How do branes come into existence according to string theory? [closed]

1. How do branes come into existence according to string theory?

2. Also what are branes made out of?

• – Qmechanic May 9 '20 at 19:00
• @Qmechanic thank you very much sir. – Anvari May 9 '20 at 19:01

When we study an open string, we must assign boundary conditions for its end points. An open string in $$D$$-dimensional spacetime can be described by $$D$$ fields, $$X^\mu(\tau,\sigma)$$ with $$\mu=0,...,D-1$$. Suppose the end points of the string have $$\sigma=0,\pi$$. There are two types of boundary conditions
1. Neumann boundary conditions: you fix the velocity of the end points, $$\frac{\partial X^\mu}{\partial\tau}|_{\sigma=0,\pi}$$ for $$\mu=0,1,..., p$$.
2. Dirichlet boundary conditions: you fix the position of the end points, $$X^\mu(\tau)|_{\sigma=0,\pi}$$ for $$\mu=p+1,..., D-1$$.
The first type boundary condition simply means that the string end points move freely along the directions $$X^\mu$$ with $$\mu=1,...,p$$ (note for the time $$X^0$$, we must have Neumann boundary condition). The second type boundary condition means that the string end points are fixed at some position for $$X^\mu$$ with $$\mu=p+1,...,D-1$$.
Now, for the latter, what does the string end points attach to? There must be something for the strings to end at. Further study can show that the object carry energy-momentum in order to have energy-momentum conservation. This is the $$p$$-dimensional D-brane. The dimension of the brane is equal to the number of directions that the string end points can move freely.