scholarly journals KNOTS, FEYNMAN DIAGRAMS AND MATRIX MODELS

1999 ◽  
Vol 02 (03) ◽  
pp. 359-380 ◽  
Author(s):  
MARTIN GROTHAUS ◽  
LUDWIG STREIT ◽  
IGOR V. VOLOVICH
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Matrix Model ◽  
Feynman Diagrams ◽  
Generalized Function ◽  
Explicit Formulas ◽  
The Matrix ◽  
Wick Theorem ◽  
Knot Diagrams ◽  
Generalized Expectation

A U (N)-invariant matrix model with d matrix variables is studied. It was shown that in the limit N → ∞ and d→0 the model describes the knot diagrams. We realize the free partition function of the matrix model as the generalized expectation of a Hida distribution ΦN,d. This enables us to give a mathematically rigorous meaning to the partition function with interaction. For the generalized function ΦN,d, we prove a Wick theorem and we derive explicit formulas for the propagators.

β-DEFORMED MATRIX MODELS AND NEKRASOV PARTITION FUNCTION

2013 ◽  
Vol 21 ◽  
pp. 92-100
Author(s):  
TAKESHI OOTA
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Matrix Models ◽  
Matrix Model ◽  
The Matrix

The β-deformed matrix models of Selberg type are introduced. They are exactly calculable by using the Macdonald-Kadell formula. With an appropriate choice of the integration contours and interactions, the partition function of the matrix model can be identified with the Nekrasov partition function for SU(2) gauge theory with Nf = 4. Known properties of good q-expansion basis for the matrix model are summarized.

MATRIX MODELS AND GAUGE-INVARIANT FIELD THEORY OF SUBCRITICAL STRINGS

1992 ◽  
Vol 07 (11) ◽  
pp. 2559-2588 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Matrix Models ◽  
Matrix Model ◽  
String Field Theory ◽  
Correlation Functions ◽  
Ward Identities ◽  
Gauge Invariant ◽  
The Matrix

A gauge-invariant interacting field theory of subcritical closed strings is constructed. It is shown that for d ≤ 1 this field theory reproduces many of the features of the corresponding matrix model. Among them are the scaling dimensions of the relevant primary fields, identities involving the correlation functions of some of the redundant operators in the matrix model, and the flow between different matrix models under appropriate perturbation. In particular, it is shown that some of the constraints on the partition function derived recently by Dijkgraaf et al. and Fukuma et al. may be interpreted as Ward identities in string field theory.

scholarly journals Multiple phases in a generalized Gross-Witten-Wadia matrix model

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

scholarly journals STAR-MATRIX MODELS

1995 ◽  
Vol 10 (35) ◽  
pp. 2709-2725
Author(s):  
E. VINTELER
Keyword(s):  
Ising Model ◽  
Partition Function ◽  
Matrix Models ◽  
Critical Behavior ◽  
Gaussian Model ◽  
Explicit Formulas ◽  
Special Cases ◽  
Q Matrix

The star-matrix models are difficult to solve due to the multiple powers of the Vandermonde determinants in the partition function. We apply to these models a modified Q-matrix aprpoach and we get results consistent with those obtained by other methods. As examples we study the inhomogeneous Gaussian model on Bethe tree and matrix q-Potts-like model. For the last model in the special cases q=2 and q=3, we write down explicit formulas which determine the critical behavior of the system. For q=2 we argue that the critical behavior is indeed that of the Ising model on the ϕ3 lattice.

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 Demonstrating the Effect of Height Variation on Stand-Level Optimization with Diameter-Structured Matrix Model

Forests ◽  
2020 ◽  
Vol 11 (2) ◽  
pp. 226
Author(s):  
Johanna Pyy ◽  
Erkki Laitinen ◽  
Anssi Ahtikoski
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Net Present Value ◽  
Rotation Period ◽  
Present Value ◽  
Height Variation ◽  
Structured Matrix ◽  
The Matrix ◽  
Log Price ◽  
Financial Outcome

The weakness of the population matrix models is that they do not take into account the variation inside the class. In this study, we introduce an approach to add height variation of the trees to the diameter-structured matrix models. In this approach, a new sub-model that describes the height growth of the trees is included in the diameter-structured model. We used this height- and diameter-structured matrix model to maximize the net present value (NPV) for the remaining part of the ongoing rotation for Scots pine (Pinus sylvestris L.) stand and studied how the height variation affects to the results obtained through stand-level optimization. In the optimization, the height variation was taken into account by setting the lower saw-log price for the short trees. The results show that including the height variation into the optimization reduced the financial outcome by 16–18% and considerably changed the structure of optimal management (e.g., timings for thinnings, rotation period and intensity of thinnings). We introduced an approach that can be applied to include not only height variation but also variation of other tree properties (such as branchiness or the amount of heartwood and sapwood) into the matrix models.

scholarly journals PROJECTORS, MATRIX MODELS AND NONCOMMUTATIVE INSTANTONS

2004 ◽  
Vol 19 (28) ◽  
pp. 4789-4811 ◽  
Author(s):  
P. VALTANCOLI
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Projective Modules ◽  
Noncommutative Topology ◽  
The Matrix ◽  
Noncommutative Instantons ◽  
Smooth Deformation ◽  
Model Approach

We deconstruct the finite projective modules for the fuzzy four-sphere, described in a previous paper, and correlate them with the matrix model approach, making manifest the physical implications of noncommutative topology. We briefly discuss also the U (2) case, being a smooth deformation of the celebrated BPST SU (2) classical instantons on a sphere.

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 INTEGRABLE STRUCTURES IN MATRIX MODELS AND PHYSICS OF 2D GRAVITY

1993 ◽  
Vol 08 (22) ◽  
pp. 3831-3882 ◽  
Author(s):  
A. MARSHAKOV
Keyword(s):  
Field Theory ◽  
Matrix Models ◽  
Matrix Model ◽  
2D Gravity ◽  
Model Description ◽  
Physical Role ◽  
Theory Formulation ◽  
The Matrix ◽  
Free Fields ◽  
Effective Description

A review of the appearance of integrable structures in the matrix model description of 2D gravity is presented. Most of the ideas are demonstrated with technically simple but ideologically important examples. Matrix models are considered as a sort of “effective” description of continuum 2D field theory formulation. The main physical role in such a description is played by the Virasoro-W conditions, which can be interpreted as certain unitarity or factorization constraints. Both discrete and continuum (generalized Kontsevich) models are formulated as the solutions to those discrete (continuous) Virasoro-W constraints. Their integrability properties are proved, using mostly the determinant technique highly related to the representation in terms of free fields. The paper also contains some new observations connected with formulation of more-general-than-GKM solutions and deeper understanding of their relation to 2D gravity.

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.

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