# Matrix Model for Membranes and D-brane Dynamics

#### Kevin_Axion

I was looking through the HEP-th section of arXiv and I noticed this interesting paper, unfortunately the majority of the paper is in Persian.
Subjects: High Energy Physics - Theory (hep-th): http://arxiv.org/abs/1011.2135
Matrix Model for membrane and dynamics of D-Particles in a curved space-time geometry and presence of form fields
Author: Qasem Exirifard
Abstract: We study dynamics of a membrane and its matrix regularisation. We present the matrix regularisation for a membrane propagating in a curved space-time geometry in the presence of an arbitrary 3-form field. In the matrix regularisation, we then study the dynamics of D-particles. We show how the Riemann curvature of the target space-time geometry, or any other form fields can polarise the D-Particles, cause entanglement among them and create fuzzy solutions. We review the fuzzy sphere and we present fuzzy hyperbolic and ellipsoid solutions.

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#### fzero

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Gold Member
That's apparently a master's thesis that was submitted in 2002. I'm sure most of the topics are already covered in Wati Taylor's lectures: http://arxiv.org/abs/hep-th/0002016

#### Kevin_Axion

Yea, I realized that right after I posted it, thanks though.

#### elisir

That's apparently a master's thesis that was submitted in 2002. I'm sure most of the topics are already covered in Wati Taylor's lectures: http://arxiv.org/abs/hep-th/0002016
This is almost right, but not completely.Only some parts are covered in the Taylor's lecture. It cites this ref. whenever it uses it. The parts that are not covered include:

1- How Quantum Mechanics removes the spike instability due to uncertainty principle. Though this is simple, it sounds nice ( this is at the end of the first chapter.)

2- In the second chapter it demonstrates matrix regularisation in the presence of an arbitrary form field, and curved space-time geometry. In so doing it gives an insight why it is better to use the symmetric prescription. (Only within the symmetric prescription, within finite $N$ approximation, there exists no \frac{1}{N} correction in the matrix regularisation to membrane dynamics.)

3- In the last chapter, it shows how each field can entangle D-particles. It presents an ellipsoid solution when the curvature of the space-time is turned on. It also presents a family of the static excitations (with positive energy) of D-particles in curved space-time geometry, a non-compact solution which reads
[x,y]=i\theta
[z,y]=i \sqrt{2M} x
[z,x]= i \sqrt{2M} y
wherein $\theta$ is a free parameter labelling the excitation, and $M$ receives contribution from the Riemann curvature and one-form potential. The Casimir invariant of this algebra reads
J=z - \frac{2 M}{2\theta}(y^2-x^2)
Since the Casimir operator defines the shape' of fuzzy solutions, the above algebra is called the hyperbolic fuzzy solutions`.

btw, this has been my MS thesis in 2002.

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