Boundary conditions on D-Branes

In summary, the equations of motion for a classical open string have two boundary conditions, Dirichlet and Neumann. These conditions have physical implications for open string endpoints attached to objects called D-branes. The Dirichlet boundary condition forces the string to live on the brane, while the Neumann boundary condition allows the string to move in the free spatial dimensions of the brane. In order for superstring theory to be Lorentz invariant, we must have strings living in 10 dimensions, so we must compactify 6 extra dimensions. This is typically done using a mathematical concept called Calabi-Yau spaces, which explains why the extra dimensions "curl up" in a particular way.
  • #1
wam_mi
81
1
Hi there,

I recently read that the equations of motion for an classical open string naturally give rise to two boundary conditions, namely Dirichlet and Neumann boundary conditions.

(i) Could someone explain to me what do these boundary conditions physically mean, in particular for open string endpoints attached to some objects say D-branes?

(ii) Which boundary condition fixes/forces the open string to live on the brane? Which one allows open strings to move only in the free spatial dimensions of the brane?

(iii) In superstring theory, we have strings that live in 10 dimensions, in order for the theory to be Lorentz invariant. Does that mean we have to compactify 6 extra spatial dimensions? If so, how do we do that? Why do they curl up in such format?

Thank you!
 
Physics news on Phys.org

1. What are D-Branes?

D-Branes are objects that arise in string theory and are represented as hyperplanes in the space in which strings propagate. They are named after the mathematician Juan Maldacena, who first proposed their existence.

2. What are boundary conditions on D-Branes?

Boundary conditions on D-Branes refer to the constraints or rules that dictate how strings can interact with the D-Branes. These conditions are necessary for the consistency of the theory and are essential for understanding the behavior of strings in the presence of D-Branes.

3. What role do boundary conditions play in string theory?

Boundary conditions play a crucial role in string theory as they determine the properties and behavior of strings in the presence of D-Branes. They also help to explain how different types of particles arise and interact within the theory.

4. How are boundary conditions on D-Branes determined?

Boundary conditions on D-Branes are determined by the geometry and topology of the D-Branes. They are also influenced by the type of string theory being studied and the type of interactions that are allowed between strings and D-Branes.

5. What are some real-world applications of boundary conditions on D-Branes?

Boundary conditions on D-Branes have many potential real-world applications, particularly in the fields of quantum computing and high-energy physics. They may also have implications for understanding the nature of the universe and could potentially lead to new technologies or advancements in our understanding of fundamental physics.

Similar threads

I Why do dimensions curl up or expand?
    • Beyond the Standard Models
Replies
5
Views
2K
A The double copy of (2,0) theory
    • Beyond the Standard Models
Replies
1
Views
2K
What are strings with endpoint boundary conditions NN, DD, ND and DN?
    • Beyond the Standard Models
Replies
3
Views
5K
I Green's function boundary conditions
    • Classical Physics
Replies
1
Views
142
I Good positing in electrostatics problem with dielectrics - Poisson problem with conditions at the Dirichlet or Neumann edge
    • Differential Equations
Replies
1
Views
594
I Mass spectrum of open bosonic strings
    • Beyond the Standard Models
Replies
3
Views
1K
A "Monstrous Higgs and Leech Spacetime"
    • Beyond the Standard Models
Replies
0
Views
1K
I Trying To Conceptualize Two Dimensions Of Time
    • Beyond the Standard Models
Replies
2
Views
2K
How do D-Brane arrangements affect particle masses and the standard model?
    • Beyond the Standard Models
Replies
1
Views
4K
I Boundary conditions of a forced oscillator (string)
    • Other Physics Topics
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top