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 Divergent ⇒ complex amplitudes in two dimensional string theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Matrix Model ◽  
Two Dimensional ◽  
Full Matrix ◽  
Instanton Contribution ◽  
The Matrix ◽  
Theory Result ◽  
The One ◽  
Remarkable Agreement

Abstract In a recent paper, Balthazar, Rodriguez and Yin found remarkable agreement between the one instanton contribution to the scattering amplitudes of two dimensional string theory and those in the matrix model to the first subleading order. The comparison was carried out numerically by analytically continuing the external energies to imaginary values, since for real energies the string theory result diverges. We use insights from string field theory to give finite expressions for the string theory amplitudes for real energies. We also show analytically that the imaginary parts of the string theory amplitudes computed this way reproduce the full matrix model results for general scattering amplitudes involving multiple closed strings.

scholarly journals Quantum gravity as a multitrace matrix model

2017 ◽  
Vol 32 (31) ◽  
pp. 1750180
Author(s):  
Badis Ydri ◽  
Cherine Soudani ◽  
Ahlam Rouag
Keyword(s):  
Quantum Gravity ◽  
Matrix Models ◽  
Large Class ◽  
Matrix Model ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Topology Change ◽  
New Model ◽  
And Topology ◽  
Emergent Geometry

We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of two-dimensional quantum gravity which works away from two dimensions and captures a large class of spaces admitting a finite spectral triple. These multitrace matrix models sustain emergent geometry as well as growing dimensions and topology change.

scholarly journals OPEN-CLOSED DUALITY: LESSONS FROM MATRIX MODEL

2004 ◽  
Vol 19 (11) ◽  
pp. 841-853 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Matrix Model ◽  
String Field Theory ◽  
Classical Result ◽  
Open String ◽  
Closed String ◽  
Tree Level ◽  
Two Dimensional

Recent investigations involving the decay of unstable D-branes in string theory suggest that the tree level open string theory which describes the dynamics of the D-brane already knows about the closed string states produced in the decay of the brane. We propose a specific conjecture involving quantum open string field theory to explain this classical result, and show that the recent results in two-dimensional string theory are in exact accordance with this conjecture.

scholarly journals D-instantons, string field theory and two dimensional string theory

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Ashoke Sen
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Matrix Model ◽  
String Field Theory ◽  
Scattering Amplitude ◽  
Two Dimensional ◽  
World Sheet ◽  
Numerical Result ◽  
Instanton Contribution ◽  
The Matrix

Abstract In [4] Balthazar, Rodriguez and Yin (BRY) computed the one instanton contribution to the two point scattering amplitude in two dimensional string theory to first subleading order in the string coupling. Their analysis left undetermined two constants due to divergences in the integration over world-sheet variables, but they were fixed by numerically comparing the result with that of the dual matrix model. If we consider n-point scattering amplitudes to the same order, there are actually four undetermined constants in the world-sheet approach. We show that using string field theory we can get finite unambiguous values of all of these constants, and we explicitly compute three of these four constants. Two of the three constants determined this way agree with the numerical result of BRY within the accuracy of numerical analysis, but the third constant seems to differ by 1/2. We also discuss a shortcut to determining the fourth constant if we assume the equality of the quantum corrected D-instanton action and the action of the matrix model instanton. This also agrees with the numerical result of BRY.

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.

CORRELATION FUNCTIONS AND ZERO MODES ON HIGHER GENUS RIEMANN SURFACES

1988 ◽  
Vol 03 (04) ◽  
pp. 841-860 ◽  
Author(s):  
M. BONINI ◽  
R. IENGO
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Covariant Formulation ◽  
Two Dimensional ◽  
Zero Modes ◽  
Modular Transformation ◽  
Higher Genus

We describe systematically the propagators and the zero modes of the various two dimensional fields which appear in the construction of the scattering amplitudes in the string theory, within the framework of the covariant formulation, and we discuss also their modular transformation properties.

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.

PROPERTIES OF LOOP EQUATIONS FOR THE HERMITIAN MATRIX MODEL AND FOR TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 05 (22) ◽  
pp. 1753-1763 ◽  
Author(s):  
J. AMBJØRN ◽  
YU. M. MAKEENKO
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
General Procedure ◽  
Iterative Solution ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Continuum Equation ◽  
Hermitian Matrix Model ◽  
The Continuum

We study the properties of the loop equations for the N × N Hermitian matrix model with arbitrary (even) interaction as well as of their continuum limit, associated with the two-dimensional quantum gravity. We apply the general procedure of iterative solution proposed recently by David. We relate the specific heat to the singular behavior of the connected correlator of two loops. We solve the continuum equation to a few lower orders in the string coupling constant, obtaining results for macroscopic loops including the case of a multicritical fixed point.

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