From maximal to minimal supersymmetry in string loop amplitudes

Abstract

We calculate one-loop string amplitudes of open and closed strings with N=1,2,4 supersymmetry in four and six dimensions, by compactification on Calabi-Yau and K3 orbifolds. In particular, we develop a method to combine contributions from all spin structures for an arbitrary number of legs at minimal supersymmetry. Each amplitude is cast into a compact form by reorganizing the kinematic building blocks and casting the worldsheet integrals in a basis. Infrared regularization plays an important role to exhibit the expected factorization limits. We comment on implications for the one-loop string effective action.

Figures (7)

• Figure 1: Factorization onto (tree-level 3-point) $\times$ (propagator) $\times$ (1-loop 3-point).
• Figure 2: The distinction between "delta function" and "delta function and propagator".
• Figure 3: Collapse of specific propagator avoids double factorization limit.
• Figure 4: Orbifold compactification: identification under ${\mathbb Z}_N$ creates a conical singularity. The orbifold twist $kv$ (that we will call $\gamma$, see eq. \ref{['orbtw']}) will occur in all our amplitudes.
• Figure 5: The double-pole residue ensures that tachyons do not propagate. This statement holds universally for both the present open-string calculation and its closed-string counterpart in section \ref{['sec:closedstring']}, and we are drawing its representative for a torus worldsheet.