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 THE TOPOLOGICAL CP1 MODEL AND THE LARGE-N MATRIX INTEGRAL

1994 ◽  
Vol 09 (31) ◽  
pp. 2893-2902 ◽  
Author(s):  
TOHRU EGUCHI ◽  
SUNG-KIL YANG
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Riemann Surfaces ◽  
Hermitian Matrix ◽  
Coupling Constants ◽  
Holomorphic Maps ◽  
Matrix Integral ◽  
Large N

We discuss the topological CP 1 model which consists of the holomorphic maps from Riemann surfaces onto CP 1. We construct a large-N matrix model which reproduces precisely the partition function of the CP 1 model at all genera of Riemann surfaces. The action of our matrix model has the form [Formula: see text] where M is an N × N Hermitian matrix and tn,P(tn,Q), (n = 0, 1, 2, …) are the coupling constants of the nth descendant of the puncture (Kähler) operator.

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).

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.

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.

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.

Peierls Model and Vacuum Structure in the N = 2 Supersymmetric Field Theories

1997 ◽  
Vol 12 (10) ◽  
pp. 719-727 ◽  
Author(s):  
A. Gorsky
Keyword(s):  
Temperature Phase ◽  
Integrable Structure ◽  
Mass Gap ◽  
Supersymmetric Field Theories ◽  
Temperature Phase Transition ◽  
Lax Operator ◽  
The One ◽  
Bps States ◽  
Peierls Model ◽  
Quasiparticle Picture

We suggest the quasiparticle picture behind the integrable structure of N=2 SYM theory which arises if the Lax operator is considered as a Hamiltonian for the fermionic system. We compare the meaning of BPS states with the one coming from the D-brane interpretation and give some evidence for the compositeness of the self-dual strings. The temperature phase transition with the disappearance of the mass gap is conjectured.

scholarly journals CRITICAL SCALING IN THE MATRIX MODEL ON A BETHE TREE

1994 ◽  
Vol 09 (21) ◽  
pp. 1963-1973 ◽  
Author(s):  
D.V. BOULATOV
Keyword(s):  
Matrix Model ◽  
Explicit Solutions ◽  
Critical Scaling ◽  
Edge Singularity ◽  
Large N ◽  
The Matrix

The matrix model with a Bethe tree embedding space (coincides at large N with the Kazakov-Migdal “induced QCD” model1) is investigated. We further elaborate the Riemann-Hilbert approach of Ref. 2 assuming certain holomorphic properties of the solution. The critical scaling (an edge singularity of the density) is found to be [Formula: see text][Formula: see text] arccos D, for |D|<1, and [Formula: see text] arccos [Formula: see text] for D>1. Explicit solutions are constructed at D=1/2 and D=∞.

scholarly journals INTERACTION OF F- andD-STRINGS IN THE MATRIX MODEL

1998 ◽  
Vol 13 (12) ◽  
pp. 921-936 ◽  
Author(s):  
N. D. HARI DASS ◽  
B. SATHIAPALAN
Keyword(s):  
String Theory ◽  
Matrix Models ◽  
Matrix Model ◽  
Bound State ◽  
Model Description ◽  
Large N ◽  
The Matrix ◽  
M Theory

We study a configuration of a parallel F- (fundamental) and D-string in IIB string theory by considering its T-dual configuration in the matrix model description of M-theory. We show that certain nonperturbative features of string theory such as O(e-1/gs) effects due to soliton loops, the existence of bound state (1,1) strings and manifest S-duality, can be seen in matrix models. We discuss certain subtleties that arise in the large-N limit when membranes are wrapped around compact dimensions.

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