Branes: Exploring the Complex Relationship with Spacetime

[rodsika]

Branes are confusing subject. Branes are objects. Yet Branes are also Spacetime. But how could that be. General Relativity says geometry is not physical, but just math relationship. Now how could Branes itself be spacetime when Branes are objects like strings?

http://universe-review.ca/R15-18-string.htm says:

"D-branes - A D-brane is a submanifold of space-time with the property that open strings can end or begin on it. Strings can have various kinds of boundary conditions. For example closed strings have periodic boundary conditions (the string comes back onto itself)."

and

"Branes are not merely places; they are also objects that possesses finite tension and carry charges. Thus, they can be distorted and can interact with other charged objects and gravitational field"

Branes are supposed to be submanifold of spacetime. But spacetime is just an abstract mathematical idea, how could branes or spacetime submanifold contain charges?!

 

[suprised]

General Relativity says geometry is not physical, but just math relationship.

There is no difference in shape between the Earth and a bottle of beer?

Branes are supposed to be submanifold of spacetime. But spacetime is just an abstract mathematical idea, how could branes or spacetime submanifold contain charges?!

No, they _occupy_ a submanifold of spacetime. Think eg of a rubber band stretched around a tube.

http://universe-review.ca/R15-18-string.htm says:

"D-branes - A D-brane is a submanifold of space-time with the property that open strings can end or begin on it. Strings can have various kinds of boundary conditions. For example closed strings have periodic boundary conditions (the string comes back onto itself)."

This definition "where open strings can end" has created confusion without end and unfortunately has been copied all the time without illuminating anybody.

A brane is simply a certain extended classical field configuration, or solution of the equations of motions, call it soliton if you like. Depending on the boundary conditions, the fields are concentrated in certain regions ("submanifolds") of spacetime. Such branes correspond to non-perturbative sectors in the closed string theory.

A D-brane is a "dual" formulation of such a brane, for which the non-perturbative sector of closed strings is reformulated in terms of the perturbative sector of open strings. In other words, the extended soliton is transformed into a "local" degree of freedom, which in the language of conformal field theory can be represented by certain boundary conditions of open strings (namely regions "where open strings can end").

Note that D-branes are special in this and more general branes cannot be transformed to simple boundary conditions for open strings. So focusing on this "where open strings can end" does not capture the essence of branes, this is just a feature of a subclass of branes.