scholarly journals Comments on the Large N Matrix Model

2000 ◽  
Vol 103 (1) ◽  
pp. 197-223
Author(s):  
H. Kajiura ◽  
A. Kato ◽  
S. Ogushi
Keyword(s):  
Matrix Model ◽  
Large N

PHASE DIAGRAM AND ORTHOGONAL POLYNOMIALS IN MULTIPLE-WELL MATRIX MODELS

1991 ◽  
Vol 06 (25) ◽  
pp. 4491-4515 ◽  
Author(s):  
OLAF LECHTENFELD ◽  
RASHMI RAY ◽  
ARUP RAY
Keyword(s):  
Phase Diagram ◽  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Matrix Model ◽  
Phase Structure ◽  
Saddle Points ◽  
Tree Level ◽  
Potential Wells ◽  
Large N

We investigate a zero-dimensional Hermitian one-matrix model in a triple-well potential. Its tree-level phase structure is analyzed semiclassically as well as in the framework of orthogonal polynomials. Some multiple-arc eigenvalue distributions in the first method correspond to quasiperiodic large-N behavior of recursion coefficients for the second. We further establish this connection between the two approaches by finding three-arc saddle points from orthogonal polynomials. The latter require a modification for nondegenerate potential minima; we propose weighing the average over potential wells.

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 Large N behaviors of the IIB matrix model and the regularized Schild models

2001 ◽  
Vol 2001 (10) ◽  
pp. 033-033 ◽  
Author(s):  
Naofumi Kitsunezaki ◽  
Shozo Uehara
Keyword(s):  
Matrix Model ◽  
Large N

scholarly journals Comparative studies of the deformation techniques for the singular-drift problem in the complex Langevin method

2018 ◽  
Vol 175 ◽  
pp. 07019 ◽  
Author(s):  
Yuta Ito ◽  
Jun Nishimura
Keyword(s):  
Low Temperature ◽  
Dirac Operator ◽  
Matrix Model ◽  
Comparative Studies ◽  
Deformation Parameter ◽  
High Density ◽  
Large N ◽  
Singular Drift ◽  
Different Types ◽  
Data Points

In application of the complex Langevin method to QCD at high density and low temperature, the singular-drift problem occurs due to the appearance of near-zero eigenvalues of the Dirac operator. In order to avoid this problem, we proposed to de-form the Dirac operator in such a way that the near-zero eigenvalues do not appear and to extrapolate the deformation parameter to zero from the available data points. Here we test three different types of deformation in a simple large-N matrix model, which under-goes an SSB due to the phase of the fermion determinant, and compare them to see the consistency with one another.

scholarly journals Large N structure of IIB matrix model

2002 ◽  
Author(s):  
Naofumi Kitsunezaki
Keyword(s):  
Matrix Model ◽  
Large N

scholarly journals Monte Carlo studies of the IIB matrix model at large N

2000 ◽  
Vol 2000 (07) ◽  
pp. 011-011 ◽  
Author(s):  
Jan Ambjørn ◽  
Jun Nishimura ◽  
Konstantinos N Anagnostopoulos ◽  
Wolfgang Bietenholz ◽  
Tomohiro Hotta
Keyword(s):  
Monte Carlo ◽  
Matrix Model ◽  
Large N ◽  
Monte Carlo Studies

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 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=∞.

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