In Maldacena paper he writes:

We start with type IIB string theory with string coupling g, which will remain fixed. Consider N parallel D3 branes separated by some distances which we denote by r.

Obviously when r=0 the branes are on 'top of each other'.

However what mechanism keeps branes parallel at exactly of a distance r? At the planck level one expects quantum effects to set in and such a position can't be, as far as I understand it, maintained given Heisenbergs uncertainty principle (the positions of the branes are precisely determined and the velocities of the branes are precisely all the same)

Is the situation, for example, being considered before quantisation?


1 Answer 1


D-branes are defined by fixing a Dirichlet boundary condition to the open string. This configuration describes extended objects that, in the small coupling limit, are very heavy. The open strings will describe the fluctuations of this object (i.e. the standard deviation), and the only way to really move this object (i.e. changing the expectation value of its location), is by a coherent state of open string, an infinity many open string.

The same happens to the space-time in string theory. The space-time in perturbative string theory is a fixed background, but the theory really tells you that the space-time is dynamical. Again, in the small coupling limit, the space-time is very "heavy", and just a coherent state of closed strings can move it. The small fluctuations of the space-time are described by the closed strings.

Both the space-time and the D-branes are quantized, but we are in an appropriate limit where just small fluctuations are relevant (perturbation theory). In the perturbative string theory all fluctuations of the background are described by the strings, and all this is powered by state-operator correspondence.


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