Summing planar diagrams
arXiv:hep-th/0703218 · doi:10.1088/1126-6708/2008/10/075
Abstract
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.
40 pages, 9 figures, LaTeX. v2: references added v3: Appendices added expanding some calculations
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Cited by in corpus (8)
- Quantum AdS_5 x S^5 superstring in the AdS light-cone gauge
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- Bethe-Salpeter scattering amplitude in Minkowski space
- Summing Planar Diagrams by an Integrable Bootstrap II
- Light-quarkonium spectra and orbital-angular-momentum decomposition in a Bethe-Salpeter-equation approach
- Summing Planar Diagrams by an Integrable Bootstrap
- Exact Quantization of a Superparticle in AdS_5 x S^5
- Heavy baryon spectroscopy in a quark-diquark approach