scholarly journals W-representation of Rainbow tensor model

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Bei Kang ◽  
Lu-Yao Wang ◽  
Ke Wu ◽  
Jie Yang ◽  
Wei-Zhong Zhao
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Crucial Role ◽  
Elementary Function ◽  
Tensor Model ◽  
Witt Algebra ◽  
Virasoro Constraints ◽  
Compact Expression ◽  
Non Gaussian ◽  
Dual Expression

Abstract We analyze the rainbow tensor model and present the Virasoro constraints, where the constraint operators obey the Witt algebra and null 3-algebra. We generalize the method of W-representation in matrix model to the rainbow tensor model, where the operators preserving and increasing the grading play a crucial role. It is shown that the rainbow tensor model can be realized by acting on elementary function with exponent of the operator increasing the grading. We derive the compact expression of correlators and apply it to several models, i.e., the red tensor model, Aristotelian tensor model and r = 4 rainbow tensor model. Furthermore, we discuss the case of the non-Gaussian red tensor model and present a dual expression for partition function through differentiation.

scholarly journals NON-PERTURBATIVE SOLUTION OF THE SUPER-VIRASORO CONSTRAINTS

1993 ◽  
Vol 08 (13) ◽  
pp. 1205-1214 ◽  
Author(s):  
K. BECKER ◽  
M. BECKER
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Scaling Limit ◽  
Virasoro Constraints ◽  
Perturbative Solution ◽  
The One ◽  
Genus Expansion ◽  
Double Scaling Limit

We present the solution of the discrete super-Virasoro constraints to all orders of the genus expansion. Integrating over the fermionic variables we get a representation of the partition function in terms of the one-matrix model. We also obtain the non-perturbative solution of the super-Virasoro constraints in the double scaling limit but do not find agreement between our flows and the known supersymmetric extensions of KdV.

scholarly journals PARTITION FUNCTIONS OF MATRIX MODELS: FIRST SPECIAL FUNCTIONS OF STRING THEORY

2004 ◽  
Vol 19 (24) ◽  
pp. 4127-4163 ◽  
Author(s):  
A. ALEXANDROV ◽  
A. MOROZOV ◽  
A. MIRONOV
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Matrix Model ◽  
Special Functions ◽  
Finite Size ◽  
Building Blocks ◽  
Partition Functions ◽  
Virasoro Constraints ◽  
Elementary Building

Even though matrix model partition functions do not exhaust the entire set of τ-functions relevant for string theory, they seem to be elementary building blocks for many others and they seem to properly capture the fundamental symplicial nature of quantum gravity and string theory. We propose to consider matrix model partition functions as new special functions. Here we restrict our consideration to the finite-size Hermitian 1-matrix model and concentrate mostly on its phase/branch structure arising when the partition function is considered as a D-module. We discuss the role of the CIV–DV prepotential (as generating a possible basis in the linear space of solutions to the Virasoro constraints, but with a lack of understanding of why and how this basis is distinguished).

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.

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.

scholarly journals FROM VIRASORO CONSTRAINTS IN KONTSEVICH’S MODEL TO ${\mathcal W}$-CONSTRAINTS IN TWO-MATRIX MODELS

1992 ◽  
Vol 07 (15) ◽  
pp. 1345-1359 ◽  
Author(s):  
A. MARSHAKOV ◽  
A. MIRONOV ◽  
A. MOROZOV
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Matrix Model ◽  
Ward Identities ◽  
Virasoro Constraints

The Ward identities in Kontsevich-like one-matrix models are used to prove at the level of discrete matrix models the suggestion of Gava and Narain, which relates the degree of potential in asymmetric two-matrix model to the form of [Formula: see text]-constraints imposed on its partition function.

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 DETERMINING SOURCE CUMULANTS IN FEMTOSCOPY WITH GRAM–CHARLIER AND EDGEWORTH SERIES

2011 ◽  
Vol 26 (24) ◽  
pp. 1771-1782 ◽  
Author(s):  
H. C. EGGERS ◽  
M. B. DE KOCK ◽  
J. SCHMIEGEL
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Fourth Order ◽  
Momentum Space ◽  
Crucial Role ◽  
Gaussian Distributions ◽  
Edgeworth Series ◽  
The Central Limit Theorem ◽  
Non Gaussian

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram–Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for non-Gaussian distributions.

scholarly journals Asymptotics of the partition function of a random matrix model

2005 ◽  
Vol 55 (6) ◽  
pp. 1943-2000 ◽  
Author(s):  
Pavel M. Bleher ◽  
Alexander Its
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Random Matrix ◽  
Random Matrix Model

scholarly journals Quiver matrix model of ADHM type and BPS state counting in diverse dimensions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Hiroaki Kanno
Keyword(s):  
Partition Function ◽  
Matrix Model ◽  
Characteristic Property ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Torus Action ◽  
Localization Theorem ◽  
Counting Problem ◽  
Expectation Value ◽  
Four Dimensions

Abstract We review the problem of Bogomol’nyi–Prasad–Sommerfield (BPS) state counting described by the generalized quiver matrix model of Atiyah–Drinfield–Hitchin–Manin type. In four dimensions the generating function of the counting gives the Nekrasov partition function, and we obtain a generalization in higher dimensions. By the localization theorem, the partition function is given by the sum of contributions from the fixed points of the torus action, which are labeled by partitions, plane partitions and solid partitions. The measure or the Boltzmann weight of the path integral can take the form of the plethystic exponential. Remarkably, after integration the partition function or the vacuum expectation value is again expressed in plethystic form. We regard it as a characteristic property of the BPS state counting problem, which is closely related to the integrability.

scholarly journals SUPERLOOP EQUATIONS AND TWO-DIMENSIONAL SUPERGRAVITY

1992 ◽  
Vol 07 (21) ◽  
pp. 5337-5367 ◽  
Author(s):  
L. ALVAREZ-GAUMÉ ◽  
H. ITOYAMA ◽  
J.L. MAÑES ◽  
A. ZADRA
Keyword(s):  
Partition Function ◽  
Discrete Model ◽  
Continuum Limit ◽  
Basic Assumption ◽  
Scaling Limit ◽  
Integrable Hierarchy ◽  
Two Dimensional ◽  
Virasoro Constraints ◽  
Double Scaling Limit ◽  
The Continuum

We propose a discrete model whose continuum limit reproduces the string susceptibility and the scaling dimensions of (2, 4m) minimal superconformal models coupled to 2D supergravity. The basic assumption in our presentation is a set of super-Virasoro constraints imposed on the partition function. We recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also able to evaluate all planar loop correlation functions in the continuum limit. We find evidence to identify the integrable hierarchy of nonlinear equations describing the double scaling limit as a supersymmetric generalization of KP studied by Rabin.

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