Conformal anomaly, virasoro algebra and Chern?Simons cohomology

1986 ◽  
Vol 12 (3) ◽  
pp. 181-188
Author(s):  
Han-Ying Guo ◽  
Hai-Cang Ren ◽  
Ke Wu
Keyword(s):  
Virasoro Algebra ◽  
Conformal Anomaly ◽  
Chern Simons

scholarly journals THREE-DIMENSIONAL FIELD THEORIES FROM INFINITE-DIMENSIONAL LIE ALGEBRAS

1994 ◽  
Vol 09 (23) ◽  
pp. 4063-4076
Author(s):  
R. E. C. PERRET
Keyword(s):  
Field Theory ◽  
Lie Algebras ◽  
Three Dimensional ◽  
Virasoro Algebra ◽  
Simons Theory ◽  
Topological Field Theory ◽  
Induced Gravity ◽  
Infinite Dimensional ◽  
Topological Field ◽  
Chern Simons

A procedure for constructing topological actions from centrally extended Lie algebras is introduced. For a Kac–Moody algebra, this produces the three-dimensional Chern–Simons theory, while for the Virasoro algebra, the result is a new three-dimensional topological field theory whose physical states satisfy the Virasoro Ward identity. This topological field theory is shown to be a first order formulation of two-dimensional induced gravity in the chiral gauge. The extension to W3 gravity is discussed.

scholarly journals SYMPLECTIC REDUCTION AND SYMMETRY ALGEBRA IN BOUNDARY CHERN–SIMONS THEORY

1999 ◽  
Vol 14 (03) ◽  
pp. 231-237 ◽  
Author(s):  
PHILLIAL OH ◽  
MU-IN PARK
Keyword(s):  
Reduction Method ◽  
Virasoro Algebra ◽  
Symmetry Algebra ◽  
Symplectic Reduction ◽  
Simons Theory ◽  
Moody Algebra ◽  
Chern Simons ◽  
Chern Simons Theory

We derive the Kac–Moody algebra and Virasoro algebra in Chern–Simons theory with boundary by using the symplectic reduction method and the Noether procedures.

scholarly journals CONFORMAL ANOMALY IN NON-HERMITIAN QUANTUM MECHANICS

2010 ◽  
Vol 25 (01) ◽  
pp. 155-161
Author(s):  
PULAK RANJAN GIRI
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Virasoro Algebra ◽  
Symmetry Algebra ◽  
Conformal Anomaly ◽  
Axially Symmetric ◽  
Dirac Monopole ◽  
Symmetric Potential ◽  
Abelian Algebra ◽  
Enveloping Algebra

A model of an electron and a Dirac monopole interacting in an axially symmetric non-Hermitian but [Formula: see text]-symmetric potential is discussed in detail. The intriguing localization of the wave-packet is observed as a result of the anomalous breaking of the scale symmetry. The symmetry algebra for the system, which is the conformal algebra SO(2, 1), is discussed as a subalgebra of the enveloping algebra of an algebra, composed of the Virasoro algebra, {Ln, n ∈ ℕ} and an Abelian algebra, {Pn, n ∈ ℕ}.

scholarly journals Conformal anomaly for amplitudes in $\mathcal {N}=6$ superconformal Chern–Simons theory

2012 ◽  
Vol 45 (47) ◽  
pp. 475402 ◽  
Author(s):  
Till Bargheer ◽  
Niklas Beisert ◽  
Florian Loebbert ◽  
Tristan McLoughlin
Keyword(s):  
Simons Theory ◽  
Conformal Anomaly ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals SELF-DUAL YANG–MILLS: SYMMETRIES AND MODULI SPACE

1999 ◽  
Vol 11 (09) ◽  
pp. 1091-1149 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Dimensional Space ◽  
Solution Space ◽  
Virasoro Algebra ◽  
Simons Theory ◽  
Affine Lie Algebras ◽  
Field Equations ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Conformal Field ◽  
Chern Simons

Geometry of the solution space of the self-dual Yang–Mills (SDYM) equations in Euclidean four-dimensional space is studied. Combining the twistor and group-theoretic approaches, we describe the full infinite-dimensional symmetry group of the SDYM equations and its action on the space of local solutions to the field equations. It is argued that owing to the relation to a holomorphic analogue of the Chern–Simons theory, the SDYM theory may be as solvable as 2D rational conformal field theories, and successful nonperturbative quantization may be developed. An algebra acting on the space of self-dual conformal structures on a 4-space (an analogue of the Virasoro algebra) and an algebra acting on the space of self-dual connections (an analogue of affine Lie algebras) are described. Relations to problems of topological and N=2 strings are briefly discussed.

scholarly journals Chiral massive news: null boundary symmetries in topologically massive gravity

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
H. Adami ◽  
M.M. Sheikh-Jabbari ◽  
V. Taghiloo ◽  
H. Yavartanoo ◽  
C. Zwikel
Keyword(s):  
Central Charge ◽  
Three Dimensional ◽  
Virasoro Algebra ◽  
Symmetry Algebra ◽  
Massive Gravity ◽  
Surface Charges ◽  
Null Surface ◽  
Independent Functions ◽  
Chern Simons ◽  
Topologically Massive Gravity

Abstract We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG). We construct the solution phase space which involves four independent functions over the two dimensional null boundary. One of these functions corresponds to the massive chiral propagating graviton mode of TMG. The other three correspond to three surface charges of the theory, two of which can always be made integrable, while the last one can become integrable only in the absence of the chiral massive graviton flux through the null boundary. As the null boundary symmetry algebra we obtain Heisenberg ⊕ Virasoro algebra with a central charge proportional to the gravitational Chern-Simons term of TMG. We also discuss that the flux of the chiral massive gravitons appears as the (Bondi) news through the null surface.

scholarly journals Hilbert schemes, Verma modules and spectral functions of hyperbolic geometry with application to quantum invariants

2019 ◽  
Vol 34 (11) ◽  
pp. 1930060
Author(s):  
A. A. Bytsenko ◽  
M. Chaichian ◽  
A. E. Gonçalves
Keyword(s):  
Virasoro Algebra ◽  
Simons Theory ◽  
Verma Modules ◽  
Hilbert Schemes ◽  
Spectral Functions ◽  
Quantum Invariants ◽  
Flat Connections ◽  
Locally Symmetric Manifolds ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper we exploit Ruelle-type spectral functions and analyze the Verma module over Virasoro algebra, boson–fermion correspondence, the analytic torsion, the Chern–Simons and [Formula: see text] invariants, as well as the generating function associated to dimensions of the Hochschild homology of the crossed product [Formula: see text] ([Formula: see text] is the [Formula: see text]-Weyl algebra). After analyzing the Chern–Simons and [Formula: see text] invariants of Dirac operators by using irreducible [Formula: see text]-flat connections on locally symmetric manifolds of nonpositive section curvature, we describe the exponential action for the Chern–Simons theory.

Conformal Symmetry in Statistical Mechanics

2019 ◽  
pp. 188-240
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Statistical Mechanics ◽  
Central Charge ◽  
Conformal Symmetry ◽  
Finite Size ◽  
Virasoro Algebra ◽  
Momentum Tensor ◽  
Critical Parameters ◽  
Operator Product ◽  
Conformal Anomaly ◽  
Conformal Transformations

The core of the exposition of the theory of conformal symmetry in statistical mechanics are the concepts of correlation functions of order parameter fields, whose behaviour under conformal transformations are the defining characteristic of conformal field theories. Chapter 7 discusses the transformation properties of the energy-momentum tensor, the conformal Ward identities, and the operator product expansion lead to the loop or Witt algebra with central extension, the Virasoro algebra, allowing the characterization of the possible universality classes, in particular through the conformal anomaly or central charge. It discusses how the finite-size corrections to thermodynamic quantities, obtained from conformal transformations to finite geometries, can be used to determine critical parameters, especially the central charge.

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
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