scholarly journals SPONTANEOUS SUPERSYMMETRY BREAKING BY LARGE-N MATRICES

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2192-2194
Author(s):  
TSUNEHIDE KUROKI ◽  
FUMIHIKO SUGINO
Keyword(s):  
Matrix Models ◽  
Supersymmetry Breaking ◽  
Matrix Model ◽  
Field Theories ◽  
Supersymmetric Field Theories ◽  
Large N ◽  
Rank Of Matrix

Motivated by supersymmetry breaking in matrix model formulations of superstrings, we present some concrete models, in which the supersymmetry is preserved for any finite N, but gets broken at infinite N, where N is the rank of matrix variables. The models are defined as supersymmetric field theories coupled to some matrix models, and in the induced action obtained after integrating out the matrices, supersymmetry is spontaneously broken only when N is infinity.

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 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.

scholarly journals THE AREA LAW IN MATRIX MODELS FOR LARGE N QCD STRINGS

2002 ◽  
Vol 13 (04) ◽  
pp. 555-563 ◽  
Author(s):  
K. N. ANAGNOSTOPOULOS ◽  
W. BIETENHOLZ ◽  
J. NISHIMURA
Keyword(s):  
Numerical Simulations ◽  
Matrix Models ◽  
Matrix Model ◽  
Hermitian Matrices ◽  
Yang Mills ◽  
Loop Area ◽  
Large N ◽  
Volume Limit ◽  
The Matrix ◽  
Area Law

We study the question whether matrix models obtained in the zero volume limit of 4d Yang–Mills theories can describe large N QCD strings. The matrix model we use is a variant of the Eguchi–Kawai model in terms of Hermitian matrices, but without any twists or quenching. This model was originally proposed as a toy model of the IIB matrix model. In contrast to common expectations, we do observe the area law for Wilson loops in a significant range of scale of the loop area. Numerical simulations show that this range is stable as N increases up to 768, which strongly suggests that it persists in the large N limit. Hence the equivalence to QCD strings may hold for length scales inside a finite regime.

scholarly journals LARGE N REDUCTION ON GROUP MANIFOLDS

2010 ◽  
Vol 25 (17) ◽  
pp. 3389-3406 ◽  
Author(s):  
HIKARU KAWAI ◽  
SHINJI SHIMASAKI ◽  
ASATO TSUCHIYA
Keyword(s):  
Matrix Models ◽  
Gauge Theories ◽  
Field Theories ◽  
Gauge Invariant ◽  
Large N

We show that the large N reduction holds on group manifolds. Large N field theories defined on group manifolds are equivalent to some corresponding matrix models. For instance, gauge theories on S3 can be regularized in a gauge invariant and SO(4) invariant manner.

scholarly journals FIBER BUNDLE AND MATRIX MODELS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2165-2168 ◽  
Author(s):  
ASATO TSUCHIYA
Keyword(s):  
Matrix Models ◽  
Topological Field Theories ◽  
Fiber Bundle ◽  
Field Theories ◽  
Fiber Bundles ◽  
Large N ◽  
Topological Field

We extend the large N reduction and the compactification in matrix models to those on manifolds represented as fiber bundles. We also discuss application of our results to the AdS/CFT correspondence and topological field theories.

scholarly journals LARGE-N AND BETHE ANSATZ

2004 ◽  
Vol 19 (22) ◽  
pp. 1661-1667 ◽  
Author(s):  
BRANISLAV JURČO
Keyword(s):  
Saddle Point ◽  
Orthogonal Polynomials ◽  
Matrix Models ◽  
Bethe Ansatz ◽  
Integrable System ◽  
Matrix Model ◽  
Integrable Model ◽  
Saddle Point Approximation ◽  
Large N ◽  
The Matrix

We describe an integrable model, related to the Gaudin magnet, and its relation to the matrix model of Brézin, Itzykson, Parisi and Zuber. Relation is based on Bethe ansatz for the integrable model and its interpretation using orthogonal polynomials and saddle point approximation. Large-N limit of the matrix model corresponds to the thermodynamic limit of the integrable system. In this limit (functional) Bethe ansatz is the same as the generating function for correlators of the matrix models.

ON p-BRANES AND ANTISYMMETRIC NON-ABELIAN TENSORIAL GAUGE FIELD THEORIES OF DIFFEOMORPHISMS

2011 ◽  
Vol 26 (02) ◽  
pp. 251-271
Author(s):  
CARLOS CASTRO
Keyword(s):  
Quantum Mechanics ◽  
Matrix Models ◽  
Gauge Field ◽  
Open Problem ◽  
Deformation Quantization ◽  
Classical Mechanics ◽  
Gauge Field Theories ◽  
Field Theories ◽  
Large N

It is shown how actions corresponding to antisymmetric non-Abelian tensorial gauge field theories of (p+1)-dimensional diffeomorphisms yield p-brane actions associated with their (p+1)-dimensional worldvolume evolution. We conclude with a discussion of how to obtain p-brane actions from the large N limit of covariant matrix models based on generalized hypermatrices. A deformation quantization of Nambu classical mechanics furnishing Nambu quantum mechanics by constructing the n-ary noncommutative product of n functions f1 •f2 • ⋯ •fn, the n-ary version of the Moyal bracket, and the analog of the Weyl–Wigner–Groenowold–Moyal map among operators and c-functions remains an open problem. A solution to this problem will reveal important relations between the physics of p-branes and matrix models based on generalized hypermatrices in the large N limit.

PROPERTIES OF HERMITIAN MATRIX MODELS IN AN EXTERNAL FIELD

1991 ◽  
Vol 06 (37) ◽  
pp. 3455-3466 ◽  
Author(s):  
YU. MAKEENKO ◽  
G. W. SEMENOFF
Keyword(s):  
Integral Equation ◽  
Partition Function ◽  
External Field ◽  
Matrix Models ◽  
Matrix Model ◽  
Hermitian Matrix ◽  
Genus Zero ◽  
Virasoro Constraints ◽  
Large N ◽  
Single Integral

We consider a Hermitian one-matrix model in an (Hermitian) external field. We drive the Schwinger-Dyson equations and show that those can be represented as a set of Virasoro constraints which are imposed on the partition function. We prove that these Virasoro constraints are equivalent (at least at large N) to a single integral equation whose solution can be found. We use this solution to study properties of the Kontsevich model in genus zero.

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