Recent content by maverick280857

Hi, In chapter 12 of GSW volume 2, the authors remark, "spinors form a representation of SO(n) that does not arise from a representation of GL(2,R)." What do they mean by this? More generally, since SO(n) is a subgroup of GL(2,R) won't every representation of GL(2,R) be a representation of...

Thank you Terandol!

Hey Greg. I can't think of anything new, but I've kept it on my pending/to-do list. The argument used in the "physicist's proof" I had access to is already listed in my post. I don't have any more information.

Hi, I am trying to work through a proof/argument to show that the adjoint representation of a semisimple Lie algebra is completely reducible. Suppose S denotes an invariant subspace of the Lie algebra, and we pick Y_i in the invariant subspace S. The rest of the generators X_r are such that...

To the moderator: this should probably be moved to the "Beyond the Standard Model" subforum. Apologies for the inconvenience!

Hi, I'm trying to prove that the conformal weight of the bosonic vertex operator :e^{ik\cdot X}: is \left(\frac{\alpha'k^2}{4},\frac{\alpha'k^2}{4}\right). I've done some algebra but I think I am making some mistake with a factor of 2 somewhere because I get a 1/2 instead of a 1/4. My attempt...

Hi, Why does "holomorphic" have to be identified with "left-moving" (and not right-moving) in Polchinski's book, in chapter 2 (page 34)? The way I see it, a function of \sigma^0-\sigma^1 is like a function of x-vt so it should be "right moving". Am I missing something here? Thanks!

Solved. There is a sign error but this can be fixed by replacing \omega with -\omega and taking the trace of both sides.

Hi, First of all, I'm not sure if this thread belongs to the BSM forum because the question I'm posing here is a simple CFT question which could well be posed in the forum on GR or Particle Physics/QFT. I will defer to the judgment of the moderator to put this in the right place if it already...

Thanks samalkhaiat, yes, I got that. I would also like to show that (a) \delta_E(h^{\alpha\beta}\partial_\alpha X^\mu \partial_\beta X_\mu) = \xi^\rho \partial_\rho(h^{\alpha\beta}\partial_\alpha X^\mu \partial_\beta X_\mu) because "h^{\alpha\beta}\partial_\alpha X^\mu \partial_\beta X_\mu is...

Solved. Thanks anyway!

[SOLVED] Diffeomorphism invariance of the Polyakov action Hi, I'm struggling with something that is quite elementary. I know that the Polyakov action is diffeomorphism invariant and Weyl invariant. Denoting the world-sheet coordinates \sigma^0 = \sigma and \sigma^1 = t and the independent...

Thanks Physics Monkey and Ipetrich. I have a few questions: 1. What is x^{\sigma\tau} in terms of x^{\mu}? Am I correct in thinking that this is just a vector described by a symmetric rank-2 spinor (as mentioned on page 2) 2. What is the basis for defining the derivatives as above?

Hi, While reading "Superspace: One Thousand and One Lessons in Supersymmetry" by Gates et al. I came across the following paragraph: Maybe I haven't understood what exactly they're trying to say here, but 1. Why is the Lorentz Group SL(2, R) instead of SL(2, C)? 2. Why is the two-component...

I know what a Weyl anomaly is. I see terms like "type-A" anomaly and "D-type" anomalies in the literature. What does this classification refer to, and where was it originally introduced? Specifically, what does a D-type Weyl anomaly mean?