scholarly journals Wilson-’t Hooft lines as transfer matrices

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kazunobu Maruyoshi ◽  
Toshihiro Ota ◽  
Junya Yagi
Keyword(s):  
Vacuum Expectation ◽  
Simons Theory ◽  
Transfer Matrices ◽  
Quantum Integrable Systems ◽  
Expectation Values ◽  
Twisted Product ◽  
Agt Correspondence ◽  
Supersymmetric Gauge ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We establish a correspondence between a class of Wilson-’t Hooft lines in four-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-’t Hooft lines in a twisted product space S1 × ϵ ℝ2 × ℝ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities.

CHERN-SIMONS THEORY, MODULAR FUNCTIONS AND QUANTUM MECHANICS IN AN ALCOVE

1991 ◽  
Vol 06 (10) ◽  
pp. 1815-1827 ◽  
Author(s):  
SHAHN MAJID ◽  
YA. S. SOIBELMAN
Keyword(s):  
Regular Representation ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Simons Theory ◽  
Mathematical Work ◽  
Modular Functions ◽  
Left Regular Representation ◽  
Left Regular ◽  
Chern Simons ◽  
Chern Simons Theory

We show how the vacuum expectation value of the Wilson loop of the trivial knot in the left-regular representation in a Chern-Simons theory is basically the partition function for a quantum particle confined to a certain bounded region (namely, an alcove of the gauge group Lie algebra). For example, for su(3) the particle is confined to an equilateral triangle. The result follows from mathematical work on the category-theoretic rank of quantum groups obtained in a previous paper. In the present paper we give the details of the physical interpretation and discuss the implications. In particular, both these physical systems are connected with number theory.

scholarly journals Matter in 2+1 Dimensions at Finite Density with Chern Simons Interactions

2020 ◽  
Author(s):  
◽  
Stanislav Stratiev
Keyword(s):  
Ground State ◽  
Particle Number ◽  
Chemical Potential ◽  
Vacuum Expectation ◽  
Simons Theory ◽  
Vortex Solutions ◽  
Scalar Potentials ◽  
Chern Simons ◽  
Do So ◽  
Chern Simons Theory

We study several matter Chern-Simons models at finite chemical potential. In the SU(N) theory we discover a colour-flavour locked Bose condensed ground state with vacuum expectation values for both the scalar and gauge fields. We identify this ground state with the non-commutative Chern-Simons description of the quan-tum Hall eect. We compute the quadratic spectrum and discover roton excitations. We find a self-consistent circularly symmetric ansatz for topological non-abelian vortices. We examine vortices in abelian Chern-Simons theory coupled to a relativistic scalar field with a chemical potential for particle number or U(1) charge. The Gauss constraint requires chemical potential for the local symme-try to be accompanied by a constant background charge density/ma-gnetic field. Focusing attention on power law scalar potentials |Φ|2s, s ∈ Z, which do not support vortex configurations in vacuum but do so at finite chemical potential, we numerically study classical vortex solutions for a large winding number |n|  1.

CHERN-SIMONS THEORY AND KAUFFMAN POLYNOMIALS

1990 ◽  
Vol 05 (06) ◽  
pp. 1165-1195 ◽  
Author(s):  
YONG-SHI WU ◽  
KENGO YAMAGISHI
Keyword(s):  
Lie Algebras ◽  
Simons Theory ◽  
Wilson Loops ◽  
Expectation Values ◽  
Simple Lie Algebras ◽  
Link Invariants ◽  
Chern Simons ◽  
Knots And Links ◽  
Chern Simons Theory

We report on a study of the expectation values of Wilson loops in D=3 Chern-Simons theory. The general skein relations (of higher orders) are derived for these expectation values. We show that the skein relations for the Wilson loops carrying the fundamental representations of the simple Lie algebras SO(n) and Sp(n) are sufficient to determine invariants for all knots and links and that the resulting link invariants agree with Kauffman polynomials. The polynomial for an unknotted circle is identified to the formal characters of the fundamental representations of these Lie algebras.

TRANSVERSE LATTICE CONSTRUCTION OF 2+1 CHERN-SIMONS THEORY

1992 ◽  
Vol 07 (07) ◽  
pp. 601-610 ◽  
Author(s):  
PAUL A. GRIFFIN
Keyword(s):  
Lattice Model ◽  
Sigma Model ◽  
Simons Theory ◽  
Nonlinear Sigma Model ◽  
Expectation Values ◽  
Transverse Lattice ◽  
Lattice Construction ◽  
Chern Simons ◽  
Lattice Dimension ◽  
Chern Simons Theory

A transverse lattice model, with one lattice dimension and two continuum dimensions, is constructed by introducing Wess-Zumino terms into the gauged (1+1)-dimensional nonlinear sigma model action of the link fields. Its continuum limit is the pure Chern-Simons gauge theory in 2+1 dimensions. The lattice model is quantized, and some simple expectation values for Wilson loops on M2×S1 are evaluated. This construction provides an explicit connection between Chern-Simons theory and the gauged Wess-Zumino-Witten model.

scholarly journals GAUGE DEPENDENCE IN CHERN–SIMONS THEORY

1999 ◽  
Vol 14 (03) ◽  
pp. 463-479 ◽  
Author(s):  
F. A. DILKES ◽  
L. C. MARTIN ◽  
D. G. C. MCKEON ◽  
T. N. SHERRY
Keyword(s):  
Proper Time ◽  
Three Dimensional ◽  
Vacuum Expectation ◽  
Three Dimensions ◽  
Simons Theory ◽  
Gauge Parameter ◽  
Gauge Dependence ◽  
Gauge Fixing ◽  
Chern Simons ◽  
Chern Simons Theory

We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern–Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter (α) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form [Formula: see text]. This is possible as in three dimensions α is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and ∊μλν is handled unambiguously since the system is three-dimensional at all stages of the calculation. The results are shown to be consistent with the so-called Nielsen identities which predict the explicit gauge parameter dependence using an extension of BRS symmetry. We demonstrate that this α dependence may potentially contribute to the vacuum expectation values of products of Wilson loops.

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.

Chern-Simons theory for electrons in high Landau levels

1999 ◽  
Vol 09 (PR10) ◽  
pp. Pr10-223-Pr10-225
Author(s):  
S. Scheidl ◽  
B. Rosenow
Keyword(s):  
Landau Levels ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons 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.

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

1995 ◽  
Vol 73 (5-6) ◽  
pp. 344-348 ◽  
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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