EXCITATIONS AND INTERACTIONS IN d=1 STRING THEORY

1991 ◽  
Vol 06 (11) ◽  
pp. 1961-1984 ◽  
Author(s):  
ANIRVAN M. SENGUPTA ◽  
SPENTA R. WADIA
Keyword(s):  
Matrix Model ◽  
Periodic Wave ◽  
Density Fluctuations ◽  
Dirac Fermion ◽  
Unitary Matrix ◽  
Additional Parameter ◽  
Continuum Approach ◽  
The Matrix ◽  
The One ◽  
The Continuum

We discuss the singlet sector of the d=1 matrix model in terms of a Dirac fermion formalism. The leading order two- and three-point functions of the density fluctuations are obtained by this method. This allows us to construct the effective action to that order and hence provide the equation of motion. This equation is compared with the one obtained from the continuum approach. We also compare continuum results for correlation functions with the matrix model ones and discuss the nature of gravitational dressing for this regularization. Finally, we address the question of boundary conditions within the framework of the d=1 unitary matrix model, considered as a regularized version of the Hermitian model, and study the implications of a generalized action with an additional parameter (analogous to the θ parameter) which give rise to quasi-periodic wave functions.

scholarly journals THREE-POINT FUNCTIONS OF NON-UNITARY MINIMAL MATTER COUPLED TO GRAVITY

1993 ◽  
Vol 08 (03) ◽  
pp. 197-207 ◽  
Author(s):  
DEBASHIS GHOSHAL ◽  
SWAPNA MAHAPATRA
Keyword(s):  
Matrix Model ◽  
Correlation Functions ◽  
The Other ◽  
Tree Level ◽  
Minimal Models ◽  
Continuum Approach ◽  
Point Correlation ◽  
Local Operators ◽  
The One ◽  
The Continuum

The tree-level three-point correlation functions of local operators in the general (p, q) minimal models coupled to gravity are calculated in the continuum approach. On one hand, the result agrees with the unitary series (q=p+1); and on the other hand, for p=2, q=2k−1, we find agreement with the one-matrix model results.

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 Effective Action and Measure in Matrix Model of IIB Superstrings

1997 ◽  
Vol 12 (31) ◽  
pp. 2331-2340 ◽  
Author(s):  
L. Chekhov ◽  
K. Zarembo
Keyword(s):  
Matrix Model ◽  
Effective Action ◽  
Continuum Limit ◽  
Auxiliary Field ◽  
Large N ◽  
The Matrix ◽  
Reparametrization Invariance ◽  
The Continuum ◽  
Induced Measure

We calculate an effective action and measure induced by the integration over the auxiliary field in the matrix model recently proposed to describe IIB superstrings. It is shown that the measure of integration over the auxiliary matrix is uniquely determined by locality and reparametrization invariance of the resulting effective action. The large-N limit of the induced measure for string coordinates is discussed in detail. It is found to be ultralocal and, thus, is possibly irrelevant in the continuum limit. The model of the GKM type is considered in relation to the effective action problem.

scholarly journals THE HAGEDORN TRANSITION AND THE MATRIX MODEL FOR STRINGS

1998 ◽  
Vol 13 (26) ◽  
pp. 2085-2094 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Matrix Model ◽  
Light Cone ◽  
Degrees Of Freedom ◽  
Low Energy ◽  
Matrix Formalism ◽  
Yang Mills ◽  
Large N ◽  
The Matrix ◽  
The Continuum ◽  
String Worldsheet

We use the matrix formalism to investigate what happens to strings above the Hagedorn temperature. We show that is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of N D-0-branes arranged to form a string having N units of light-cone momentum. We find that at high temperatures the favored phase is one where the string worldsheet has disappeared and the low-energy degrees of freedom consists of N2 massless particles ("gluons"). The nature of the transition is very similar to the deconfinement transition in large-N Yang–Mills theories.

TOPOLOGICAL σ MODELS AND LARGE N MATRIX INTEGRAL

1995 ◽  
Vol 10 (29) ◽  
pp. 4203-4224 ◽  
Author(s):  
TOHRU EGUCHI ◽  
KENTARO HORI ◽  
SUNG-KIL YANG
Keyword(s):  
Matrix Model ◽  
Riemann Surfaces ◽  
Holomorphic Maps ◽  
Integrable Structure ◽  
Toda Hierarchy ◽  
Matrix Integral ◽  
Large N ◽  
The Matrix ◽  
Lax Operator ◽  
The One

In this paper we describe in some detail the representation of the topological CP1 model in terms of a matrix integral which we have introduced in a previous article. We first discuss the integrable structure of the CP1 model and show that it is governed by an extension of the one-dimensional Toda hierarchy. We then introduce a matrix model which reproduces the sum over holomorphic maps from arbitrary Riemann surfaces onto CP1. We compute intersection numbers on the moduli space of curves using a geometrical method and show that the results agree with those predicted by the matrix model. We also develop a Landau-Ginzburg (LG) description of the CP1 model using a superpotential eX + et0,Q e-X given by the Lax operator of the Toda hierarchy (X is the LG field and t0,Q is the coupling constant of the Kähler class). The form of the superpotential indicates the close connection between CP1 and N=2 supersymmetric sine-Gordon theory which was noted sometime ago by several authors. We also discuss possible generalizations of our construction to other manifolds and present an LG formulation of the topological CP2 model.

scholarly journals COVARIANT MATRIX MODEL OF SUPERPARTICLE IN THE PURE SPINOR FORMALISM

2003 ◽  
Vol 18 (15) ◽  
pp. 1023-1035 ◽  
Author(s):  
ICHIRO ODA
Keyword(s):  
Matrix Model ◽  
Brst Symmetry ◽  
Explicit Calculation ◽  
Pure Spinor ◽  
First Order ◽  
Free Theory ◽  
The Matrix ◽  
The One ◽  
Spinor Formalism ◽  
Pure Spinor Formalism

On the basis of the Berkovits pure spinor formalism of covariant quantization of supermembrane, we attempt to construct a M(atrix) theory which is covariant under SO(1, 10) Lorentz group. We first construct a bosonic M(atrix) theory by starting with the first-order formalism of bosonic membrane, which precisely gives us a bosonic sector of M(atrix) theory by BFSS. Next we generalize this method to the construction of M(atrix) theory of supermembranes. However, it seems to be difficult to obtain a covariant and supersymmetric M(atrix) theory from the Berkovits pure spinor formalism of supermembrane because of the matrix character of the BRST symmetry. Instead, in this paper, we construct a supersymmetric and covariant matrix model of 11D superparticle, which corresponds to a particle limit of covariant M(atrix) theory. By an explicit calculation, we show that the one-loop effective potential is trivial, thereby implying that this matrix model is a free theory at least at the one-loop level.

scholarly journals Fundamental Strings and D-Strings in the IIB Matrix Model

1997 ◽  
Vol 12 (18) ◽  
pp. 1301-1315 ◽  
Author(s):  
B. Sathiapalan
Keyword(s):  
Matrix Model ◽  
Scaling Limit ◽  
Duality Group ◽  
Fundamental String ◽  
Large N ◽  
The Matrix ◽  
Model Derivation ◽  
The One ◽  
The Right ◽  
String Worldsheet

The matrix model for IIB superstring proposed by Ishibashi, Kawai, Kitazawa and Tsuchiya is investigated. Consideration of planar and non-planar diagrams suggests that large-N perturbative expansion is consistent with the double scaling limit proposed by the above authors. We write down a Wilson loop that can be interpreted as a fundamental string vertex operator. The one-point tadpole in the presence of a D-string has the right form and this can be viewed as a matrix model derivation of the boundary conditions that define a D-string. We also argue that if worldsheet coordinates σ and τ are introduced to the fundamental string, then the conjugate variable d/dσ and d/dτ can be interpreted as the D-string worldsheet coordinates. In this way the SL (2Z) duality group of the IIB superstring becomes identified with the symplectic group acting on (p,q).

THE CUBIC MATRIX MODEL WITH IMAGINARY COUPLING AND 2D GRAVITY

1992 ◽  
Vol 07 (03) ◽  
pp. 501-534
Author(s):  
MAHA SAADI ◽  
GUILLERMO ZEMBA
Keyword(s):  
Analytic Continuation ◽  
Matrix Model ◽  
Continuum Limit ◽  
2D Gravity ◽  
Positive Definite ◽  
Model Formulation ◽  
Loop Equation ◽  
Pure Gravity ◽  
The One ◽  
The Continuum

We study the continuum properties of the Hermitian one-matrix model defined by a cubic potential with imaginary coupling, using the orthogonal polynomials and loop-equation approaches. The model is well defined mathematically and has a continuum limit which cannot be naively interpreted as pure gravity since each term of the sum over surfaces is not positive-definite. Nevertheless, the model may be considered as an analytic continuation of the standard matrix-model formulation of gravity. We study in detail the conditions under which the analytic continuation may be performed. In particular, the specific heat is found to obey a Painlevé equation. Although we find a solution that is compatible, as far as global stability is concerned, with the one proposed by David, it is not completely clear that the two solutions are the same.

VIRASORO CONSTRAINTS ON THE MATRIX-MODEL PARTITION FUNCTION AND STRING FIELD THEORY

1992 ◽  
Vol 07 (07) ◽  
pp. 1553-1581 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Matrix Model ◽  
String Field Theory ◽  
Minimal Model ◽  
Differential Operators ◽  
Tree Level ◽  
Virasoro Constraints ◽  
The Matrix ◽  
The One

The one-matrix model at the kth multicritical point is known to describe the (2, 2k–1) minimal model coupled to gravity, and the partition function of this model is known to obey a set of Virasoro constraints generated by a set of differential operators Ln. Working at the tree level of string theory, and using the Feigin-Fuchs description of the (2, 2k–1) minimal model, we show that the Virasoro constraints generated by Li (0≤i≤k−2) can be identified with a set of gauge symmetries of the corresponding string field theory.

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