scholarly journals Emergent geometry and gravity from matrix models: an introduction

2010 ◽  
Vol 27 (13) ◽  
pp. 133001 ◽  
Author(s):  
Harold Steinacker
Keyword(s):  
Matrix Models ◽  
Emergent Geometry

scholarly journals Quantum gravity as a multitrace matrix model

2017 ◽  
Vol 32 (31) ◽  
pp. 1750180
Author(s):  
Badis Ydri ◽  
Cherine Soudani ◽  
Ahlam Rouag
Keyword(s):  
Quantum Gravity ◽  
Matrix Models ◽  
Large Class ◽  
Matrix Model ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Topology Change ◽  
New Model ◽  
And Topology ◽  
Emergent Geometry

We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of two-dimensional quantum gravity which works away from two dimensions and captures a large class of spaces admitting a finite spectral triple. These multitrace matrix models sustain emergent geometry as well as growing dimensions and topology change.

scholarly journals Emergent geometry from random multitrace matrix models

2016 ◽  
Vol 93 (6) ◽  
Author(s):  
B. Ydri ◽  
A. Rouag ◽  
K. Ramda
Keyword(s):  
Matrix Models ◽  
Emergent Geometry

scholarly journals Probing emergent geometry through phase transitions in free vector and matrix models

2017 ◽  
Vol 2017 (2) ◽  
Author(s):  
Irene Amado ◽  
Bo Sundborg ◽  
Larus Thorlacius ◽  
Nico Wintergerst
Keyword(s):  
Phase Transitions ◽  
Matrix Models ◽  
Emergent Geometry

scholarly journals IMPACT OF SUPERSYMMETRY ON EMERGENT GEOMETRY IN YANG–MILLS MATRIX MODELS II

2012 ◽  
Vol 27 (17) ◽  
pp. 1250088 ◽  
Author(s):  
BADIS YDRI
Keyword(s):  
Matrix Models ◽  
Transition Point ◽  
Joint Probability ◽  
Gauge Coupling ◽  
Second Order ◽  
Joint Probability Distribution ◽  
Fuzzy Sphere ◽  
Yang Mills ◽  
Commuting Matrices ◽  
Emergent Geometry

We present a study of D = 4 supersymmetric Yang–Mills matrix models with SO(3) mass terms based on the Monte Carlo method. In the bosonic models we show the existence of an exotic first-/second-order transition from a phase with a well defined background geometry (the fuzzy sphere) to a phase with commuting matrices with no geometry in the sense of Connes. At the transition point the sphere expands abruptly to infinite size then it evaporates as we increase the temperature (the gauge coupling constant). The transition looks first-order due to the discontinuity in the action whereas it looks second-order due to the divergent peak in the specific heat. The fuzzy sphere is stable for the supersymmetric models in the sense that the bosonic phase transition is turned into a very slow crossover transition. The transition point is found to scale to zero with N. We conjecture that the transition from the background sphere to the phase of commuting matrices is associated with spontaneous supersymmetry breaking. The eigenvalues distribution of any of the bosonic matrices in the matrix phase is found to be given by a nonpolynomial law obtained from the fact that the joint probability distribution of the four matrices is uniform inside a solid ball with radius R. The eigenvalues of the gauge field on the background geometry are also found to be distributed according to this nonpolynomial law.

scholarly journals Multi-matrix models and emergent geometry

2009 ◽  
Vol 2009 (02) ◽  
pp. 010-010 ◽  
Author(s):  
David E Berenstein ◽  
Masanori Hanada ◽  
Sean A Hartnoll
Keyword(s):  
Matrix Models ◽  
Emergent Geometry

scholarly journals Matrix models, gauge theory and emergent geometry

2009 ◽  
Vol 2009 (05) ◽  
pp. 049-049 ◽  
Author(s):  
Rodrigo Delgadillo-Blando ◽  
Denjoe O'Connor ◽  
Badis Ydri
Keyword(s):  
Gauge Theory ◽  
Matrix Models ◽  
Emergent Geometry

scholarly journals Genus expansion of matrix models and ћ expansion of KP hierarchy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Special Interest ◽  
Hermitian Matrix ◽  
Geometric Meaning ◽  
Kp Hierarchy ◽  
Hurwitz Numbers ◽  
Kp Equations ◽  
Genus Expansion ◽  
Hermitian Matrix Model

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

Sign in / Sign up

Export Citation Format

Share Document