scholarly journals Comment on “The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization”

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Carlos I. Perez-Sanchez
Keyword(s):  
Phase Diagram ◽  
Matrix Model ◽  
Loop Structure ◽  
The One

Abstract Recently, [JHEP12 131 (2020)] obtained (a similar, scaled version of) the (a, b)-phase diagram derived from the Kazakov-Zinn-Justin solution of the Hermitian two-matrix model with interactions$$ -\mathrm{Tr}\left\{\frac{a}{4}\left({A}^4+{B}^4\right)+\frac{b}{2} ABAB\right\}, $$ − Tr a 4 A 4 + B 4 + b 2 ABAB , starting from Functional Renormalization. We comment on something unexpected: the phase diagram of [JHEP12 131 (2020)] is based on a βb-function that does not have the one-loop structure of the Wetterich-Morris equation. This raises the question of how to reproduce the phase diagram from a set of β-functions that is, in its totality, consistent with Functional Renormalization. A non-minimalist, yet simple truncation that could lead to the phase diagram is provided. Additionally, we identify the ensemble for which the result of op. cit. would be entirely correct.

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.

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 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.

The Phase Diagram of the One-Dimensional Extended Hubbard Model

1995 ◽  
pp. 315-326 ◽  
Author(s):  
H. Q. Lin ◽  
E. R. Gagliano ◽  
D. K. Campbell ◽  
E. H. Fradkin ◽  
J. E. Gubernatis
Keyword(s):  
Phase Diagram ◽  
Hubbard Model ◽  
Extended Hubbard Model ◽  
One Dimensional ◽  
The One

Phase diagram of the one-dimensional t−J model

1992 ◽  
Vol 82 (7) ◽  
pp. 523-525 ◽  
Author(s):  
K. Hallberg ◽  
C.A. Balseiro
Keyword(s):  
Phase Diagram ◽  
One Dimensional ◽  
The One

scholarly journals MATRIX MODEL PERTURBED BY HIGHER ORDER CURVATURE TERMS

1992 ◽  
Vol 07 (33) ◽  
pp. 3081-3100 ◽  
Author(s):  
G.P. KORCHEMSKY
Keyword(s):  
Phase Diagram ◽  
Matrix Model ◽  
Critical Behavior ◽  
Intermediate Phase ◽  
Higher Order ◽  
Bosonic String ◽  
Branched Polymers ◽  
Nonlocal Term ◽  
Random Surfaces ◽  
The Third

The critical behavior of the D=0 matrix model with the potential perturbed by a nonlocal term generating touchings between random surfaces is studied. It is found that the phase diagram of the model has many features of the phase diagram of discretized Polyakov’s bosonic string with higher order curvature terms included. It contains the phase of smooth (Liouville) surfaces, the intermediate phase and the phase of branched polymers. The perturbation becomes irrelevant at the first phase and dominates at the third one.

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