# Questions tagged [matrix-model]

A matrix model is a non-peturbative formulation of a theory, such as string theory based on Matrix quantum mechanics

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### Reference request: scalar $O(N)$ gauge theory

I am interested in scalar $O(N)$ gauge theory and what you can do with it. Is there a standard reference section in a textbook/monograph/paper/whatever that has a decent overview? Wikipedia has a ...
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### What does the matrix mean in matrix models?

I'm learning what a matrix model means, for example, in Yang–Mills matrix models, IKKT matrix model and BFSS matrix model. I have consulted a large amount of information but still not sure what the ...
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### Do matrix models capture the string landscape?

Essentially what the title asks-- are matrix models, such as BFSS, believed to capture in any way the large possible space of false string vacua, for instance as saddles in the action with nonminimal ...
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### Why does the eigenvalues of an angular frequency matrix are the natural frequency? (INTUITION)

lest say we have a system of differential equations of some coupled oscillator such that: $$\overrightarrow a = [w^2]\overrightarrow x$$ if we find the eigenvalues of $[w^2] = \lambda$ why those ...
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### What are the 9 matrices used in the BFSS model of quantum mechanics?

The BFSS matrix model (Wikipedia) "describes the behavior of nine large matrices" using $$H = Tr(\frac{1}{2}\{\dot X^i \dot X^i - \frac{1}{2}[X^i,X^j] + \theta^T \gamma_i[X^i,\theta]\})$$ ...
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### Dirac delta of matrix argument - Matrix model path integral vs Hilbert space

Assume a Hamiltonian $H$ with $N$ orthonormal eigenstates $\{\vert n\rangle\}$ of energies $\epsilon_n$. One can define a density of states, \begin{align} \rho(E)&=\mathrm{tr}\,\hat{\delta}(E-\hat{...
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### Jackiw-Teitelboim (JT) gravity as a matrix integral

I am reading https://arxiv.org/abs/1903.11115 by Saad, Shenker and Stanford. They relate an (averaged) $n$-point function in a random double-scaled matrix model to a path integral genus expansion in ...
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### Gaussian Matrix Integral

I couldn't quite understand how we calculate the Gaussian Matrix Integral $$\mathcal{Z}=\int dM\ e^{-N\text{tr}\left(\frac{1}{2}M^2+JM\right)},$$ where the integration measure $dM$ over the $N$ by $N$ ...
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### Difference between resolvent and degeneracy

I am studying https://arxiv.org/abs/1903.11115. In equation (62), the resolvent is defined as the integral transform of partition function as $$R(E) = -\int_0^\infty d\beta\ e^{\beta E} Z(\beta)$$ ...
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### Analytical expression for density of random matrix level ratios

Consider a hermitian matrix $H$ with eigenvalues $E_{i-1}<E_i$. The level spacings are defined as $s_i=E_i-E_{i-1}$ and the level ratios as $r_i = s_i/s_{i-1}$. To make the support of an underlying ...
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### Matrix Integrals, Riemann Surfaces & Black Holes. A question regarding one of J.M. Maldacena's talks

I was watching this presentation of Juan Martin Maldacena at Princeton: https://www.youtube.com/watch?v=OMb_P5qPpMc&ab_channel=GraduatePhysics. In one slide he shows an interesting integral. (I ...
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### How can I show that $1/N$ expansion for large $N$ matrix models have a string theoretical perturbation expansion?

While surfing through some further reading suggestions on string theory, I stumbled upon this slide from a talk by Nathan Seiberg. I wanted to derive the main argument by applying a perturbation ...
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### Why is a static potential between supergravitons problematic?

When deriving the one and two-loop result for the effective potential between two scattering supergravitons, for example from here, we see that it is always a velocity dependent potential. ...
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### Validity of DLCQ Matrix Theory near the Big Bang

In this paper,section 3.2, Craps, Sethi and Verlinde claim that DLCQ matrix theory is valid near the big bang if The open string oscillators decouple and Gravity decouples from the matrix description ...
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### Why is there an additional $NI$ term in this ${\rm SU}(N)$ generator, from Matrix Quantum Mechanics?

This question refers to equation (11) in the latest preprint of the following paper: X. Han, S. A. Hartnoll and J. Kruthoff, "Bootstrapping Matrix Quantum Mechanics", Phys. Rev. Lett. 125, ...
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### Applications of the Gaussian unitary ensemble

It is well known that the pair correlation function of the zeros of the Riemann zeta function reproduces the correlation function of the random matrices from the Gaussian unitary ensemble (GUE). ...
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### How are the saddle-point equations derived in the single random matrix model?

In this question, I'm referring to a specific step in https://arxiv.org/abs/hep-th/9306153. I want to reproduce equation (2.4) on page 15. I think I lack the experience required for dealing with ...
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### Equivalence of 2d quantum and topological gravity

I have heard of the statement that 2d quantum gravity (defined as minimal models of CFT coupled to Liouville theory) and 2d topological gravity are equivalent. The former is described by the continuum ...
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### Good starting point for quantum Hall matrix models

I am a recent Masters in theoretical condensed matter physics and have experience in working on topological insulators and Weyl semimetals. I have also dabbled a bit in the fractional quantum Hall ...
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### Can we generalize matrix model theory?

As in the question, can matrix model theory be generalized to a tensor model theory? Will the results be different or useful in describing real world phenomena? Details: in matrix model theory we ...
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### $\delta^{(2)}$ convention

In this note: https://arxiv.org/abs/hep-th/0410165 at page 12 there is a delta-function constraint written as: \begin{align} \delta \left( ^ { U } M \right) = \prod _ { i < j } \delta ^ { ( 2 ) } \...
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### Simultaneous shifted diagonalization of bunch of operators

I have the following Lie algebra which is generated by $\{L_n|n\geq 0\}.$ It satisfies the following commutation rule $$\Big[ L_i ,L_j \Big]= (i-j)(L_{i+j}-\frac14 L_{i+j-1}).....*$$ My question is ...
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### Singular behavior of pure gravity

Can anyone plese explain what means singular part of partition function for pure gravity? Let me specify my question. I am dealing with 2D quantum gravity and starts from path integral formulation of ...
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### How to relate random matrix theory with Quantum mechanics approach

In Quantum mechanics we first built Hamiltonian and then find its eigenvalues and eigenvectors. How I can relate this with random matrix theory?
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### References to Random Matrix Theory

I am looking for some good references - books/lecture notes/articles which contains Random Matrix Theory for Physicists. I am not particularly looking for mathematical rigor in derivations. I am more ...
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### Relation between $1/N$ and perturbative expansions in QFT

I heard many times phrases like "large $N$ is a clever way to organize the diagrammatic expansion" or "each diagram in the large $N$ expansion contains an infinite number of usual perturbative ...
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