Two-dimensional gravity as the gauge theory of the Clifford algebra for an even-dimensional generalized Chern-Simons action

1992 ◽  
Vol 45 (2) ◽  
pp. 605-617 ◽  
Author(s):  
Noboru Kawamoto ◽  
Yoshiyuki Watabiki
Keyword(s):  
Gauge Theory ◽  
Clifford Algebra ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Chern Simons

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals HIGHER GAUGE THEORY AND GRAVITY IN 2+1 DIMENSIONS

2007 ◽  
Vol 22 (28) ◽  
pp. 5155-5172 ◽  
Author(s):  
R. B. MANN ◽  
E. M. POPESCU
Keyword(s):  
Gauge Theory ◽  
Two Dimensional ◽  
Yang Mills ◽  
Higher Dimensional ◽  
Present Context ◽  
Dimensional Gravity ◽  
Wide Perspective ◽  
Higher Gauge Theory ◽  
Matter Fields ◽  
New Framework

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black-hole BTZ-like geometries, particle-like geometries as well as Robertson–Friedman–Walker cosmological-like expanding geometries — this opens a wide perspective for higher gauge theory to be tested and understood in a relevant gravitational context. Additionally, it offers the possibility of studying gravity in 2+1 dimensions coupled to matter in an entirely new framework.

AN INTEGRABLE MODEL WITH SOLITON SOLUTIONS WHICH HAVE APPLICATIONS TO TWO-DIMENSIONAL GRAVITY

2005 ◽  
Vol 20 (07) ◽  
pp. 1503-1514 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Integrable Model ◽  
Soliton Solutions ◽  
Integrable Equation ◽  
Two Dimensions ◽  
Spin Connection ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Chern Simons

The equations of motion for a theory described by a Chern–Simons type of action in two dimensions are obtained and investigated. The equation for the classical, continuous Heisenberg model is used as a form of gauge constraint to obtain a result which provides a completely integrable dynamics and which partially fixes the gauge degrees of freedom. Under a particular form of the spin connection, an integrable equation which can be analytically extended to a form of the nonlinear Schrödinger equation is obtained. Some explicit solutions are presented, and in particular a soliton solution is shown to lead to an integrable two-dimensional model of gravity.

THE LATTICE ABELIAN CHERN-SIMONS GAUGE THEORY

1991 ◽  
Vol 06 (22) ◽  
pp. 3919-3931 ◽  
Author(s):  
AL. R. KAVALOV ◽  
R.L. MKRTCHYAN
Keyword(s):  
Gauge Theory ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Close Correspondence ◽  
Dimensional Lattice ◽  
Lattice Version ◽  
Continuous Theory ◽  
Statistical Systems ◽  
Chern Simons

Some properties of the previously proposed lattice version of the Abelian Chern-Simons gauge theory are studied. The lattice analog of BF systems is constructed, and the properties of both theories are found to be in close correspondence with those of the continuous theory. The correspondence with two-dimensional lattice statistical systems is established and the lattice origin of the framing of Wilson loops is shown.

Gauge theory of two-dimensional gravity

1985 ◽  
Vol 160 (4-5) ◽  
pp. 259-262 ◽  
Author(s):  
Takeshi Fukuyama ◽  
Kiyoshi Kamimura
Keyword(s):  
Gauge Theory ◽  
Two Dimensional ◽  
Dimensional Gravity

scholarly journals Bosonization based on Clifford algebras and its gauge theoretic interpretation

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Bochniak ◽  
B. Ruba
Keyword(s):  
Gauge Theory ◽  
Clifford Algebra ◽  
Gauge Field ◽  
Degrees Of Freedom ◽  
Clifford Algebras ◽  
Gauge Fields ◽  
Field Solution ◽  
Chern Simons

Abstract We study the properties of a bosonization procedure based on Clifford algebra valued degrees of freedom, valid for spaces of any dimension. We present its interpretation in terms of fermions in presence of ℤ2 gauge fields satisfying a modified Gauss’ law, resembling Chern-Simons-like theories. Our bosonization prescription involves constraints, which are interpreted as a flatness condition for the gauge field. Solution of the constraints is presented for toroidal geometries of dimension two. Duality between our model and (d − 1)- form ℤ2 gauge theory is derived, which elucidates the relation between the approach taken here with another bosonization map proposed recently.

LINEAL GRAVITY WITH DYNAMICAL TORSION

1996 ◽  
Vol 11 (15) ◽  
pp. 1235-1245 ◽  
Author(s):  
S. MIGNEMI
Keyword(s):  
Black Hole ◽  
Gauge Theory ◽  
Hamiltonian Formulation ◽  
Two Dimensional ◽  
Static Black Hole ◽  
Nonlinear Generalization ◽  
Poincaré Algebra ◽  
Dimensional Gravity ◽  
Black Hole Solutions ◽  
Dirac Formalism

We investigate the string-inspired action for two-dimensional gravity with the addition of dynamical torsion and obtain the most general static black hole solutions. We also consider the Hamiltonian formulation of the model and discuss its symmetries, showing that it can be considered as a gauge theory of a nonlinear generalization of the two-dimensional Poincare algebra. Finally, we briefly discuss the quantization of the theory in the Dirac formalism.

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