scholarly journals WESS–ZUMINO–WITTEN MODEL FOR GALILEAN CONFORMAL ALGEBRA

2013 ◽  
Vol 28 (38) ◽  
pp. 1350176
Author(s):  
SOMDEB CHAKRABORTY ◽  
PARIJAT DEY
Keyword(s):  
Conformal Invariance ◽  
Central Charge ◽  
Conformal Algebra ◽  
Model Based ◽  
Group Manifold ◽  
Type Construction ◽  
Spacetime Metric ◽  
Six Dimensions ◽  
Physical Spacetime

In this note, we construct a Wess–Zumino–Witten model based on the Galilean conformal algebra in two-spacetime dimensions, which is a nonrelativistic analogue of the relativistic conformal algebra. We obtain exact background corresponding to σ-models in six dimensions (the dimension of the group manifold) and a central charge c = 6. We carry out a Sugawara type construction to verify the conformal invariance of the model. Further, we discuss the feasibility of the background obtained as a physical spacetime metric.

scholarly journals THE ROLE OF QUANTIZED 2-DIM. GRAVITY IN STRING THEORY

1990 ◽  
Vol 05 (11) ◽  
pp. 863-876 ◽  
Author(s):  
AVINASH DHAR ◽  
T. JAYARAMAN ◽  
K. S. NARAIN ◽  
SPENTA R. WADIA
Keyword(s):  
String Theory ◽  
Time Dependence ◽  
Current Algebra ◽  
Conformal Invariance ◽  
Arbitrary Number ◽  
Central Charge ◽  
Vertex Operators ◽  
Extra Time ◽  
Reparametrization Invariance

We present a formulation of string theory in which the 2-dim. metric is exactly quantized in the framework of SL (2, R) current algebra. In this way we replace the conformal invariance prescription by the principle of reparametrization invariance. The theory is formulated in arbitrary number of dimensions since the usual restriction of fixed matter central charge is not present. As a concrete illustration of our approach, we show that in 25 Euclidean dimensions the usual amplitudes of the 26-dimensional bosonic string theory arise. The extra time-like dimension emerges as a mode of the 2-dim. metric and the gravitational dressing of vertex operators gives rise to their time dependence.

scholarly journals Conformal invariance, the central charge, and universal finite-size amplitudes at criticality

1986 ◽  
Vol 56 (7) ◽  
pp. 742-745 ◽  
Author(s):  
H. W. J. Blöte ◽  
John L. Cardy ◽  
M. P. Nightingale
Keyword(s):  
Conformal Invariance ◽  
Central Charge ◽  
Finite Size

scholarly journals Cosmological New Massive Gravity and Galilean Conformal Algebra in 2 Dimensions

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
M. R. Setare ◽  
V. Kamali
Keyword(s):  
Black Hole ◽  
Black Hole Solution ◽  
Central Charge ◽  
Massive Gravity ◽  
Nonrelativistic Limit ◽  
Conformal Algebra ◽  
Btz Black Hole ◽  
Entropy Formula ◽  
Scaling Dimension

We consider the realization of 2-dimensional Galilean conformal algebra (GCA2) on the boundary of cosmological new massive gravity. At first, we consider the contracted BTZ black hole solution. We obtain entropy formula for the GCA2in terms of contracted scaling dimension Δ and central chargeC1. This entropy formula exactly matches with the nonrelativistic limit of Bekenstein-Hawking entropy of BTZ black hole. Then, we extend our study to the contracted warped AdS3black hole solution of CNMG. We obtain the entropy of dual GCA2in terms of central charges and finite temperatures,T1,T2. Again, this expression coincides with the nonrelativistic limit of Bekenstein-Hawking entropy formula of warped AdS3black hole.

c=3d CONFORMAL ALGEBRA WITH EXTENDED SUPERSYMMETRY

1990 ◽  
Vol 05 (08) ◽  
pp. 561-580 ◽  
Author(s):  
SATORU ODAKE
Keyword(s):  
Extended Supersymmetry ◽  
Representation Theory ◽  
Central Charge ◽  
Superconformal Algebra ◽  
Conformal Algebra ◽  
Spectral Flow ◽  
Modular Transformation ◽  
Non Linear ◽  
Character Formulas

We define a superconformal algebra with the central charge c=3d, which is the symmetry of the non-linear σ model on a complex d dimensional Calabi-Yau manifold. The c=3d algebra is an extended superconformal algebra obtained by adding the spectral flow generators to the N=2 superconformal algebra. We study the representation theory and show that its representations are invariant under the integer-shift spectral flow. We present the character formulas and their modular transformation properties. We also discuss the relation to the N=4 superconformal algebra.

THE ALGEBRA OF THE ENERGY-MOMENTUM TENSOR AND THE NOETHER CURRENTS IN OFF-CRITICAL WZNW MODELS

1993 ◽  
Vol 08 (09) ◽  
pp. 803-809
Author(s):  
M. FORGER ◽  
J. LAARTZ
Keyword(s):  
Current Algebra ◽  
Conformal Invariance ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Virasoro Algebra ◽  
Momentum Tensor ◽  
Global Symmetry ◽  
Composite Field ◽  
Derivatives Of ◽  
Algebra Part

The recently derived current algebra of classical principal chiral models with a Wess-Zumino term is extended to include the energy-momentum tensor. It is found that the energy-momentum tensor θµν, the Noether currents [Formula: see text] and [Formula: see text] associated with the global symmetry of the theory and the composite field t appearing as the coefficient of the Schwinger term in the current algebra, together with the derivatives of [Formula: see text] and t, generate a closed algebra. The subalgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central charge c=0, reflecting the classical conformal invariance of the theory, but the current algebra part and the semidirect product structure are a deformation of the usual affine Kac-Moody/Sugawara construction.

SEARCH FOR EXTENDED CONFORMAL ALGEBRA

1990 ◽  
Vol 05 (19) ◽  
pp. 1511-1519
Author(s):  
DARWIN CHANG ◽  
ALOK KUMAR ◽  
JIN WANG
Keyword(s):  
Central Charge ◽  
Gaussian Model ◽  
Fusion Rule ◽  
Conformal Algebra ◽  
Chiral Algebra ◽  
Conformal Generator

We search for the extended conformal algebra with two spin-s (s: integer) and one spin-1 generators. This search is inspired by the existence of chiral algebra in the Gaussian model for rational radius. For odd s, the conformal properties of the three-point functions imply that a general fusion rule can be reduced to those of the Gaussian model. For arbitrary even s, these conditions are weaker. In particular, for s=2 we show that the chiral algebra of the Gaussian model is the unique extended conformal algebra with the value of the central charge fixed to be c=1. It is also shown that the conformal generator is necessarily a bilinear of the spin-1 generator just as the Gaussian model. We conjecture that this remains true for arbitrary value of s.

scholarly journals QUANTUM NON-ABELIAN TODA FIELD THEORIES

1994 ◽  
Vol 09 (20) ◽  
pp. 3631-3656 ◽  
Author(s):  
I. JACK ◽  
D.R.T. JONES ◽  
J. PANVEL
Keyword(s):  
Field Theory ◽  
Conformal Invariance ◽  
Central Charge ◽  
Field Theories ◽  
Invariant Form ◽  
Conformally Invariant ◽  
A Value ◽  
Toda Field Theory

We derive an explicit, exactly conformally invariant form for the action for the non-Abelian Toda field theory. We demonstrate that the conformal invariance conditions, expressed in terms of the β functions of the theory, are satisfied to all orders, and we use our results to obtain a value for the central charge agreeing with previous calculations.

scholarly journals TYPE II SUPERSTRINGS ON TWISTED GROUP MANIFOLDS AND THEIR HETEROTIC COUNTERPARTS

1990 ◽  
Vol 05 (05) ◽  
pp. 989-1024 ◽  
Author(s):  
SERGIO FERRARA ◽  
PIETRO FRE’
Keyword(s):  
Compact Manifold ◽  
Space Time ◽  
Spin Connection ◽  
Type Ii ◽  
Model Based ◽  
Twisted Group ◽  
Six Dimensions ◽  
Chiral Bosons ◽  
Gauge Connection ◽  
Complete Analogy

We construct Type II superstrings in four space-time dimensions compactified on a twisted Wess-Zumino-Witten model based on the group SU(2)3. It is shown that within this framework, it is possible to obtain models with N=6, 5 and 3 space-time supersymmetries, in addition to the usual models with N=8, 4 and 2. The map of these models into the corresponding heterotic superstrings with N=4, 2 and 1 space-time supersymmetries is also derived: in complete analogy to the compactifications on six-dimensional manifolds also in this case this map from Type II to heterotic superstrings corresponds geometrically to the embedding of the 9-dimensional compact manifold spin-connection into the gauge connection. The superstring compactifications we discussed are equivalent to asymmetric orbifold constructions in six-dimensions with no necessity, however, of introducing chiral bosons.

Representation, abstraction, and simple-minded sophisticates

2020 ◽  
Vol 43 ◽  
Author(s):  
Peter Dayan
Keyword(s):  
Decision Theory ◽  
Predictive Coding ◽  
Bayesian Decision Theory ◽  
Bayesian Decision ◽  
Model Based ◽  
Model Free

Abstract Bayesian decision theory provides a simple formal elucidation of some of the ways that representation and representational abstraction are involved with, and exploit, both prediction and its rather distant cousin, predictive coding. Both model-free and model-based methods are involved.

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