ACTION PRINCIPLE, VIRASORO STRUCTURE AND ANALYTICITY IN NONPERTURBATIVE TWO-DIMENSIONAL GRAVITY

1992 ◽  
Vol 07 (17) ◽  
pp. 4015-4038 ◽  
Author(s):  
TAMIAKI YONEYA
Keyword(s):  
Dimensional Space ◽  
Conformal Symmetry ◽  
Scaling Limit ◽  
Closed String ◽  
Action Principle ◽  
String Equation ◽  
Two Dimensional ◽  
Polynomial Potential ◽  
Symmetry Properties ◽  
Dimensional Gravity

The consequences of symmetry properties of a previously proposed action principle which describes the theory space of two-dimensional gravity are investigated. The string equation corresponding to the double scaling limit of the one-matrix model with general polynomial potential is expressed as a bilinear equation for the τ function of the KP hierarchy. The Virasoro condition for the τ function is then shown to be a Ward-like identity derived from the string equation corresponding to a conformal symmetry of the action principle. The possibility of a Ginzburg-Landau type integral representation of the τ function as a version of noncritical closed string field theory in less-than-one-dimensional space-time is discussed. Finally, the role of analyticity with respect to the eigenvalue of the puncture operator in interpreting the action principle is emphasized.

scholarly journals BRST-FIXED POINTS AND TOPOLOGICAL CONFORMAL SYMMETRY

1992 ◽  
Vol 07 (24) ◽  
pp. 2215-2222 ◽  
Author(s):  
TOSHIO NAKATSU ◽  
YUJI SUGAWARA
Keyword(s):  
Field Theory ◽  
Fixed Points ◽  
Conformal Symmetry ◽  
Topological Field Theory ◽  
Two Dimensional ◽  
Brst Transformation ◽  
Dimensional Gravity ◽  
Matter System ◽  
Topological Field ◽  
Topological Matter

We study the twisted version of the supersymmetric G/T = SU (n)/ U (1)⊗(n−1) gauged Wess-Zumino-Witten model. By studying its fixed points under BRST transformation this model is shown to be reduced to a simple topological Field theory, that is, the topological matter system in the K. Li's theory of two-dimensional gravity for the case of n = 2, and its generalization for n ≥ 3.

scholarly journals Conformal Symmetry and Supersymmetry in Rindler Space

Universe ◽  
2020 ◽  
Vol 6 (9) ◽  
pp. 144
Author(s):  
Jan-Willem van Holten
Keyword(s):  
Dimensional Space ◽  
Conformal Symmetry ◽  
Space Time ◽  
Two Dimensional ◽  
Extended Space ◽  
Rindler Space ◽  
Dimensional Space Time ◽  
Critical Spectrum ◽  
Infinite Strings ◽  
Bogoliubov Transformations

This paper addresses the fate of extended space-time symmetries, in particular conformal symmetry and supersymmetry, in two-dimensional Rindler space-time appropriate to a uniformly accelerated non-inertial frame in flat 1+1-dimensional space-time. Generically, in addition to a conformal co-ordinate transformation, the transformation of fields from Minkowski to Rindler space is accompanied by local conformal and Lorentz transformations of the components, which also affect the Bogoliubov transformations between the associated Fock spaces. I construct these transformations for massless scalars and spinors, as well as for the ghost and super-ghost fields necessary in theories with local conformal and supersymmetries, as arising from coupling to two-dimensional (2-D) gravity or supergravity. Cancellation of the anomalies in Minkowski and in Rindler space requires theories with the well-known critical spectrum of particles that arise in string theory in the limit of infinite strings, and it is relevant for the equivalence of Minkowski and Rindler frame theories.

scholarly journals MATRIX MODELS OF TWO-DIMENSIONAL GRAVITY AND DISCRETE TODA THEORY

1996 ◽  
Vol 11 (22) ◽  
pp. 1797-1806 ◽  
Author(s):  
MASATO HISAKADO ◽  
MIKI WADATI
Keyword(s):  
Discrete Time ◽  
Matrix Model ◽  
Scaling Limit ◽  
Toda Chain ◽  
Partition Functions ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
The Matrix ◽  
Dimensional Gravity ◽  
Molecule Equation

Recursion relations for orthogonal polynomials, arising in the study of one-matrix model of two-dimensional gravity, are shown to be equivalent to the equations of the Toda-chain hierarchy supplemented by additional Virasoro constraints. This is the case without the double scaling limit. A discrete time variable to the matrix model is introduced. The discrete time dependent partition functions are given by τ functions which satisfy the discrete Toda molecule equation. Further the relations between the matrix model and the discrete time Toda theory are discussed.

METHOD OF SOLVING CONFORMAL MODELS IN D-DIMENSIONAL SPACE III SECONDARY FIELDS IN D>2 AND THE SOLUTION OF TWO-DIMENSIONAL MODELS

1998 ◽  
Vol 13 (28) ◽  
pp. 4837-4888
Author(s):  
E. S. FRADKIN ◽  
M. YA. PALCHIK
Keyword(s):  
Hilbert Space ◽  
Dimensional Space ◽  
Conformal Symmetry ◽  
Solvable Model ◽  
Virasoro Algebra ◽  
Green Functions ◽  
Two Dimensional ◽  
Ward Identities ◽  
Fundamental Field ◽  
Conformal Models

We proceed with the study (started in Refs. 1 and 2) of the Hilbert space of conformal field theory in D di mensions. We discuss an infinite family of secondary fields [Formula: see text] generated by the action of the components of energy–momentum tensor Tμν on the fundamental (primary) field. It is shown that the states of these fields form a specific sector of the Hilbert space H which is determined by the Ward identities and [Formula: see text]-dimensional conformal symmetry. We demonstrate that for D = 2 the subspace H coincides with the space of representation of the Virasoro algebra. Each exactly solvable model in the case of D ≥ 2 is defined by the requirement of vanishing of a certain state Qs(x)|0> ⊂ H analogous to the null vector of two-dimensional theory. The Green functions of the fields [Formula: see text] are calculated in terms of the Green functions of the fundamental field. It is shown that all the Green functions of the type [Formula: see text] satisfy the anomalous Ward identities. The anomalous contributions are given by the fields [Formula: see text], where s′≤s-1. The fields Qs are constructed as superpositions of secondary fields with the anomalous contribution equal to zero, An approach developed is based on a finite-dimensional conformal symmetry for any D ≥ 2. Nevertheless the resulting models have the structure analogous to that of two-dimensional conformal theories. This analogy is discussed in detail. It is shown that for D = 2 the family of models coincides with the well-known family of conformal models based on infinite-dimensional conformal symmetry. The analysis of this phenomenon indicates the existence of the D-dimensional analog of the Virasoro algebra.

scholarly journals FLOWS FOR RECTANGULAR MATRIX MODELS

1994 ◽  
Vol 09 (02) ◽  
pp. 101-113 ◽  
Author(s):  
RENÉ LAFRANCE ◽  
ROBERT C. MYERS
Keyword(s):  
Matrix Models ◽  
Scaling Limit ◽  
Flow Equation ◽  
Closed String ◽  
String Equation ◽  
Saddle Point Approximation ◽  
Parametric Solutions ◽  
Rectangular Matrix ◽  
Multicritical Points ◽  
Recursion Formulas

Several new results on the multicritical behavior of rectangular matrix models are presented. We calculate the free energy in the saddle point approximation, and show that at the triple-scaling point, the result is the same as that derived from the recursion formulas. In the triple-scaling limit, we obtain the string equation and a flow equation for arbitrary multicritical points. Parametric solutions are also examined for the limit of almost-square matrix models. This limit is shown to provide an explicit matrix model realization of the scaling equations proposed to describe open-closed string theory.

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

Political Cleavages and Political Parties

2018 ◽  
Author(s):  
Russell J. Dalton
Keyword(s):  
Political Parties ◽  
Dimensional Space ◽  
New Left ◽  
Party Systems ◽  
European Parliament ◽  
Two Dimensional ◽  
Far Right ◽  
Policy Positions ◽  
Cultural Policies ◽  
Policy Choices

This chapter uses the cleavage positions of Candidates to the European Parliament (CEPs) to as representative of their parties’ political positions. Three surveys of CEPs track the evolution of party supply in European party systems. In 1979 parties were primarily aligned along a Left–Right economic cleavage. Gradually new left and Green parties began to compete in elections and crystallized and represented liberal cultural policies. In recent decades new far-right parties arose to represent culturally conservative positions. The cross-cutting cultural cleavage has also prompted many of the established parties to alter their policy positions. In most multiparty systems, political parties now compete in a fully populated two-dimensional space. This increases the supply of policy choices for the voters. The analyses are based on the Candidates to the European Parliament Studies in 1979, 1994, and 2009.

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