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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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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How to calculate correlators in a 1D Conformally invariant Matrix Model?

I am working on a 1D Conformally invariant Matrix Model with the following Partition function: $$ Z(g) = \int \mathcal{D}M(t) \exp \left[ -\text{tr}\int dt \left( \frac{1}{2} \dot{M}^2(t)+V(M) \...
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How to get the eigenvalue density contribution $\rho_1(x)$?

I'm studying the $1/N$ expansion beyond the planar limit in matrix models. Currently I'm trying to understand and reproduce the results of: Antisymmetric Wilson loops in $\mathcal N \geq 4$ SYM ...
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517 views

Basis of eigenvectors common to H and B

Considering a three-dimensional state space spanned by the orthonormal basis formed by the three kets $|u_1\rangle,|u_2\rangle,|u_3\rangle $. In the basis of these three vectors, taken in order, are ...
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437 views

Hamiltonian matrix for a delta potential with periodic boundary condition

I'm trying to find the energy eigenvalues of a Dirac delta potential: $$V(x)=-\alpha\delta(x)$$ with periodic boundary condition over some length $L$: $$\psi(x+L)=\psi(x)$$ and only even ...
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Massless limit of Matrix Quantum Mechanics

I am working on a Matrix Quantum Mechanics model that is related to 2d string theory as defined here: http://arxiv.org/abs/hep-th/0311273 §Chapter III The action is defined as $$ S = \text{Tr} \int ...
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Lumped mechanical system - Base Change and asymmetric matrices

Let's assume I have a system which can be wrote as: $$ \underbrace{\begin{bmatrix} m_{1} & 0 & \dots & 0 \\ 0 & m_{2} & \...
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Gaussian beam propagation with ABCD matrix through a grin lens

I am currently trying to simulate a Gaussian beam that has a transverse offset of around 20um from the optic axis where the Gaussian beam travels through a grin lens using the ABCD matrix method. I ...
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1answer
150 views

Generalization of Itzykson-Zuber Formula to Path Integrals?

Some Background: In mathematical physics (matrix quantum mechanics in particular), one often runs into path integrals of the form: $$ Z = \int \prod_{ab} DM^1_{ab}(\tau) DM^2_{ab}(\tau) e^{-NS(M^1,M^2,...
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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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1answer
306 views

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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Matching measured eigenvalue of a matrix [closed]

Given a Matrix of the form below, we have 8 variables, $\omega_{i}$ and $J_{ij}$. we want to diagonalise the Matrix to obtain values to match the observed Eigenvalue in an Experiment. i.e. $\bar{\...
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Emergence of space from quantum mechanics

Once talking to a visiting professor at my institute, I heard about some simple model that captures the emergence of space coordinates as the eigenvalues of some infinite-dimensional quantum ...
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500 views

How are unitary matrices and unitary random matrices associated with physics or quantum mechanics? [closed]

Please forgive my ignorance, my back ground is not physics. I am looking for distance measure between two unitary matrix (for my work). So my starting point is where else unitary matrix is applicable?...
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301 views

ADHM construction and Momentum Map

while I was reading about ADHM construction I had some troubles with precise geometrical identification of the various quantities. My doubts is well manifest in these two Wikipedia pages 1) ADHM ...
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Chern Simons Theory over S^3 as integral - what is domain of integration?

I found these nice lecture notes Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories so I am hoping to understand some parts of the Chern Simons theory better. ...
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Bloch's theorem for Semi-Infinite Lattice

If we have a lattice Hamiltonian $$ \sum_{n'\in\mathbb{Z}}H_{n,n'}\psi_{n'} = E\psi_{n} \,\forall n\in\mathbb{Z} $$ such that $ H_{n,n'} = H_{n+q,n'+q}$ for some $q\in\mathbb{N}$ and for all $\left(n,...
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654 views

On the Equivalence of Schrodinger and Heisenberg Descriptions of Quantum Mechanics and Observability

I'm not a physicist, but rather a control (feedback) systems engineer eager to understand more than just a cursory explanation of quantum mechanics. The StackExchange has been an excellent forum for ...
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What information does the trace of a matrix give?

I was recently thinking what information do we get from a matrix. So if we say the columns (or rows) of a matrix define the basis of a system, say vectors of 3 dimensional space. Then the determinant ...
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What is the current state of research about the Hayden-Preskill circuit? [duplicate]

Can someone summarize as to what are the problems and/or the open questions with the Hayden-Preskill circuit? (in the context of understanding black-holes or as a computer science question)It gives a ...
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Is there a physical interpretation to invariant random matrix ensembles?

Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
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The curvature of the space of commuting hermitian matrices

This is a question that I asked in the mathematics section, but I believe it may get more attention here. I am working on a project dedicated to the quantisation of commuting matrix models. In the ...
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What do matrices in the Gaussian orthogonal ensemble look like?

I've been reading a fair amount about quantum chaos, and random matrix theory comes up a lot. I get that they're looking at the distribution of eigenvalues from an ensemble of random matrices, but I ...
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Relation between holography and matrix models

Let's consider a 0-dimensional $N \times N$ Hermitean one matrix model. It is defined by a potential V(M). Its partition function is $$Z = \int_{H_{N}} dM e^{-\frac{1}{g}V(M)}$$ where $H_{N}$ is the ...
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Matrix integral in multi-matrix model

Though it is a mathematical problem, maybe more physicists know it well. In quiver matrix model which is reviewed DV or CKR, the path integral reduce to the matrix integral $$Z \sim \int \prod_{i=1}^r ...
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Degrees of freedom in m(atrix) theory

The Hamiltonian for m(atrix) theory is given by $$H=\frac{1}{2\lambda}\text{Tr}\left(P^{a}P_{a}+\frac{1}{2}\left[X^{a},X^{b}\right]^{2}+\theta^{T}\gamma_{a}\left[X^{a},\theta\right]\right).$$ Where $X^...
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Dimensional reduction of Yang-Mills to m(atrix) theory

The Yang-Mills action are usually given by $$S= \int\text{d}^{10}\sigma\,\text{Tr}\left(-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-\theta^{T}\gamma^{\mu}D_{\mu}\theta\right)$$ with the field strength defined ...
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Diagonalize mass matrix term for fermions and “doubling trick” in m(atrix) theory

Can someone help me understand the "Doubling trick" at page 36 in http://inspirehep.net/record/887513/files/sis-2002-060.pdf (named "Scattering in Supersymmetric M(atrix) Models" by Robert Helling) or ...
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Questions about Type HE Matrix String Theory

I was reading the heterotic string section of this thesis desertation by Luboš Motl, since I think I now understand the Type IIA Matrix String Theory. The only thing I knew about Type HE Matrix ...
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M(atrix) theory and things other than D0-branes? And is it non-peturbative M-theory or non-peturbative Type IIA theory?

When I first read the BFSS Paper on M(atrix)-theory, I was under the impression that it was a non-peturbative formulation of M-theory. But recently, upon reading this paper of Nathan Seiberg's, I ...
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$U(N)$ gauged quantum mechanics

I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic? The action I am interested in is $$...
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Schwarzschild radius in matrix models

The Schwarzschild radius for 11D BHs is given by $l_{11}(l_{11}m)^{1/8}$, which is the special case ($D=11$) of the general dimensional case of $(G_Dm)^{\frac{1}{D-3}}$. Here $m$ is the BH mass and $...
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218 views

M-theory on a Planck scale torus

We know that 11D M-theory is described by BFSS matrix model and for M-theory on a torus $T^p$ (at least for small $p$s) the description is given by SYM theory in $p+1$ dimensions by using the ...
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Path integral on matrix model

I was looking at a 0-dimensional matrix model, where the variables are $N\cdot N$ Hermitean matrices. It had a gauge symmetry, e.g. $U(N)$. And in the path integral, the Faddeev-Popov trick was used. ...
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random matrix ensembles from BMN model

My friends working on Thermalization of Black Holes explained solutions to their matrix-valued differential equations (from numerical implementation of the Berenstein-Maldacena-Nastase matrix model) ...
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Advanced topics in string theory

I'm looking for texts about topics in string theory that are "advanced" in the sense that they go beyond perturbative string theory. Specifically I'm interested in String field theory (including ...
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Matrix geometry for F-strings

A stack of N D-branes has the strange property that the traverse D-brane coordinates are matrix-valued. When the matrices commute, they can be interpreted as ordinary coordinates for N ...
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Good introductory text for matrix string theory

Where can I find a good introductory text for matrix string theory? Most textbooks don't cover it, or only cover it very superficially. What is the basic idea behind matrix string theory? How can ...