One-Loop BPS amplitudes as BPS-state sums

Abstract

Recently, we introduced a new procedure for computing a class of one-loop BPS-saturated amplitudes in String Theory, which expresses them as a sum of one-loop contributions of all perturbative BPS states in a manifestly T-duality invariant fashion. In this paper, we extend this procedure to all BPS-saturated amplitudes of the form \int_F Γ_{d+k,d} Φ, with Φ being a weak (almost) holomorphic modular form of weight -k/2. We use the fact that any such Φ can be expressed as a linear combination of certain absolutely convergent Poincaré series, against which the fundamental domain F can be unfolded. The resulting BPS-state sum neatly exhibits the singularities of the amplitude at points of gauge symmetry enhancement, in a chamber-independent fashion. We illustrate our method with concrete examples of interest in heterotic string compactifications.

42 pages; v4: a few misprints corrected

References in corpus (4)

• One-Loop BPS amplitudes as BPS-state sums
• Vacuum stability, string density of states and the Riemann zeta function
• Gauge Threshold Corrections for N = 2 Heterotic Local Models with Flux, and Mock Modular Forms
• Error Estimates in Horocycle Averages Asymptotics: Challenges from String Theory

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