Supergravity prerequisites for branes in string theory

Question

I have a one-semester background in string theory (bosonic string theory, the NSR string, conformal field theory), but I have not taken any full length courses on supersymmetry and supergravity. I'm presently taking a second string theory course, but I'm forced to build the background I lack myself, in an attempt to understand the new material.

So, here are some questions. My hope is that instead of just receiving answers, I will get some suggestions about specific books or reviews I could refer to, without getting carried away, to build some background for these topics.

1. In D = 11 supergravity, there's a Majorana gravitino with 44 independent components, and the gamma-tracelessness condition gives $\frac{1}{2}(D-3)2^{[D/2]} = 128$ components. Here it is said that the factor of half accounts for the fact that "spinors have half as many physical states as components". What does this statement in quotes mean?

2. The three form (totally antisymmetric) gauge field in D = 11 supergravity has a dimension of 9/2. How does dimensional analysis work here? Why does the gravitino field have a dimension of 5?

3. What is a super-covariant spin connection? I read that it equals the usual spin connection with sermonic terms of the form $\psi\Gamma\psi$. Why is this called "super-covariant"?

4. In order to get solutions like the M2 brane, the M5 brane, and the KK1 and KK6 solutions, one sets the fermions to zero (for bosonic backgrounds) and also imposes the BPS condition $\delta \psi = 0$. This condition is linear in derivatives. Is that sufficient to say that it is BPS? Why would quadratic derivatives result in non-BPS solutions?

Finally, is there a fairly quick resource to learn everything that is required in the vielbein formalism of general relativity, to work with string theory/supergravity?

This post imported from StackExchange Physics at 2015-02-13 11:43 (UTC), posted by SE-user leastaction

Comments

These are all separate questions. I'm voting to close your post for being too broad. Regarding the vielbein formalism, have a look at the first few gravitational physics lectures at pirsa.org.

This post imported from StackExchange Physics at 2015-02-13 11:43 (UTC), posted by SE-user JamalS

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Do you suggest that for now, I post one of these questions as a separate post?

This post imported from StackExchange Physics at 2015-02-13 11:43 (UTC), posted by SE-user leastaction

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For Supergravity and tetrad formalism try "supergravity" of Van Proeyen and Freedman. The notation is not the best you can get, but at least the book covers a lot of material from basis QFT to ADS/CFT.

This post imported from StackExchange Physics at 2015-02-13 11:43 (UTC), posted by SE-user Rexcirus

Answer 1

I think the superior textbook for all these matters is

• Leonardo Castellani, Riccardo D'Auria, Pietro Fré, Supergravity and Superstrings - A Geometric Perspective, World Scientific, 1991

Unfortunately it is out of print. If you have trouble getting hold of a copy, ask me for advice.