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.

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 Higher-derivative supergravity, wrapped M5-branes, and theories of class $$ \mathrm{\mathcal{R}} $$

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Nikolay Bobev ◽  
Anthony M. Charles ◽  
Dongmin Gang ◽  
Kiril Hristov ◽  
Valentin Reys
Keyword(s):  
Black Holes ◽  
Three Dimensional ◽  
Simons Theory ◽  
Partition Functions ◽  
Infinite Class ◽  
Gauge Groups ◽  
Higher Derivative ◽  
Hyperbolic Three Manifolds ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class $$ \mathrm{\mathcal{R}} $$ ℛ . Using results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d correspondence we are able to constrain the two independent coefficients in the four-derivative supergravity Lagrangian. This in turn allows us to calculate the subleading terms in the large-N expansion of supersymmetric partition functions for an infinite class of three-dimensional $$ \mathcal{N} $$ N = 2 SCFTs of class $$ \mathrm{\mathcal{R}} $$ ℛ . We also determine the leading correction to the Bekenstein-Hawking entropy of asymptotically AdS4 black holes arising from wrapped M5-branes. In addition, we propose and test some conjectures about the perturbative partition function of Chern-Simons theory with complexified ADE gauge groups on closed hyperbolic three-manifolds.

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.

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.

Operator regularization in Chern–Simons theory

1990 ◽  
Vol 68 (11) ◽  
pp. 1291-1295 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Vacuum Polarization ◽  
Three Dimensional ◽  
Field Theories ◽  
Kinetic Term ◽  
Explicit Calculation ◽  
Simons Theory ◽  
Loop Order ◽  
Self Energy ◽  
Chern Simons ◽  
Chern Simons Theory

We demonstrate how operator regularization can be employed in three-dimensional Chern–Simons field theories. An explicit calculation of the vacuum polarization to one-loop order using this technique gives a nonlocal, transverse result that suggest a radiatively induced kinetic term for the vector field. Similarly, the spinor self-energy is finite and nonlocal when it interacts with a Chern–Simons field.

3D MANIFOLDS, GRAPH INVARIANTS AND CHERN-SIMONS THEORY

1992 ◽  
Vol 07 (23) ◽  
pp. 2065-2076 ◽  
Author(s):  
S. KALYANA RAMA ◽  
SIDDHARTHA SEN
Keyword(s):  
Partition Function ◽  
Closed Form ◽  
Three Dimensional ◽  
Simons Theory ◽  
Partition Functions ◽  
Graph Invariants ◽  
Absolute Value ◽  
Dimensional Gravity ◽  
Chern Simons ◽  
Chern Simons Theory

We show how the Turaev-Viro invariant, which is closely related to the partition function of three-dimensional gravity, can be understood within the framework of SU(2) Chern-Simons theory. We also show that, for S3 and RP3, this invariant is equal to the absolute value square of their respective partition functions in SU(2) Chern-Simons theory and give a method of evaluating the latter in a closed form for a class of 3D manifolds, thus in effect obtaining the partition function of three-dimensional gravity for these manifolds. By interpreting the triangulation of a manifold as a graph consisting of crossings and vertices with three lines we also describe a new invariant for certain class of graphs.

scholarly journals Non-perturbative tests of duality cascades in three dimensional supersymmetric gauge theories

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Masazumi Honda ◽  
Naotaka Kubo
Keyword(s):  
Gauge Group ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Simons Theory ◽  
Partition Functions ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
Supersymmetric Theories ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract It has been conjectured that duality cascade occurs in the $$ \mathcal{N} $$ N = 3 supersymmetric Yang-Mills Chern-Simons theory with the gauge group U(N)k × U(N + M)−k coupled to two bi-fundamental hypermultiplets. The brane picture suggests that this duality cascade can be generalized to a class of 3d $$ \mathcal{N} $$ N = 3 supersymmetric quiver gauge theories coming from so-called Hanany-Witten type brane configurations. In this paper we perform non-perturbative tests of the duality cascades using supersymmetry localization. We focus on S3 partition functions and prove predictions from the duality cascades. We also discuss that our result can be applied to generate new dualities for more general theories which include less supersymmetric theories and theories without brane constructions.

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.

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