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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questions
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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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votes
1answer
16 views
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
$$
R(E) = -\int_0^\infty d\beta\ e^{\beta E} Z(\beta)
$$
...
1
vote
1answer
13 views
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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1answer
128 views
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 ...
6
votes
1answer
179 views
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 ...
2
votes
1answer
31 views
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
...
1
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1answer
47 views
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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1answer
90 views
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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1answer
78 views
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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1answer
32 views
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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0answers
40 views
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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votes
1answer
81 views
$\delta^{(2)}$ 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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0answers
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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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0answers
45 views
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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1answer
351 views
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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92 views
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:
$$
Z(g) = \int \mathcal{D}M(t) \exp \left[ -\text{tr}\int dt \left( \frac{1}{2} \dot{M}^2(t)+V(M) \...
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votes
0answers
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How to get the eigenvalue density contribution $\rho_1(x)$?
I'm studying the $1/N$ expansion beyond the planar limit in matrix models. Currently I'm trying to understand and reproduce the results of:
Antisymmetric Wilson loops in $\mathcal N \geq 4$ SYM ...
1
vote
1answer
779 views
Basis of eigenvectors common to H and B
Considering a three-dimensional state space spanned by the orthonormal basis formed by the three kets $|u_1\rangle,|u_2\rangle,|u_3\rangle $. In the basis of these three vectors, taken in order, are ...
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votes
1answer
544 views
Hamiltonian matrix for a delta potential with periodic boundary condition
I'm trying to find the energy eigenvalues of a Dirac delta potential:
$$V(x)=-\alpha\delta(x)$$
with periodic boundary condition over some length $L$:
$$\psi(x+L)=\psi(x)$$
and only even ...
3
votes
0answers
107 views
Massless limit of Matrix Quantum Mechanics
I am working on a Matrix Quantum Mechanics model that is related to 2d string theory as defined here: http://arxiv.org/abs/hep-th/0311273 §Chapter III
The action is defined as $$
S = \text{Tr} \int ...
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0answers
26 views
Lumped mechanical system - Base Change and asymmetric matrices
Let's assume I have a system which can be wrote as:
$$ \underbrace{\begin{bmatrix}
m_{1} & 0 & \dots & 0 \\
0 & m_{2} & \...
3
votes
1answer
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Gaussian beam propagation with ABCD matrix through a grin lens
I am currently trying to simulate a Gaussian beam that has a transverse offset of around 20um from the optic axis where the Gaussian beam travels through a grin lens using the ABCD matrix method. I ...
3
votes
1answer
161 views
Generalization of Itzykson-Zuber Formula to Path Integrals?
Some Background: In mathematical physics (matrix quantum mechanics in particular), one often runs into path integrals of the form:
$$ Z = \int \prod_{ab} DM^1_{ab}(\tau) DM^2_{ab}(\tau) e^{-NS(M^1,M^2,...
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vote
2answers
467 views
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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vote
1answer
345 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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0answers
62 views
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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2answers
510 views
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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2answers
563 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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1answer
324 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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0answers
214 views
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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0answers
159 views
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,...
3
votes
1answer
721 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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2answers
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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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0answers
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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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votes
2answers
750 views
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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1answer
217 views
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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votes
1answer
1k views
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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votes
0answers
322 views
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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0answers
217 views
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
$$Z \sim \int \prod_{i=1}^r ...
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votes
0answers
125 views
Degrees of freedom in m(atrix) theory
The Hamiltonian for m(atrix) theory is given by
$$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).$$
Where $X^...
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votes
1answer
384 views
Dimensional reduction of Yang-Mills to m(atrix) theory
The Yang-Mills action are usually given by $$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)$$
with the field strength defined ...
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votes
1answer
812 views
Diagonalize mass matrix term for fermions and “doubling trick” in m(atrix) theory
Can someone help me understand the "Doubling trick" at page 36 in http://inspirehep.net/record/887513/files/sis-2002-060.pdf (named "Scattering in Supersymmetric M(atrix) Models" by Robert Helling) or ...
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Questions about Type HE Matrix String Theory
I was reading the heterotic string section of this thesis desertation by Luboš Motl, since I think I now understand the Type IIA Matrix String Theory. The only thing I knew about Type HE Matrix ...
asked Sep 28 '13 at 9:30
Abhimanyu Pallavi Sudhir
5,7954 gold badges31 silver badges48 bronze badges
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1answer
955 views
M(atrix) theory and things other than D0-branes? And is it non-peturbative M-theory or non-peturbative Type IIA theory?
When I first read the BFSS Paper on M(atrix)-theory, I was under the impression that it was a non-peturbative formulation of M-theory. But recently, upon reading this paper of Nathan Seiberg's, I ...
asked Jun 21 '13 at 9:48
Abhimanyu Pallavi Sudhir
5,7954 gold badges31 silver badges48 bronze badges
8
votes
0answers
293 views
$U(N)$ gauged quantum mechanics
I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic?
The action I am interested in is
$$...
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votes
1answer
195 views
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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1answer
232 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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2answers
757 views
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. ...
