SYMMETRY IN TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (13) ◽  
pp. 2331-2346 ◽  
Author(s):  
KAI-WEN XU ◽  
CHUAN-JIE ZHU
Keyword(s):  
Light Cone ◽  
Integration Method ◽  
Symmetry Algebra ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Simple Interpretation ◽  
Brst Charge ◽  
Dimensional Gravity ◽  
Covariant Gauge ◽  
Liouville Action

We study the symmetry of two-dimensional gravity by choosing a generic gauge. A local action is derived which reduces to either the Liouville action or the Polyakov one by reducing to the conformal or light-cone gauge respectively. The theory is also solved classically. We show that an SL (2, R) covariant gauge can be chosen so that the two-dimensional gravity has a manifest Virasoro and the sl (2, R)-current symmetry discovered by Polyakov. The symmetry algebra of the light-cone gauge is shown to be isomorphic to the Beltrami algebra. By using the contour integration method we construct the BRST charge QB corresponding to this algebra following the Fradkin-Vilkovisky procedure and prove that the nilpotence of QB requires c=28 and α0=1. We give a simple interpretation of these conditions.

TOPOLOGICAL CONFORMAL ALGEBRA IN POLYAKOV’S LIGHT-CONE GAUGE GRAVITY

1992 ◽  
Vol 07 (35) ◽  
pp. 3291-3302 ◽  
Author(s):  
KIYONORI YAMADA
Keyword(s):  
Light Cone ◽  
Matter Field ◽  
Conformal Algebra ◽  
Two Dimensional ◽  
Topological Algebras ◽  
Light Cone Gauge ◽  
Brst Cohomology ◽  
Dimensional Gravity ◽  
Conformal Gauge ◽  
Gauge Gravity

We show that the two-dimensional gravity coupled to c=−2 matter field in Polyakov’s light-cone gauge has a twisted N=2 superconformal algebra. We also show that the BRST cohomology in the light-cone gauge actually coincides with that in the conformal gauge. Based on this observation the relations between the topological algebras are discussed.

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.

SEMICLASSICAL TWO-DIMENSIONAL GRAVITY IN LIGHT-CONE GAUGE

1989 ◽  
Vol 04 (05) ◽  
pp. 419-425 ◽  
Author(s):  
R. FLOREANINI
Keyword(s):  
Light Cone ◽  
Einstein Equations ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
Conformal Gauge

Semiclassical Einstein equations for two-dimensional gravity are investigated in lightcone gauge and their group of invariance is discussed. One finds differences with respect to the corresponding results in conformal gauge.

ON THE BRST APPROACH TO TWO-DIMENSIONAL GRAVITY IN THE LIGHT-CONE GAUGE

1991 ◽  
Vol 06 (26) ◽  
pp. 4639-4654 ◽  
Author(s):  
YOSHIAKI TANII
Keyword(s):  
Gravitational Field ◽  
Brst Symmetry ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Light Cone Gauge ◽  
Conformal Field ◽  
Brst Charge ◽  
Dimensional Gravity ◽  
The Right

The BRST approach to two-dimensional gravity coupled to conformal field theories is discussed. The ordinary BRST symmetry acts only on the left-moving sector of the theory. It is found that there exists a BRST-like symmetry also in the right-moving sector. The conserved charge of this new symmetry is found to be nilpotent. This symmetry is a result of a redundancy of the parametrization of the gravitational field in terms of a scalar field. We propose that the physical states of the theory should belong to the cohomology of this BRST-like charge to eliminate the redundancy. It is also discussed how to derive the BRST charge from the action and the transformation laws of fields.

ON THE BRST APPROACH TO TWO-DIMENSIONAL GAUGE THEORIES IN THE LIGHT-CONE GAUGE

1990 ◽  
Vol 05 (12) ◽  
pp. 927-933 ◽  
Author(s):  
YOSHIAKI TANII
Keyword(s):  
Scalar Field ◽  
Gauge Field ◽  
Physical Meaning ◽  
Light Cone ◽  
Gauge Theories ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Brst Charge

The physical meaning of the second BRST-like charge, which exists in addition to the ordinary BRST charge in two-dimensional gauge theories in the light-cone gauge, is clarified. It results from the redundancy of the parametrization of the gauge field in terms of a group-valued scalar field and has a similar structure to the ordinary one.

scholarly journals EXACT SOLUTIONS TO THE TWO-DIMENSIONAL BF AND YANG–MILLS THEORIES IN THE LIGHT-CONE GAUGE

2002 ◽  
Vol 17 (11) ◽  
pp. 1491-1502 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Quantum Gravity ◽  
Light Cone ◽  
Lagrangian Density ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Bf Theory ◽  
Conformal Gauge

It is shown that the BRS (= Becchi–Rouet–Stora)-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the [Formula: see text] term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang–Mills theory is also obtained.

scholarly journals A NOTE ON 2D CHIRAL GRAVITY AND CHIRAL BOSONS

1992 ◽  
Vol 07 (40) ◽  
pp. 3777-3782 ◽  
Author(s):  
FIORENZO BASTIANELLI
Keyword(s):  
Effective Action ◽  
Light Cone ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Conformal Gauge ◽  
Chiral Bosons

Quantization of two-dimensional chiral matter coupled to gravity induces an effective action for the zweibein field which is both Weyl and Lorentz anomalous. Recently, the quantization of this induced action has been analyzed in the light-cone gauge as well as in the conformal gauge. An apparent mismatch between the results obtained in the two gauges is analyzed and resolved by properly treating the Lorentz field as a chiral boson.

scholarly journals QUANTUM DILATON GRAVITY IN THE LIGHT-CONE GAUGE

1993 ◽  
Vol 08 (08) ◽  
pp. 697-710 ◽  
Author(s):  
X. SHEN
Keyword(s):  
Black Hole ◽  
Light Cone ◽  
Black Hole Physics ◽  
Two Dimensional ◽  
Dilaton Gravity ◽  
Light Cone Gauge ◽  
Conformal Gauge ◽  
Matter Fields ◽  
Black Hole Solutions ◽  
New Framework

Recently, models of two-dimensional dilaton gravity have been shown to admit classical black hole solutions that exhibit Hawking radiation at the semiclassical level. These classical and semiclassical analyzes have been performed in conformal gauge. We show in this paper that a similar analysis in the light-cone gauge leads to the same results. Moreover, quantization of matter fields in light-cone gauge can be naturally extended to include quantizing the metric field à la KPZ. We argue that this may provide a new framework to address many issues associated to black hole physics.

RENORMALIZATION OF TWO-DIMENSIONAL SUPERGRAVITY IN LIGHT-CONE GAUGE

1990 ◽  
Vol 05 (02) ◽  
pp. 125-131
Author(s):  
ANAIS SMAILAGIC
Keyword(s):  
Wave Function ◽  
Current Algebra ◽  
Light Cone ◽  
Central Charge ◽  
Two Dimensional ◽  
Perturbative Calculation ◽  
Light Cone Gauge ◽  
D Region

Perturbative calculation of two-dimensional (1, 0) supergravity due to gravitation fluctuations is performed. Renormalization of Kac-Moody central charge of SL(2, R) graded current algebra and wave function to one-loop is obtained. The result agrees perfectly with Polyakov’s formula in the large d region.

scholarly journals Exact symmetries and threshold states in two-dimensional models for QCD

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Ross Dempsey ◽  
Igor R. Klebanov ◽  
Silviu S. Pufu
Keyword(s):  
Light Cone ◽  
Bound States ◽  
Symmetry Algebra ◽  
Adjoint Representation ◽  
String Tension ◽  
Majorana Fermion ◽  
Extended Model ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Single Trace

Abstract Two-dimensional SU(N) gauge theory coupled to a Majorana fermion in the adjoint representation is a nice toy model for higher-dimensional gauge dynamics. It possesses a multitude of “gluinoball” bound states whose spectrum has been studied using numerical diagonalizations of the light-cone Hamiltonian. We extend this model by coupling it to Nf flavors of fundamental Dirac fermions (quarks). The extended model also contains meson-like bound states, both bosonic and fermionic, which in the large-N limit decouple from the gluinoballs. We study the large-N meson spectrum using the Discretized Light-Cone Quantization (DLCQ). When all the fermions are massless, we exhibit an exact $$ \mathfrak{osp} $$ osp (1|4) symmetry algebra that leads to an infinite number of degeneracies in the DLCQ approach. More generally, we show that many single-trace states in the theory are threshold bound states that are degenerate with multi-trace states. These exact degeneracies can be explained using the Kac-Moody algebra of the SU(N) current. We also present strong numerical evidence that additional threshold states appear in the continuum limit. Finally, we make the quarks massive while keeping the adjoint fermion massless. In this case too, we observe some exact degeneracies that show that the spectrum of mesons becomes continuous above a certain threshold. This demonstrates quantitatively that the fundamental string tension vanishes in the massless adjoint QCD2 without explicit four-fermion operators.

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