Why M2 and M5 branes are called electric and magnetic?

M-theory, that is a theory describing dynamics of 2 and 5 dimensional membranes, is believed to be a certain generalisation of 11 dimensional supergravity. It is often said that 11D SURGA is a low energy limit of M-theory. Basically, this is the only information known about M-theory to the moment. So why the fundamental objects of M-theory are known to be M2 and M5 branes? In one of the previous posts it has been figured out that this can be related to 11-dimensional superalgebra and Fierz identities. However, this does not explain why M5 branes are called magnetic. Here we will approach from the side of the supergravity in 11 dimensions and see that its fundamental gauge fields interact with electric and magnetic currents represented by 3- and 6-forms.

Database of Hep-TH people

Almost a year ago being in Seoul I was thinking about visiting say the Far East Federal University with a seminar. Trying to find any information on their official website about people working on HEP I realized, how a complicated task it is. Almost all webpages of institutions contain very fragmented, insufficient, outdated or even wrong information on the subject, that makes it very hard to understand who is working at which institute and what are his/her research interests. Precisely to overcome this problem I started developing a website, storing a database for all HEP-people.

Why there are only M2 and M5 branes?

A short answer to the question the title asks would be: Because Clifford algebra in odd dimensions is not simple.

An extended and more understandable explanation obviously needs some calculations, that will relate Fierz identities in 11 dimensions to central charges of $\mathcal{N}=1$ superalgebra. And the reducibility argument will allow to include the correct amount of central charges.

Certainly, one should realise that the arguments below do not give an exhaustive answer to the question, one necessarily needs to consider solutions of EOM of 11 dimensional sugra, look at the realisation of superalgebra and susy multiplets. But these simple calculations certainly give a hint to at least intuitive understanding, that is obviously necessary for our work.

Video Lectures on MathPhys

Here are some sources where one can find video lectures on basics of theoretical physics and/or mathematical tools that we use. Of course, this list is not comprehensive, but may be useful anyway. (All links open in a new window.)

1. Perimeter Institute graduate lectures for 2012/2013 can be found here . The other years from 2009 to 2014 are hidden in the "Course" menu of this page.

2. Seminars at Isaas Newton Institute in Cambridge. Navigation on this site may be not clear, so lets try find some videos there. Firstly, one chooses a program. Go to "Past programs" that is in the bottom of the page, then find there entry The Mathematics and Applications of Branes in String and M-theory . Click "Full list" in the left menu list and that's done.

3. YouTube channel of Stanford University contains a lot of information on the university itself and in addition one may find interesting lectures there. E.g. lectures on cosmology by Prof Leonard Susskind of Stanford University.

I'm sure that there are much more of this kind of sites, please add in the comments below if you know some. This will be of much help.

PG lectures on spin geometry

When reading papers on string compactifications it is very soon becomes necessary to know such things as Killing spinors, holonomy, spin connection etc. In other words, spin geometry is very relevant to string phenomenology.

Here one can find a course of lectures for postgraduate students by José Figueroa-O'Farrill, Professor of Geometric Physics in the School of Mathematics. These are written in a compact and more or less understandable way. 

There are some references at the bottom of the page. I would recommend to take a look at Real Killing spinors and holonomy by Christian Bär as it contains the classification of manifolds with real Killing spinors. For example, this theorem is used in heterotic compactifications. Actually, it is easier to follow thesis by Christoph Nölle.

What is...?

I have found an interesting series of articles under the common topic "What is..?" One can browse a small archive of these articles or go to the home page home page of AMS Notices to search for more.

In these notes one can find brief introductions to some mathematical stuff that is usually hard to understand reading books or articles.

The ones that I would like to recommend for reading are "What is a gerbe?" by Nigel Hitchin and "What is a G_2 manifold?" by Spiro Karigiannis. These are interesting because gerbes appear as nice generalisations of fibre bundle and are relevant to the recently developed duality covariant approaches. G2 manifolds play the same role for M-theory compactifications as Calaby-Yau manifolds play for stringy compactifications. These are 7-dimensional (compact) manifolds with a lot of nice properties.

Exotic branes

In the theory of open string one imposes boundary conditions on string ends. in general there are two types of these conditions: Dirichlet and Newmann. Newmann boundary conditions effectively allow the string end to move arbitrarily. Dirichlet conditions restrict movement of the string end to some p-dimensional surface in the bulk space, that is called Dp-brane. From the point of view of external space a D-brane wrapped around internal torus looks as a point particle.

Interestingly, that in the spectrum of supergravity compactified to 3 dimensions one meets exotic states whose higher dimensional origin is not obvious. In string theory these correspond to the so-called exotic branes. A fascinating feature of these branes is that they typically generate non-geometric backgrounds, i.e. such configurations of the space-time metric and p-form fields that cannot be globally described in geometric terms [1].