Abstract
Starting from the superstring amplitude describing interactions among D-branes with a constant world-volume field strength, we present a detailed analysis of how the open string degeneration limits reproduce the corresponding field theory Feynman diagrams. A key ingredient in the string construction is represented by the twisted (Prym) super differentials, as their periods encode the information about the background field. We provide an efficient method to calculate perturbatively the determinant of the twisted period matrix in terms of sets of super-moduli appropriate to the degeneration limits. Using this result we show that there is a precise one-to-one correspondence between the degeneration of different factors in the superstring amplitudes and one-particle irreducible Feynman diagrams capturing the gauge theory effective action at the two-loop level.
Highlights
Level, are free of ultraviolet divergences and anomalies
Starting from the superstring amplitude describing interactions among Dbranes with a constant world-volume field strength, we present a detailed analysis of how the open string degeneration limits reproduce the corresponding field theory Feynman diagrams
We extend these past results in two directions: first we generalise the twisted period matrix to the supersymmetric case; we must calculate the supersymmetric version of the twisted determinant to sufficiently high order in the complete degeneration limit, so as to obtain the gauge theory Feynman graphs with multiple gluon propagators
Summary
In the presence of constant abelian background fields, the theory remains free, but string coordinates in directions parallel to the magnetized plane acquire twisted boundary conditions and must be treated separately. Where a is an adjoint index, Qμa and QIa stand for a gluon mode and a scalar, depending on whether XM is parallel or perpendicular to the D-brane, and kM = {kμ, 0} This simple relation between world-sheet and space-time states is preserved in perturbation theory, when the string coupling is switched on and non-linear terms in the BRST operators must be taken into account. This is expected, since, in a perturbative analysis, fields propagating between interaction vertices are free. The only difference is that the relevant modes are ψ−1/2, β−1/2 and γ−1/2: in the superstring partition function, the low energy limit will be performed by focusing on the contributions of states with half-integer weight
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