Thank you for your answers!
Does statement (2) mean that the metric is generally an (0,2) tensor under diffeomorphisms, but a scalar in a Lorentz invariant theory? Also, the notion of Lorentz invariance is "independent" of Lorentz transformations, i.e. the notion of Lorentz transformations...
This is a very basic question, but I cannot get my head around the following: Any physical system should be invariant under changes of coordinates, because these are just a way of parametrizing the manifold/space in which my physical system is embedded.
Now, let us consider a system that...
The eigenfunctions you have written down in your relevant equations are those in 1D but we have a 2D system, so an eigenfunction of the full problem has the form
\psi_{mn}(x,y)=\psi_{m}(x)\psi_{n}(y)
where m and n label the solutions you have given.
Now, the energy of such a solution is just...
Homework Statement
The statistical and spectral functions for bosonic operators \phi_a are:
G_{ab}(t,\vec{x})=\frac{1}{2}\langle \{\phi_a(t,\vec{x}),\phi_b(0,\vec{0})\}\rangle ,
\rho_{ab}(t,\vec{x})=\langle [\phi_a(t,\vec{x}),\phi_b(0,\vec{0})]\rangle .
The expectation values are in...
This is still not very clear to me:
The string theory parameters \alpha'=l_s^2 (where l_s is the string length) and g_s are related to N,\lambda via
\frac{\lambda}{N}=4\pi g_s,
\lambda=\frac{L^4}{\alpha'^2},
where L is the AdS-radius.
\frac{1}{\sqrt{\lambda}} is also the string...
Your result doesn't make sense. You cannot add quantities with different units! You didn't use the formula correctly: the spacetime interval is given by
(\Delta s)^2=c^2(\Delta t^2)-(\Delta x)^2.
Only the time interval is multiplied with c^2.
You just calculate the difference between points...
Thank you, but could you be a bit more precise, please. From comparing the given result and what I got so far I should be able to show:
-dt^2r^2-d\psi^2y^2=R^2(-\mu^2(dx^+)^2+\mu^2(dx^+)^2)-\mu^2r^2(dx^+)^2-\mu^2y^2(dx^+)^2
The left hand sinde are those quadratic terms from the expansion of \cos...
Homework Statement
My question is about a step in the lecture notes [http://arxiv.org/abs/hep-th/0307101] on page 6, and it is probably quite trivial:
I want to see why a lightlike particle in AdS_5\times S^5 sees the metric as plane wave background. The metric is
ds^2=R^2(-dt^2...
The standard reference is a review by Ginsparg: http://arxiv.org/abs/hep-th/9108028
It is quite readable, but does not contain references to statistical physics. You might find it too mathematical.
A nice set of video lectures from Perimeter Institute are these...
Many thanks for your answer. I have some questions remaining:
1. You say it is "logically possible" that the duality only holds in certain limits. Do you mean that, because there is no proper proof, we simply cannot exclude the possibility that the duality does not hold generally?
2. In...
Hi, sorry for the quite long text. Thanks in advance for any help!
I am a little confused about the different limits in which the AdS/CFT correspondence is conjectured to hold in its stong, intermediate, weak form.
I am trying to understand the correspondence motivated by Maldacena's...
Could you tell me why it is r and not r^2? Don't I get one factor of r from the Jacobian when I go to polar coordinates in the integral plus another factor of r from the determinant in the square root?
Thanks, that helped a lot. However, I have questions remaining. Special covariance requires equations to be covariant under certain transformations (i.e. the isometries) even after plugging in the explicit form of the metric. That means there are components that behave nicely under isometries...
Thank you two! Ok, I agree that for a certain metric space there is a canonical isomorphism between its tangent space and the cotangent space, which is defined by the metric.
However, there are more isomorphisms. I can simply map an arbitrary basis of the tangent space to an arbitrary basis...