# A 2 M Branes to 5 M Branes

1. Mar 12, 2016

### MacRudi

Hello
I was not sure, if I should post it in mathematical forum or here. But my question is more a physical than mathematical.
Does someone know anything about the physical view on the devolopement from 2 M Branes to 5 M Branes? I can only find mathematical describings and mathematical explanations, which don't really help me to understand it.
What I understand so far is, that we cannot use anymore like in D Branes the langrangian physics of Yang Mill and Lie algrebra. So far so good. We need a 3 algebra. Understood so far.
But what are the consequences for scalar vacuum and the delaton?
This I cannot really understand, what that means for it.

2. Mar 12, 2016

### MacRudi

3. Mar 12, 2016

### arivero

4. Mar 13, 2016

### MacRudi

thanks
yes this is the mathematics. But now I need a physical background for the scalar vacuum and Delaton. Do you know any work on it? physics description (devlopement from 2M to 5M in 11 D)

Last edited: Mar 13, 2016
5. Mar 14, 2016

### mitchell porter

The VEV of the string theory dilaton is actually telling you about the size of the 11th dimension from M-theory. The exact relation depends on which string theory you work in. In Type IIA and E8xE8 heterotic, which can directly be understood as compactifications of M-theory, the dilaton VEV is directly proportional to the size of the 11th dimension. In the other string theories, the mapping to M-theory involves a T-duality, and the dilaton VEV is then the ratio of the size of the 11th dimension, to the radius of the dimension along which the T-duality is performed.

The construction of M-theory as a quantum theory is still a work in progress. The original construction of M-theory occurred at a classical level - e.g. one would consider a ten-dimensional string theory in the limit of infinite coupling, and find that there were extra states corresponding to momentum in an 11th dimension. If you look for a derivation that starts with a membrane in 11 dimensions and derives string-and-dilaton in 10 dimensions, this is the closest thing I have seen. They start with a rough model of a quantum M2-brane wrapped around a compact dimension, and argue that the path-integral measure for the membrane implies a radius-dependent factor in the path integral for the string.

There is still a close connection between Yang-Mills theory, and the worldvolume theories of the branes in M-theory. M2-branes are described by "Chern-Simons-matter theories" that are like a Yang-Mills theory in which the gauge field kinetic terms have vanished (ref, page 4), and the nonlagrangian theory of the M5-branes may actually be 5D super-Yang-Mills with a hidden extra dimension (ref).

I don't know why the 3-algebra structure shows up or what it means.

6. Mar 14, 2016

### MacRudi

thank you very much
this will help me now. Many thanks for the links. especially the last work is helping a lot with references

http://arxiv.org/pdf/1012.2882v3.pdf

I'm not sure, if I will understand it really. But it seems to give some more deep insights for 11 dimensions.
What we can say is that there are now mathematically from different views similar expressions, which don't use gauge kinetic terms of lagrangian expression.
We use partial grassmann integrals as the proper expression and have to think in them. To think in lagrangian expression would not be successful.

Last edited: Mar 14, 2016