scholarly journals Liouville Action for Harmonic Diffeomorphisms

2021 ◽  
Author(s):  
Jinsung Park ◽  
Keyword(s):  
Liouville Action

scholarly journals BMS field theories and Weyl anomaly

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Arjun Bagchi ◽  
Sudipta Dutta ◽  
Kedar S. Kolekar ◽  
Punit Sharma
Keyword(s):  
Three Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Two Dimensional ◽  
Speed Of Light ◽  
Asymptotically Flat ◽  
Weyl Invariance ◽  
Flat Spacetimes ◽  
Liouville Action ◽  
Null Surfaces

Abstract Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.

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.

2-D QUANTUM GRAVITY AND LIOUVILLE THEORY

1990 ◽  
Vol 05 (18) ◽  
pp. 1411-1421 ◽  
Author(s):  
ERIC D’HOKER ◽  
P.S. KURZEPA
Keyword(s):  
Invariant Measure ◽  
Quantum Gravity ◽  
First Principles ◽  
Liouville Theory ◽  
Translation Invariant ◽  
Anomalous Dimensions ◽  
Conformal Gauge ◽  
Liouville Action

We quantize the Liouville theory, or 2-D quantum gravity, and quantum supergravity in the conformal gauge. We explicitly calculate the Jacobian accompanying the change from the Weyl invariant measure to the translation invariant one. We show that it is of the same form as the original Liouville action, thus establishing a conjecture of David and Distler and Kawai. This calculation yields dressed gravitational central charges and anomalous dimensions from first principles.

scholarly journals Super-Liouville action for Regge surfaces

1999 ◽  
Vol 543 (1-2) ◽  
pp. 518-532
Author(s):  
Pietro Menotti ◽  
Giuseppe Policastro
Keyword(s):  
Liouville Action

scholarly journals TRACE ANOMALIES AND COCYCLES OF WEYL AND DIFFEOMORPHISMS GROUPS

1996 ◽  
Vol 11 (05) ◽  
pp. 409-421 ◽  
Author(s):  
D.R. KARAKHANYAN ◽  
R.P. MANVELYAN ◽  
R.L. MKRTCHYAN
Keyword(s):  
Partition Function ◽  
Weyl Group ◽  
Simple Form ◽  
General Structure ◽  
Consistency Condition ◽  
General Rule ◽  
Two Dimensional ◽  
Conformal Invariant ◽  
Trace Anomaly ◽  
Liouville Action

The general structure of trace anomaly, suggested recently by Deser and Schwimmer is argued to be the consequence of the Wess-Zumino consistency condition. The response of partition function on a finite Weyl transformation, which is connected with the cocycles of the Weyl group in d=2k dimensions is considered, and explicit answers for d=4, 6 are obtained. In particular, it is shown that addition of the special combination of the local counterterms leads to the simple form of that cocycle, quadratic over Weyl field σ, i.e. the form, similar to the two-dimensional Liouville action. This form also establishes the connection of the cocycles with conformal-invariant operators of order d and zero weight. We also give the general rule for transformation of that cocycles into the cocycles of diffeomorphisms group.

scholarly journals QUANTUM RIEMANN SURFACES, 2-D GRAVITY AND THE GEOMETRICAL ORIGIN OF MINIMAL MODELS

1994 ◽  
Vol 09 (31) ◽  
pp. 2871-2878 ◽  
Author(s):  
MARCO MATONE
Keyword(s):  
Quantum Gravity ◽  
Classical Limit ◽  
Riemann Surfaces ◽  
Ward Identity ◽  
Riemann Sphere ◽  
Projective Connection ◽  
Minimal Models ◽  
Standard Representation ◽  
Basic Object ◽  
Liouville Action

Based on a recent paper by Takhtajan, we propose a formulation of 2-D quantum gravity whose basic object is the Liouville action on the Riemann sphere Σ0, m+n with both parabolic and elliptic points. The identification of the classical limit of the conformal Ward identity with the Fuchsian projective connection on Σ0, m+n implies a relation between conformal weights and ramification indices. This formulation works for arbitrary d and admits a standard representation only for d ≤ 1. Furthermore, it turns out that the integerness of the ramification number constrains d = 1 − 24/(n2 − 1) that for n = 2m + 1 coincides with the unitary minimal series of CFT.

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