scholarly journals The Riemann-Hilbert Approach to Double Scaling Limit of Random Matrix Eigenvalues Near the "Birth of a Cut" Transition

2010 ◽  
Author(s):  
M. Y. Mo
Keyword(s):  
Random Matrix ◽  
Scaling Limit ◽  
Matrix Eigenvalues ◽  
Double Scaling Limit

N = ½ SUPERSTRING IN ZERO DIMENSION AND THE SPONTANEOUS BREAKDOWN OF THE SUPERSYMMETRY

1992 ◽  
Vol 07 (32) ◽  
pp. 2979-2989 ◽  
Author(s):  
SHIN’ICHI NOJIRI
Keyword(s):  
Matrix Models ◽  
Random Matrix ◽  
Continuum Limit ◽  
Scaling Limit ◽  
Partition Functions ◽  
Spontaneous Breakdown ◽  
Random Matrix Models ◽  
Double Scaling Limit ◽  
The Continuum ◽  
String Theories

We propose random matrix models which have N=1/2 supersymmetry in zero dimension. The supersymmetry breaks down spontaneously. It is shown that the double scaling limit can be defined in these models and the breakdown of the supersymmetry remains in the continuum limit. The exact non-trivial partition functions of the string theories corresponding to these matrix models are also obtained.

scholarly journals Painlevé I double scaling limit in the cubic random matrix model

2016 ◽  
Vol 05 (02) ◽  
pp. 1650004 ◽  
Author(s):  
Pavel Bleher ◽  
Alfredo Deaño
Keyword(s):  
Asymptotic Behavior ◽  
Partition Function ◽  
Matrix Model ◽  
Random Matrix ◽  
Scaling Limit ◽  
Descent Method ◽  
Steepest Descent Method ◽  
Recurrence Coefficients ◽  
Random Matrix Model ◽  
Double Scaling Limit

We obtain the double scaling asymptotic behavior of the recurrence coefficients and the partition function at the critical point of the [Formula: see text] Hermitian random matrix model with cubic potential. We prove that the recurrence coefficients admit an asymptotic expansion in powers of [Formula: see text], and in the leading order the asymptotic behavior of the recurrence coefficients is given by a Boutroux tronquée solution to the Painlevé I equation. We also obtain the double scaling limit of the partition function, and we prove that the poles of the tronquée solution are limits of zeros of the partition function. The tools used include the Riemann–Hilbert approach and the Deift–Zhou nonlinear steepest descent method for the corresponding family of complex orthogonal polynomials and their recurrence coefficients, together with the Toda equation in the parameter space.

scholarly journals Characters of irrelevant deformations

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Shouvik Datta ◽  
Yunfeng Jiang
Keyword(s):  
Deformation Parameter ◽  
Central Charge ◽  
Scaling Limit ◽  
Small Deformation ◽  
State Dependent ◽  
Dependent Change ◽  
Left And Right ◽  
Double Scaling Limit

Abstract We analyse the $$ T\overline{T} $$ T T ¯ deformation of 2d CFTs in a special double-scaling limit, of large central charge and small deformation parameter. In particular, we derive closed formulae for the deformation of the product of left and right moving CFT characters on the torus. It is shown that the 1/c contribution takes the same form as that of a CFT, but with rescalings of the modular parameter reflecting a state-dependent change of coordinates. We also extend the analysis for more general deformations that involve $$ T\overline{T} $$ T T ¯ , $$ J\overline{T} $$ J T ¯ and $$ T\overline{J} $$ T J ¯ simultaneously. We comment on the implications of our results for holographic proposals of irrelevant deformations.

scholarly journals THE CRITICAL POINT OF UNORIENTED RANDOM SURFACES WITH A NONEVEN POTENTIAL

1993 ◽  
Vol 08 (06) ◽  
pp. 1139-1152
Author(s):  
M.A. MARTÍN-DELGADO
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Critical Point ◽  
Discrete Model ◽  
Recursion Relation ◽  
Scaling Limit ◽  
Random Surfaces ◽  
Matrix Ensemble ◽  
Quartic Interaction ◽  
Double Scaling Limit

The discrete model of the real symmetric one-matrix ensemble is analyzed with a cubic interaction. The partition function is found to satisfy a recursion relation that solves the model. The double scaling-limit of the recursion relation leads to a Miura transformation relating the contributions to the free energy coming from oriented and unoriented random surfaces. This transformation is the same kind as found with a quartic interaction.

scholarly journals Hexagon bootstrap in the double scaling limit

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Vsevolod Chestnov ◽  
Georgios Papathanasiou
Keyword(s):  
Function Space ◽  
Operator Product Expansion ◽  
General Pattern ◽  
Scaling Limit ◽  
Kinematic Region ◽  
Operator Product ◽  
Yang Mills ◽  
Codimension One ◽  
Double Scaling Limit ◽  
Super Yang Mills Theory

Abstract We study the six-particle amplitude in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory in the double scaling (DS) limit, the only nontrivial codimension-one boundary of its positive kinematic region. We construct the relevant function space, which is significantly constrained due to the extended Steinmann relations, up to weight 13 in coproduct form, and up to weight 12 as an explicit polylogarithmic representation. Expanding the latter in the collinear boundary of the DS limit, and using the Pentagon Operator Product Expansion, we compute the non-divergent coefficient of a certain component of the Next-to-Maximally-Helicity-Violating amplitude through weight 12 and eight loops. We also specialize our results to the overlapping origin limit, observing a general pattern for its leading divergences.

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