Instantons in type IIA theory and correlators

In summary, the conversation discusses the possibility of computing correlation functions in type IIA theory by infinite sums over instanton areas. It is mentioned that this method may not be applicable for 2-point correlators unless vertex operators are inserted on the torus and/or branes. Furthermore, the discussion also touches on the concept of degenerate instantons and their role in correlators. The conversation concludes with the understanding that the configuration of two branes alone does not bound an open string instanton and therefore a correlator involving only these two branes would not be well-defined.
  • #1
hines
3
0
Hi,
in type IIA theory it is possible to compute correlation functions by infinite sums over instanton areas [tex]\sum e^{-Area}[/tex]. Wouldn't that mean that it is possible to get two-point correlators? Imagine a torus with one brane on each of the two lattice vectors. They bound a parallelogram which is identical to the torus covering space. Is there anything that prevents us from summing up these areas to a valid correlator coming from just two branes?
Thank you,
hines
 
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  • #2
Yes there are configurations like that but this has nothing to do with 2-point correlators unless you insert vertex operators on the torus and/or on the branes. The two branes are not fields in a correlator but define the chosen background configuration. You may leave them out as well, then you have a torus around which the "unique" (up to multicovers) genus one closed string instanton can wrap. If you add branes then there are many more possibilities for open string instantons, and all need to be summed up to get the complete result.
 
  • #3
thanks for the reply. okay, so clearly it's not a 2-point function, my bad, but could there be a 4-point function with two different field insertions only like <\Psi_1 \Psi_2 \Psi_1 \Psi_2>? From your reply I understand that these two branes alone do not bound an open string instanton and therefore this correlator would vanish, correct?
 
  • #4
hines said:
From your reply I understand that these two branes alone do not bound an open string instanton and therefore this correlator would vanish, correct?

Degenerate instantons can be quite subtle. For example, it is known that open string instantons can fuse their boundaries so start to look like closed string instantons. However, typically there will be a divergence coming from the coinciding branes and therefore a correlator must be regularized in order to make it well-defined. The configuration you consider is however not the limiting case where four branes coincide pairwise, but only two branes, so I don't think it constitutes a well-defined open string correlator.
 
  • #5
Thank you~
 

1. What are instantons in type IIA theory?

Instantons are topologically non-trivial field configurations that arise in the context of string theory, specifically in the type IIA theory. They are characterized by non-vanishing gauge field strengths and play a crucial role in understanding the dynamics of the theory.

2. How do instantons affect the dynamics of type IIA theory?

Instantons introduce non-perturbative effects in the theory, which cannot be described by traditional Feynman diagrams. They are responsible for generating new terms in the effective action, such as higher-dimensional operators, that are crucial for understanding the behavior of the theory at strong coupling.

3. What are the main properties of instantons in type IIA theory?

Instantons are characterized by their action, which is a measure of their strength. They also have a topological charge, which determines their topological nature. In addition, they have a moduli space, which describes the different ways in which they can be embedded in the theory.

4. How are instantons related to correlators in type IIA theory?

Instantons can be used to compute correlation functions in type IIA theory. This is because they contribute to the path integral in a non-perturbative way, and can therefore affect the behavior of correlation functions at strong coupling. In some cases, instantons can even dominate the behavior of correlators.

5. What are some current research topics related to instantons in type IIA theory and correlators?

Some current research topics include studying the interplay between instantons and D-branes, as well as the role of instantons in the AdS/CFT correspondence. Other areas of interest include understanding the role of instantons in supersymmetric theories and their connection to topological string theory.

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