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 D = 26 AND EXACT SOLUTION TO THE CONFORMAL-GAUGE TWO-DIMENSIONAL QUANTUM GRAVITY

1999 ◽  
Vol 14 (04) ◽  
pp. 521-536 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Field Equation ◽  
Quantum Gravity ◽  
Critical Dimension ◽  
Bosonic String ◽  
Ghost Number ◽  
Conformal Anomaly ◽  
Two Dimensional ◽  
Heisenberg Picture ◽  
Conformal Gauge

The conformal-gauge two-dimensional quantum gravity is formulated in the framework of the BRS quantization and solved completely in the Heisenberg picture: all n-point Wightman functions are explicitly obtained. The field-equation anomaly is shown to exist as in other gauges, but there is no other subtlety. At the critical dimension D = 26 of the bosonic string, the field-equation anomaly is shown to be absent. However, this result is not equivalent to the statement that the conformal anomaly is proportional to D - 26. The existence of the FP-ghost number current anomaly is seen to be an illusion.

scholarly journals EXACT SOLUTIONS TO THE TWO-DIMENSIONAL BF AND YANG–MILLS THEORIES IN THE LIGHT-CONE GAUGE

2002 ◽  
Vol 17 (11) ◽  
pp. 1491-1502 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Quantum Gravity ◽  
Light Cone ◽  
Lagrangian Density ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Bf Theory ◽  
Conformal Gauge

It is shown that the BRS (= Becchi–Rouet–Stora)-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the [Formula: see text] term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang–Mills theory is also obtained.

scholarly journals A TOY MODEL OF CLOSED STRING TACHYON EFFECTIVE ACTION

2005 ◽  
Vol 20 (07) ◽  
pp. 1481-1493
Author(s):  
J. KLUSOŇ
Keyword(s):  
Exact Solution ◽  
String Theory ◽  
Effective Action ◽  
Flat Space ◽  
Closed String ◽  
Space Time ◽  
Bosonic String ◽  
Two Dimensional ◽  
Linear Dilaton ◽  
Bosonic String Theory

In this paper we propose the toy model of the closed string tachyon effective action that has marginal tachyon profile as its exact solution in case of constant or linear dilaton background. Then we will apply this model for description of two-dimensional bosonic string theory. We will find that the background configuration with the spatial dependent linear dilaton, flat space–time metric and marginal tachyon profile is the exact solution of our model even if we take into account backreaction of tachyon on dilaton and on metric.

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 A quantized spacetime based on Spin(3,1) symmetry

2016 ◽  
Vol 25 (13) ◽  
pp. 1645004
Author(s):  
Pisin Chen ◽  
Hsu-Wen Chiang ◽  
Yao-Chieh Hu
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Uncertainty Principle ◽  
Loop Quantum Gravity ◽  
Generalized Uncertainty Principle ◽  
Spin Network ◽  
Fundamental Symmetry ◽  
New Type ◽  
Gravity Theories

We introduce a new type of the spacetime quantization based on the spinorial description suggested by loop quantum gravity. Specifically, we build our theory on a string theory inspired [Formula: see text] worldsheet action. Because of its connection with quantum gravity theories, our proposal may in principle link back to string theory, connect to loop quantum gravity where SU(2) is suggested as the fundamental symmetry, or serve as a Lorentzian spin network. We derive the generalized uncertainty principle and demonstrate the holographic nature of our theory. Due to the quantization of spacetime, geodesics in our theory are fuzzy, but the fuzziness is shown to be much below conceivable astrophysical bounds.

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.

scholarly journals THE BRST CHARGE FOR THE $\hat D (2, 1; \alpha)$ NONLINEAR QUASI-SUPERCONFORMAL ALGEBRA

1995 ◽  
Vol 10 (01) ◽  
pp. 79-90 ◽  
Author(s):  
SERGEI V. KETOV
Keyword(s):  
String Theory ◽  
Critical Dimension ◽  
Superconformal Algebra ◽  
Two Dimensional ◽  
Text Representation ◽  
Large N ◽  
Brst Charge

The quantum BRST charge for the most general, two-dimensional, nonlinear, N = 4 quasi-superconformal algebra [Formula: see text], whose linearization is the so-called 'large' N = 4 superconformal algebra, is constructed. The [Formula: see text] algebra has [Formula: see text] Kač–Moody component, and α = k−/k+. As a pre-requisite to our construction, we check the [Formula: see text] Jacobi identities and construct a classical BRST charge. Then, we analyze the quantum BRST charge nilpotency conditions and find the only solution, k+ = k− = −2. The [Formula: see text] algebra is actually isomorphic to the SO(4)-based Bershadsky–Knizhnik nonlinear quasi-superconformal algebra. We argue about the existence of a new string theory with (i) the nonlinearly realized N = 4 worldsheet supersymmetry, (ii) non-unitary matter in a [Formula: see text] representation of k = −2 and c = −6, and (iii) negative 'critical dimension'.

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.

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