Summing planar diagrams
Mar, 2007Citations per year
Abstract: (arXiv)
We consider the sum of planar diagrams for open strings propagating on N D3-branes and show that it can be recast as the propagation of a closed string with a Hamiltonian H = H_0 - g_s N P where H_0 is the free Hamiltonian and P is the hole or loop insertion operator. We compute explicitly P and study its properties. When the distance y to the D3-branes is much larger than the string length, y >> l_s, small holes dominate and H becomes a supersymmetric Hamiltonian describing the propagation of a closed string in the full D3-brane supergravity background in a particular gauge that we call sigma-gauge. At strong coupling, g_s N >> 1, there is a region 1 << y << (g_sN)^(1/4) where H is a supersymmetric Hamiltonian describing the propagation of closed strings in AdS_5xS^5. We emphasize that both results follow from the open string planar diagrams without any reference to the existence of a D3-brane supergravity background. A by-product of our analysis is a closed form for the scattering of a generic closed string state from a D3-brane. Finally, we briefly discuss how this method could be applied to a field theory and describe a way to rewrite the planar Feynman diagrams as the propagation of a string with a non-local Hamiltonian by identifying the shape of the string with the trajectory of the particle.- string theory
- QCD
- light-cone frame
- membrane model: D-brane
- membrane model: p-brane
- p-brane: 3
- string model
- supersymmetry: transformation
- string: open
- light cone gauge
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