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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Basis and inner product of the Dirac (Clifford) algebra
The Dirac algebra in 4D spacetime is composed of four $4\times 4$ gamma matrices $\{\gamma^\mu\}=\{\gamma^0,\gamma^1,\gamma^2,\gamma^3\}$ satisfying the following anticommutation relation:
$$\{\gamma^\...
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Phase transition of shift of energy level under small perturbation in random matrix theory
I'm a mathematician and I'm thinking about a question in random matrix theory.
Suppose $H_0$ is a $N\times N$ GUE random matrix (variance of each element is $\frac{1}{N}$). We consider a small ...
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Fuzzy Spheres in the Large-$N$ Limit
My question concerns fuzzy sphere solutions and how they fit into the large-$N$ limit of gauge theory.
The Berenstein-Maldacena-Natasse (BMN) model is a matrix model that arises in string theory. The ...
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Reference request: scalar $O(N)$ gauge theory
I am interested in scalar $O(N)$ gauge theory and what you can do with it. Is there a standard reference section in a textbook/monograph/paper/whatever that has a decent overview?
Wikipedia has a ...
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Different definitions of resolvent in matrix model
When I study the matrix models, I get confused of different definations of resolvent. After we define the partition function as
$$Z=\int[dM]e^{-NTrV(M)},$$
where $V(M)$ is a matrix valued function of $...
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What kind of combinations of field components are equal under $SO(9)$ symmetry?
My question is a bit long and chaotic since I haven't learnt group theory systematically.
I am looking at the Banks-Fischler-Shenker-Susskind (BFSS) matrix model. It consists of 9 bosonic matrices $...
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Implementation of Hamiltonian coupling to a bath
I want to study a system coupled to a bath, however I do not fully understand how to implement/think of the Hamiltonian. For simplicity say the bath is given by a spin chain (PBC), e.g. Ising-like
$$...
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How does the matrix model simplify path integral?
While I'm reading the introduction of matrix models in Chapter 8 in Mariño's book(https://doi.org/10.1017/CBO9781107705968), I notice this description of matrix model:
We will begin by a drastic ...
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Does any matrix integral with arbitrary potential has a 2D gravity dual?
Regarding the duality between matrix ensembles and gravity, the relationship has indeed been discussed in various papers, including arXiv:1903.11115, arXiv:1907.03363, and arXiv:2006.13414, among ...
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How to calculate the component term in BFSS matrix model?
I'm reading articles about BFSS, and confused by the calculation.
The Hamiltonian is
$$
H=\frac{g^2}{2}TrP_{I}^{2}-\frac{1}{4g^2}Tr[X_{I},X_{J}]^2
-\frac{1}{2}Tr\psi_{\alpha}\gamma_{\alpha \beta}^{I}[...
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What does the matrix mean in matrix models?
I'm learning what a matrix model means, for example, in Yang–Mills matrix models, IKKT matrix model and BFSS matrix model. I have consulted a large amount of information but still not sure what the ...
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Do matrix models capture the string landscape?
Essentially what the title asks-- are matrix models, such as BFSS, believed to capture in any way the large possible space of false string vacua, for instance as saddles in the action with nonminimal ...
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Why does the eigenvalues of an angular frequency matrix are the natural frequency? (INTUITION)
lest say we have a system of differential equations of some coupled oscillator such that:
$$\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\left(\frac{1}{2}\{ \ \dot X^i \dot X^i - \frac{1}{2}[X^i,X^j] + \theta^T \gamma_i[X^i,\...
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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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