Planar diagrams in light-cone gauge

TL;DR

This paper explores how planar diagrams in light-cone gauge relate to closed string propagation, showing that open string interactions can be effectively described by a modified closed string Hamiltonian, with implications for string dualities.

Contribution

It demonstrates that the sum of planar open string diagrams corresponds to a free closed string propagation with a specific Hamiltonian form, extending understanding of gauge-string duality in light-cone gauge.

Findings

The Hamiltonian takes the form H = H0 - (g_s N) P, matching closed string expectations.

Explicit calculation of P from open strings aligns with closed string results in certain limits.

The approach may extend to superstrings and field theory diagrams without requiring a full string action.

Abstract

We consider the open string vacuum amplitude determining the interaction between a stack of N D3-branes and a single probe brane. When using light cone gauge, it is clear that the sum of planar diagrams (relevant in the large-N limit) is described by the free propagation of a closed string. A naive calculation suggests that the Hamiltonian of the closed string is of the form H = H0 - (g_s N) P. The same form of the Hamiltonian follows from considering the bosonic part of the closed string action propagating in the full D3-brane background suggesting the naive calculation captures the correct information. Further, we compute explicitly P from the open string side in the bosonic sector and show that, in a certain limit, the result agrees with the closed string expectations up to extra terms due to the fact that we ignored the fermionic sector. We briefly discuss extensions of the results to the superstring and to the sum of planar diagrams in field theory. In particular we argue that the calculations seem valid whenever one can define a sigma <-> tau dual Hamiltonian in the world-sheet which in principle does not require the existence of a string action. This seems more generic than the existence of a string dual in the large-N limit.