scholarly journals A GENERAL SOLUTION OF THE BV-MASTER EQUATION AND BRST FIELD THEORIES

1993 ◽  
Vol 08 (22) ◽  
pp. 2087-2097 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
Master Equation ◽  
General Procedure ◽  
Field Theories ◽  
Simons Theory ◽  
Proper Solution ◽  
First Order ◽  
Brst Charge ◽  
Chern Simons ◽  
Chern Simons Theory

For a class of first order gauge theories it was shown that the proper solution of the BV-master equation can be obtained straightforwardly. Here we present the general condition which the gauge generators should satisfy to conclude that this construction is relevant. The general procedure is illustrated by its application to the Chern-Simons theory in any odd dimension. Moreover, it is shown that this formalism is also applicable to BRST field theories when one replaces the role of the exterior derivative with the BRST charge of first quantization.

scholarly journals Asymptotic States in Nonlocal Field Theories

1997 ◽  
Vol 12 (07) ◽  
pp. 493-500 ◽  
Author(s):  
D. G. Barci ◽  
L. E. Oxman
Keyword(s):  
Minkowski Space ◽  
Field Theories ◽  
Simons Theory ◽  
Asymptotic State ◽  
Topological Sector ◽  
Nonlocal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Asymptotic states in field theories containing nonlocal kinetic terms are analyzed using the canonical method, naturally defined in Minkowski space. We apply our results to study the asymptotic states of a nonlocal Maxwell–Chern–Simons theory coming from bosonization in (2+1) dimensions. We show that in this case the only asymptotic state of the theory, in the trivial (non-topological) sector, is the vacuum.

scholarly journals Quantum double and κ-Poincaré symmetries in (2+1)-gravity and Chern–Simons theoryThis paper was presented at the Theory CANADA 4 conference, held at Centre de recherches mathématiques, Montréal, Québec, Canada on 4–7 June 2008.

2009 ◽  
Vol 87 (3) ◽  
pp. 245-250
Author(s):  
C. Meusburger
Keyword(s):  
Hopf Algebra ◽  
Simons Theory ◽  
De Sitter ◽  
Quantum Double ◽  
Isometry Groups ◽  
Chern Simons ◽  
Chern Simons Theory

We clarify the role of Drinfeld doubles and κ-Poincaré symmetries in quantized (2+1)-gravity and Chern–Simons theory. We discuss the conditions under which a given Hopf algebra symmetry is compatible with a Chern–Simons theory and determine this compatibility explicitly for the Drinfeld doubles and κ-Poincaré symmetries associated with the isometry groups of (2+1)-gravity. In particular, we show that κ-Poincaré symmetries with a timelike deformation are not directly associated with (2+1)-gravity. The association between these κ-Poincaré symmetries and Chern–Simons theory is possible only in the de Sitter case and the relevant Chern–Simons theory is physically inequivalent to (2+1)-gravity.

scholarly journals NONCOMMUTATIVE BTZ BLACK HOLE IN DIFFERENT COORDINATES

2011 ◽  
Vol 01 ◽  
pp. 285-290
Author(s):  
CHANG-YOUNG EE
Keyword(s):  
Black Hole ◽  
Simons Theory ◽  
Coordinate Systems ◽  
Btz Black Hole ◽  
First Order ◽  
Rectangular Coordinates ◽  
Chern Simons ◽  
Black Hole Solutions ◽  
Chern Simons Theory

We consider noncommutative BTZ black hole solutions in two different coordinate systems, the polar and rectangular coordinates. The analysis is carried out by obtaining noncommutative solutions of U(1, 1) × U(1, 1) Chern-Simons theory on AdS3 in the two coordinate systems via the Seiberg-Witten map. This is based on the noncommutative extension of the equivalence between the classical BTZ solution and the solution of ordinary SU(1, 1) × SU(1, 1) Chern-Simons theory on AdS3. The obtained solutions in these noncommutative coordinate systems become different in the first order of the noncommutativity parameter θ.

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 4D Chern–Simons theory and affine Gaudin models

2021 ◽  
Vol 111 (1) ◽  
Author(s):  
Benoît Vicedo
Keyword(s):  
Gauge Theory ◽  
Integrable Field Theories ◽  
Field Theories ◽  
Simons Theory ◽  
Gaudin Models ◽  
Chern Simons ◽  
Classical Integrable ◽  
Integrable Field ◽  
Chern Simons Theory

AbstractWe relate two formalisms recently proposed for describing classical integrable field theories. The first (Costello and Yamazaki in Gauge Theory and Integrability, III, 2019) is based on the action of four-dimensional Chern–Simons theory introduced and studied by Costello, Witten and Yamazaki. The second (Costello and Yamazaki, in Gauge Theory and Integrability, III, 2017) makes use of classical generalised Gaudin models associated with untwisted affine Kac–Moody algebras.

ON THE ROLE OF WIGNER'S LITTLE GROUP AS A GENERATOR OF GAUGE TRANSFORMATION IN MAXWELL–CHERN–SIMONS THEORY

2001 ◽  
Vol 16 (13) ◽  
pp. 853-862 ◽  
Author(s):  
RABIN BANERJEE ◽  
BISWAJIT CHAKRABORTY ◽  
TOMY SCARIA
Keyword(s):  
Gauge Transformation ◽  
Simons Theory ◽  
Temporal Gauge ◽  
Gauge Fixing ◽  
Chern Simons ◽  
Chern Simons Theory

The role of Wigner's little group in 2 + 1 dimensions as a generator of gauge transformation in the topologically massive Maxwell–Chern–Simons (MCS) theory is discussed. The similarities and dissimilarities between the Maxwell and MCS theories in the context of gauge fixing (spatial transversality and temporal gauge) are also analyzed.

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.

scholarly journals EXTENDED BRS SYMMETRY IN TOPOLOGICAL FIELD THEORIES

2008 ◽  
Vol 23 (14) ◽  
pp. 993-998
Author(s):  
P. VALTANCOLI
Keyword(s):  
Topological Field Theories ◽  
Landau Gauge ◽  
Field Theories ◽  
Simons Theory ◽  
Gauge Fixing ◽  
Topological Field ◽  
New Type ◽  
Chern Simons ◽  
Brs Symmetry ◽  
Chern Simons Theory

A class of topological field theories like the BF model and Chern–Simons theory, when quantized in the Landau gauge, enjoys the property of invariance under a vector supersymmetry, which is responsible for their finiteness. We introduce a new type of gauge fixing which makes these theories invariant under an extended BRS symmetry, containing a new type of field, the ghost of diffeomorphisms. The presence of such an extension is naturally related to the vector supersymmetry discussed before.

scholarly journals 4-dimensional Chern-Simons theory and integrable field theories

2022 ◽  
Author(s):  
Sylvain Lacroix
Keyword(s):  
Integrable Field Theories ◽  
Sigma Models ◽  
Field Theories ◽  
Simons Theory ◽  
Chiral Model ◽  
Santiago De Compostela ◽  
Chern Simons ◽  
Classical Integrable ◽  
Integrable Field ◽  
Chern Simons Theory

Abstract These lecture notes concern the semi-holomorphic 4d Chern-Simons theory and its applications to classical integrable field theories in 2d and in particular integrable sigma-models. After introducing the main properties of the Chern-Simons theory in 3d, we will define its 4d analogue and explain how it is naturally related to the Lax formalism of integrable 2d theories. Moreover, we will explain how varying the boundary conditions imposed on this 4d theory allows to recover various occurences of integrable sigma-models through this construction, in particular illustrating this on two simple examples: the Principal Chiral Model and its Yang-Baxter deformation. These notes were written for the lectures delivered at the school “Integrability, Dualities and Deformations”, that ran from 23 to 27 August 2021 in Santiago de Compostela and virtually.

scholarly journals The Geometry of the Master Equation and Topological Quantum Field Theory

1997 ◽  
Vol 12 (07) ◽  
pp. 1405-1429 ◽  
Author(s):  
M. Alexandrov ◽  
A. Schwarz ◽  
O. Zaboronsky ◽  
M. Kontsevich
Keyword(s):  
Master Equation ◽  
Sigma Model ◽  
Target Space ◽  
Simons Theory ◽  
Quantum Field ◽  
Geometric Constructions ◽  
Topological Quantum ◽  
Chern Simons ◽  
Natural Way ◽  
Chern Simons Theory

In Batalin–Vilkovisky formalism, a classical mechanical system is specified by means of a solution to the classical master equation. Geometrically, such a solution can be considered as a QP-manifold, i.e. a supermanifold equipped with an odd vector field Q obeying {Q, Q} = 0 and with Q-invariant odd symplectic structure. We study geometry of QP-manifolds. In particular, we describe some construction of QP-manifolds and prove a classification theorem (under certain conditions). We apply these geometric constructions to obtain in a natural way the action functionals of two-dimensional topological sigma-models and to show that the Chern–Simons theory in BV-formalism arises as a sigma-model with target space [Formula: see text]. (Here [Formula: see text] stands for a Lie algebra and Π denotes parity inversion.)

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