scholarly journals Touching random surfaces, two-dimensional quantum gravity, and noncritical string theory

1998 ◽  
Vol 57 (6) ◽  
pp. 3725-3735 ◽  
Author(s):  
Oleg Andreev
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Two Dimensional ◽  
Random Surfaces

scholarly journals QUANTUM RINGS AND RECURSION RELATIONS IN 2D QUANTUM GRAVITY

1992 ◽  
Vol 07 (16) ◽  
pp. 1419-1425 ◽  
Author(s):  
SHAMIT KACHRU
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Quantum Gravity ◽  
Matrix Model ◽  
Ring Structure ◽  
Two Dimensional ◽  
Recursion Relations ◽  
Quantum Rings ◽  
Bulk Scattering

I study tachyon condensate perturbations to the action of the two-dimensional string theory corresponding to the c=1 matrix model. These are shown to deform the action of the ground ring on the tachyon modules, confirming a conjecture of Witten. The ground ring structure is used to derive recursion relations which relate (N+1) and N tachyon bulk scattering amplitudes. These recursion relations allow one to compute all bulk amplitudes.

scholarly journals QUESTION ON D=26: STRING THEORY VERSUS QUANTUM GRAVITY

1998 ◽  
Vol 13 (18) ◽  
pp. 3081-3099 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Critical Dimension ◽  
Bosonic String ◽  
Two Dimensional ◽  
Theory Versus ◽  
Covariant Gauge ◽  
New Type

In the covariant-gauge two-dimensional quantum gravity, various derivations of the critical dimension D=26 of the bosonic string are critically reviewed, and their interrelations are clarified. It is shown that the string theory is not identical with the proper framework of the two-dimensional quantum gravity, but the former should be regarded as a particular aspect of the latter. The appearance of various anomalies is shown to be explainable in terms of a new type of anomaly in a unified way.

INDEFINITENESS OF THE CONFORMAL ANOMALY OF THE STRING THEORY IN THE HARMONIC GAUGE

1992 ◽  
Vol 07 (20) ◽  
pp. 1799-1804 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Lagrangian Density ◽  
Order Approximation ◽  
Bosonic String ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Critical Dimensions ◽  
Total Divergence ◽  
Field Redefinition

The derivation of the critical dimensions D=26 of the bosonic string theory based on the two-dimensional quantum gravity in the harmonic gauge is criticized. The conformal anomaly calculated in lowest-order approximation crucially depends on the presence of a certain part of the FP-ghost Lagrangian density. However, this part can be eliminated by field redefinition and, moreover, reduces to a total divergence in lowest-order approximation. Thus the assertion that the anomaly is proportional to (D−26) is groundless.

scholarly journals IRREVERSIBILITY OF THE RENORMALIZATION GROUP FLOW IN TWO-DIMENSIONAL QUANTUM GRAVITY

1992 ◽  
Vol 07 (31) ◽  
pp. 2943-2955 ◽  
Author(s):  
DAVID KUTASOV
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Two Dimensional ◽  
Renormalization Group Flow ◽  
Group Flow

We argue that the torus partition sum in 2D (super) gravity, which counts physical states in the theory, is a decreasing function of the renormalization group scale. As an application we chart the space of [Formula: see text] models coupled to (super) gravity, confirming and extending ideas due to A. Zamolodchikov, and discuss briefly string theory, where our results imply that the number of degrees of freedom decreases with time.

TWO-DIMENSIONAL QUANTUM GRAVITY, MATRIX MODELS AND STRING THEORY

1993 ◽  
Vol 08 (07) ◽  
pp. 1185-1244 ◽  
Author(s):  
KREŠIMIR DEMETERFI
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Lattice Models ◽  
Field Method ◽  
Two Dimensional ◽  
Large N ◽  
The One ◽  
Low Dimensional ◽  
Lattice Approach

We review some results of the recent progress in understanding two-dimensional quantum gravity and low-dimensional string theories based on the lattice approach. The possibility to solve the lattice models exactly comes from their equivalence to large N matrix models. We describe various matrix models and their continuum limits, and discuss in some detail the phase structure of Hermitian one-matrix models. For the one-dimensional matrix model we discuss its field theoretic formulation through a collective field method and summarize some perturbative results. We compare the results obtained from matrix models to the results in the continuum approach to string theory.

scholarly journals CONSTRUCTION OF AN IDENTICALLY NILPOTENT BRS CHARGE IN THE KATO–OGAWA STRING THEORY

1999 ◽  
Vol 14 (09) ◽  
pp. 1357-1377 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Field Equation ◽  
String Theory ◽  
Quantum Gravity ◽  
Bosonic Strings ◽  
Open String ◽  
Indefinite Metric ◽  
Two Dimensional ◽  
Conformal Gauge ◽  
Wightman Functions ◽  
Artificial Introduction

In previous work, the conformal-gauge two-dimensional quantum gravity in the BRS formalism has been solved completely in terms of Wightman functions. In the present paper, this result is extended to the closed and open bosonic strings of finite length; the open-string case is nothing but the Kato–Ogawa string theory. The field-equation anomaly found previously, which means a slight violation of a field equation at the level of Wightman functions, remains existent in the finite-string cases. By using this fact, a BRS charge nilpotent even for D≠26 is explicitly constructed in the framework of the Kato–Ogawa string theory. The FP-ghost vacuum structure of the Kato–Ogawa theory is made more transparent; the appearance of half-integral ghost numbers and the artificial introduction of an indefinite metric are avoided.

SUPER-LIOUVILLE THEORY AS A TWO-DIMENSIONAL, SUPERCONFORMAL SUPERGRAVITY THEORY

1990 ◽  
Vol 05 (02) ◽  
pp. 391-414 ◽  
Author(s):  
JACQUES DISTLER ◽  
ZVONIMIR HLOUSEK ◽  
HIKARU KAWAI
Keyword(s):  
String Theory ◽  
Hausdorff Dimension ◽  
Critical Exponents ◽  
Liouville Theory ◽  
Two Dimensional ◽  
Random Surfaces ◽  
Supergravity Theory ◽  
Arbitrary Topology ◽  
Bosonic Case

In this paper we extend our previous results on the bosonic Liouville theory, to the supersymmetric case. As in the bosonic case, we find that the quantization of the N=1 theory is limited to the region D≤1. We compute the exact critical exponents and the analogue of the Hausdorff dimension of super random surfaces. Our procedure is manifestly covariant and our results hold for the surface of arbitrary topology. We also examine the N=2, O(2) string theory and find that it appears to be well-defined for all D.

scholarly journals A GENERALIZED MODEL FOR TWO-DIMENSIONAL QUANTUM GRAVITY AND DYNAMICS OF RANDOM SURFACES FOR d>1

1994 ◽  
Vol 09 (22) ◽  
pp. 2009-2018 ◽  
Author(s):  
M. MARTELLINI ◽  
M. SPREAFICO ◽  
K. YOSHIDA
Keyword(s):  
Quantum Gravity ◽  
Effective Field Theory ◽  
Continuum Model ◽  
Central Charge ◽  
Flat Space ◽  
Effective Field ◽  
Two Dimensional ◽  
Large Area ◽  
Random Surfaces ◽  
Area Expansion

The possible interpretations of a new continuum model for the two-dimensional quantum gravity for d>1 (d=matter central charge), obtained by carefully treating both diffeomorphism and Weyl symmetries, are discussed. In particular we note that an effective field theory is achieved in low energy (large area) expansion, that may represent smooth self-avoiding random surfaces embedded in a d-dimensional flat space-time for arbitrary d. Moreover the values of some critical exponents are computed, that are in agreement with some recent numerical results.

TWO DIMENSIONAL QUANTUM GRAVITY AND STRINGS

1990 ◽  
Vol 05 (10) ◽  
pp. 1833-1859 ◽  
Author(s):  
A.A. TSEYTLIN
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Conformal Factor ◽  
Target Space ◽  
Effective Theory ◽  
Two Dimensional ◽  
Conformal Gauge

We discuss some recent suggestions about a relation between 2-d quantum gravity and string theory. We consider the general 2-d σ model with D-dimensional target space coupled to 2-d quantum gravity and give arguments in favor of the conjecture that the effective theory which describes this system in the conformal gauge may be interpreted as a a model with a D+1-dimensional target space with the conformal factor of the metric playing the role of the D+1 coordinate. The latter σ model must be Weyl invariant while the original one may be arbitrary. The conformal “split” invariance which must be present in the conformal gauge imposes no restrictions on the original σ model couplings, but restricts the additional (D+1-dimensional) couplings which appear in the D+1-dimensional σ model.

Sign in / Sign up

Export Citation Format

Share Document