P. RAMADEVI ◽  
T.R. GOVINDARAJAN ◽  
R.K. KAUL
Keyword(s):  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Abelian Gauge ◽  
Gauge Groups ◽  
Knot Invariants ◽  
Conformal Field ◽  
Chern Simons ◽  
Knots And Links ◽  
Chern Simons Theory

We show that any of the new knot invariants obtained from Chern-Simons theory based on an arbitrary non-Abelian gauge group do not distinguish isotopically inequivalent mutant knots and links. In an attempt to distinguish these knots and links, we study Murakami (symmetrized version) r-strand composite braids. Salient features of the theory of such composite braids are presented. Representations of generators for these braids are obtained by exploiting properties of Hilbert spaces associated with the correlators of Wess-Zumino conformal field theories. The r-composite invariants for the knots are given by the sum of elementary Chern-Simons invariants associated with the irreducible representations in the product of r representations (allowed by the fusion rules of the corresponding Wess-Zumino conformal field theory) placed on r individual strands of the composite braid. On the other hand, composite invariants for links are given by a weighted sum of elementary multicolored Chern-Simons invariants. Some mutant links can be distinguished through the composite invariants, but mutant knots do not share this property. The results, though developed in detail within the framework of SU(2) Chern-Simons theory are valid for any other non-Abelian gauge groups.

scholarly journals Chern-Simons invariants from ensemble averages

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Meer Ashwinkumar ◽  
Matthew Dodelson ◽  
Abhiram Kidambi ◽  
Jacob M. Leedom ◽  
Masahito Yamazaki
Keyword(s):  
Three Dimensional ◽  
Lens Spaces ◽  
Kinetic Term ◽  
Simons Theory ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Integral Quadratic Form ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form Q. We provide evidence that the holographic dual after the ensemble average is the three-dimensional Abelian Chern-Simons theory with kinetic term determined by Q. The resulting partition function can be written as a modular form, expressed as a sum over the partition functions of Chern-Simons theories on lens spaces. For odd lattices, the dual bulk theory is a spin Chern-Simons theory, and we identify several novel phenomena in this case. We also discuss the holographic duality prior to averaging in terms of Maxwell-Chern-Simons theories.

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 NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

2000 ◽  
Vol 15 (30) ◽  
pp. 4857-4870 ◽  
Author(s):  
D. C. CABRA ◽  
E. FRADKIN ◽  
G. L. ROSSINI ◽  
F. A. SCHAPOSNIK
Keyword(s):  
Quantum Hall ◽  
Field Theories ◽  
Simons Theory ◽  
Conformal Field Theories ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Quantum Hall States ◽  
Effective Lagrangian ◽  
Chern Simons

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern–Simons (CS) actions. Our approach exploits the connection between the topological Chern–Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

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.

ABELIAN CHERN–SIMONS THEORY WITH MATTER FIELDS

1992 ◽  
Vol 07 (02) ◽  
pp. 381-405 ◽  
Author(s):  
KYUNG-HYUN CHO ◽  
CHAIHO RIM
Keyword(s):  
Hilbert Space ◽  
Gauge Field ◽  
Unitary Transformation ◽  
Simons Theory ◽  
Nonlocal Interaction ◽  
Maxwell Theory ◽  
Chern Simons ◽  
Matter Fields ◽  
Chern Simons Theory

It is shown that in the Abelian Chern–Simons plus Maxwell theory in 1 + 2 dimensions there is a unitary transformation such that massless modes of the gauge field are eliminated completely in the Hilbert space and a nonlocal interaction between matter fields (fermions or scalars) remains instead. The nonlocal interaction is given in terms of an effective gauge field satisfying the Gauss constraint. It is also pointed out that it is the nonlocal interaction that changes the statistics of pointlike particles and that makes a vortex charged.

scholarly journals Symmetry-resolved entanglement for excited states and two entangling intervals in AdS3/CFT2

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Konstantin Weisenberger ◽  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Excited States ◽  
Vertex Operator Algebra ◽  
Central Charge ◽  
Entanglement Entropy ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Chern Simons ◽  
Twist Fields

Abstract We test the proposal of [1] for the holographic computation of the charged moments and the resulting symmetry-resolved entanglement entropy in different excited states, as well as for two entangling intervals. Our holographic computations are performed in U(1) Chern-Simons-Einstein-Hilbert gravity, and are confirmed by independent results in a conformal field theory at large central charge. In particular, we consider two classes of excited states, corresponding to charged and uncharged conical defects in AdS3. In the conformal field theory, these states are generated by the insertion of charged and uncharged heavy operators. We employ the monodromy method to calculate the ensuing four-point function between the heavy operators and the twist fields. For the two-interval case, we derive our results on the AdS and the conformal field theory side, respectively, from the generating function method of [1], as well as the vertex operator algebra. In all cases considered, we find equipartition of entanglement between the different charge sectors. We also clarify an aspect of conformal field theories with a large central charge and $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry used in our calculations, namely the factorization of the Hilbert space into a gravitational Virasoro sector with large central charge, and a $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody sector.

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