EFFECTIVE ACTION FOR QUANTUM GRAVITY IN TWO DIMENSIONS

1989 ◽  
Vol 04 (01) ◽  
pp. 71-81 ◽  
Author(s):  
K. YOSHIDA
Keyword(s):  
Effective Action ◽  
Central Charge ◽  
Two Dimensions ◽  
Energy Tensor ◽  
Moody Algebra ◽  
Generating Functional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Conformal Field ◽  
Stress Energy

The generating functional of the correlation functions of the stress energy tensor in conformal field theory is derived and shown to be equal to the effective action for 2-dimensional induced gravity in the light cone gauge recently given by Polyakov. Seeking the condition for consistent quantization for such an action, one arrives at a chiral SU (2) × SU (2) current algebra. The corresponding Kac-Moody algebra has the central charge given by k = (C − 26)/6.

EFFECTIVE ACTION FOR INDUCED GRAVITY ON A 2-DIMENSIONAL MANIFOLD

1990 ◽  
Vol 05 (23) ◽  
pp. 4559-4578 ◽  
Author(s):  
K. YOSHIDA
Keyword(s):  
Euclidean Plane ◽  
Energy Tensor ◽  
Dimensional Manifold ◽  
Fundamental Change ◽  
Stress Energy Tensor ◽  
Generating Functional ◽  
Induced Gravity ◽  
Conformal Field ◽  
First Case ◽  
Stress Energy

The generating functional of the correlation functions of the stress energy-tensor in conformal field theory is explicitly constructed first on the Euclidean plane and then on an arbitrary Riemann surface. For the first case, one finds “anti-holomorphic” SL(2C) symmetry as the counterpart of the SL(2C) current algebra of Polyakov’s quantized gravity in 2 dimensions. For a general real 2-dimensional manifold, one expects a fundamental change due to the breaking of SL(2C) symmetry and to loss of locality.

scholarly journals STRESS ENERGY TENSOR IN LCFT AND LOGARITHMIC SUGAWARA CONSTRUCTION

2003 ◽  
Vol 18 (25) ◽  
pp. 4771-4788 ◽  
Author(s):  
IAN I. KOGAN ◽  
ALEXANDER NICHOLS
Keyword(s):  
Central Charge ◽  
Energy Tensor ◽  
Conformal Field Theories ◽  
Stress Energy Tensor ◽  
Moody Algebra ◽  
Conformal Field ◽  
Stress Energy ◽  
Dimension One ◽  
Independent Parameters ◽  
Construction Works

We discuss the partners of the stress energy tensor and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c=-2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra. This is an expanded version of a talk presented by A. Nichols at the conference on Logarithmic Conformal Field Theory and its Applications in Tehran Iran, 2001.

HAAG DUALITY IN CONFORMAL QUANTUM FIELD THEORY

1990 ◽  
Vol 02 (01) ◽  
pp. 105-125 ◽  
Author(s):  
DETLEV BUCHHOLZ ◽  
HANNS SCHULZ-MIRBACH
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Central Charge ◽  
Algebraic Approach ◽  
Energy Tensor ◽  
Quantum Field ◽  
Haag Duality ◽  
Conformal Fields ◽  
Stress Energy

Haag duality is established in conformal quantum field theory for observable fields on the compactified light ray S1 and Minkowski space S1×S1, respectively. This result provides the foundation for an algebraic approach to the classification of conformal theories. Haag duality can fail, however, for the restriction of conformal fields to the underlying non-compact spaces ℝ, respectively ℝ×ℝ. A prominent example is the stress energy tensor with central charge c>1.

scholarly journals LIOUVILLE THEORY: WARD IDENTITIES FOR GENERATING FUNCTIONAL AND MODULAR GEOMETRY

1994 ◽  
Vol 09 (25) ◽  
pp. 2293-2299 ◽  
Author(s):  
LEON A. TAKHTAJAN
Keyword(s):  
Moduli Spaces ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Central Charge ◽  
Perturbation Expansion ◽  
Liouville Theory ◽  
Energy Tensor ◽  
Ward Identities ◽  
Generating Functional ◽  
Local Index

We continue the study of quantum Liouville theory through Polyakov’s functional integral,1,2 started in Ref. 3. We derive the perturbation expansion for Schwinger’s generating functional for connected multi-point correlation functions involving stress-energy tensor, give the “dynamical” proof of the Virasoro symmetry of the theory and compute the value of the central charge, confirming previous calculation in Ref. 3. We show that conformal Ward identities for these correlation functions contain such basic facts from Kähler geometry of moduli spaces of Riemann surfaces, as relation between accessory parameters for the Fuchsian uniformization, Liouville action and Eichler integrals, Kähler potential for the Weil-Petersson metric, and local index theorem. These results affirm the fundamental role that universal Ward identities for the generating functional play in Friedan-Shenker modular geometry.4

scholarly journals DUAL GENERALIZATIONS OF SINE–GORDON FIELD THEORY AND INTEGRABILITY SUBMANIFOLDS IN PARAMETER SPACE

2000 ◽  
Vol 15 (21) ◽  
pp. 3315-3340
Author(s):  
P. BASEILHAC ◽  
D. REYNAUD
Keyword(s):  
Field Theory ◽  
Parameter Space ◽  
Complex Space ◽  
Central Charge ◽  
Two Dimensions ◽  
Field Theories ◽  
Complex Numbers ◽  
Quantum Field Theories ◽  
Conformal Field ◽  
Extended Complex

The dual relationship between two n-1 parameter families of quantum field theories based on extended complex numbers is investigated in two dimensions. The nonlocal conserved charges approach is used. The lowest rank affine Toda field theories are generated and identified as integrability submanifolds in parameter space. A truncation of the model leads to a conformal field theory in extended complex space. Depending on the projection over the usual complex space chosen, a parametrized central charge is calculated.

2D BLACK HOLES AND DIMENSIONAL REDUCTION

2002 ◽  
Vol 17 (20) ◽  
pp. 2745-2745
Author(s):  
R. BALBINOT ◽  
A. FABBRI
Keyword(s):  
Black Holes ◽  
Effective Action ◽  
Canonical Quantization ◽  
Scalar Fields ◽  
Mathematical Treatment ◽  
Energy Tensor ◽  
Asymptotic Results ◽  
Stress Energy ◽  
Point Splitting ◽  
Quantum Stress Tensor

The use of lower-dimensional models is exploited in many areas of physics as a way to simplify the mathematical treatment of very complicated phenomena while, at the same time, retaining the main physical ingredients. For the case of black holes, the Hawking evaporation process1 can be understood using a simple model where the gravity action is coupled to quantized matter in the form of free two-dimensional minimal scalar fields. In particular, the effective action one derives by straightforward integration of the trace anomaly2 gives a stress energy tensor which in the Schwarzschild spacetime perfectly agrees with the results one gets by standard canonical quantization. Trying to improve the model, i.e. by employing a spherically reduced 4d minimal scalar field3, one faces a number of difficulties. Unphysical results obtained for the evaporation of black holes (such as antievaporation3,4) using the anomaly induced effective action led us to perform a rigorous calculation of the quantum stress tensor in Schwarzschild by using the point-splitting regularization technique5: exact asymptotic results close to the horizon and at infinity have been derived in the three quantum states of interest (namely Boulware, Hartle-Hawking and Unruh) and two analytic approximations proposed , one valid for large r (based on the WKB) and the other being physically meaningful in the region close to the horizon. Finally, based on these results a "phenomenological" modification of the (unsatisfactory) anomaly induced effective action has been carried out6.

scholarly journals Consistent Two-Dimensional Chiral Gravity

1997 ◽  
Vol 12 (21) ◽  
pp. 3695-3722
Author(s):  
A. Smailagic ◽  
E. Spallucci
Keyword(s):  
Symmetry Group ◽  
Critical Exponents ◽  
Light Cone ◽  
Central Charge ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Residual Symmetry ◽  
Vacuum States ◽  
Forbidden Region

We study chiral induced gravity in the light-cone gauge and show that the theory is consistent for a particular choice of chiralities. The corresponding Kac–Moody central charge has no forbidden region of complex values. Generalized analysis of the critical exponents is given and their relation to the SL (2,R) vacuum states is elucidated. All the parameters containing information about the theory can be traced back to the characteristics of the residual symmetry group in the light-cone gauge.

scholarly journals Implications of a frame dependent gravitational effective action for perturbations on the Robertson–Walker metric

2017 ◽  
Vol 26 (14) ◽  
pp. 1750159 ◽  
Author(s):  
Stephen L. Adler
Keyword(s):  
Effective Action ◽  
Scalar Perturbation ◽  
Energy Tensor ◽  
Scaling Invariance ◽  
Gauge Transformations ◽  
Stress Energy ◽  
Walker Metric ◽  
Three Space ◽  
Coordinate Invariance ◽  
Metric Perturbation

In earlier work we showed that a frame dependent effective action motivated by the postulates of three-space general coordinate invariance and Weyl scaling invariance exactly mimics a cosmological constant in Robertson–Walker (RW) spacetimes. Here we study the implications of this effective action for small fluctuations around a spatially flat RW background geometry. The equations for the conserving extension of the modified stress-energy tensor can be integrated in closed form, and involve only the metric perturbation [Formula: see text]. Hence the equations for tensor and vector perturbations are unmodified, but there are Hubble scale additions to the scalar perturbation equations, which nonetheless admit no propagating wave solutions. Consequently, there are no modifications to standard gravitational wave propagation theory, but there may be observable implications for cosmology. We give a self-contained discussion, including an analysis of the restricted class of gauge transformations that act when a frame dependent effective action is present.

scholarly journals QUANTUM ENERGY INEQUALITIES IN TWO-DIMENSIONAL CONFORMAL FIELD THEORY

2005 ◽  
Vol 17 (05) ◽  
pp. 577-612 ◽  
Author(s):  
CHRISTOPHER J. FEWSTER ◽  
STEFAN HOLLANDS
Keyword(s):  
Field Theories ◽  
Positive Energy ◽  
Energy Tensor ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Stress Energy Tensor ◽  
Quantum Energy ◽  
Conformal Field ◽  
Quantum Energy Inequalities ◽  
Stress Energy

Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of interacting quantum fields, namely the unitary, positive energy conformal field theories (with stress-energy tensor) on two-dimensional Minkowski space. The QEI bound depends on the weight used to average the stress-energy tensor and the central charge(s) of the theory, but not on the quantum state. We give bounds for various situations: averaging along timelike, null and spacelike curves, as well as over a space-time volume. In addition, we consider boundary conformal field theories and more general "moving mirror" models. Our results hold for all theories obeying a minimal set of axioms which — as we show — are satisfied by all models built from unitary highest-weight representations of the Virasoro algebra. In particular, this includes all (unitary, positive energy) minimal models and rational conformal field theories. Our discussion of this issue collects together (and, in places, corrects) various results from the literature which do not appear to have been assembled in this form elsewhere.

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