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 \Gamma_{d+k,d} {\Phi}, with {\Phi} being a weak (almost) holomorphic modular form of weight -k/2. We use the fact that any such {\Phi} 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. We illustrate our method with concrete examples of interest in heterotic string compactifications.
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Submitted on : Tuesday, March 13, 2012 - 9:57:00 AM
Last modification on : Thursday, February 7, 2019 - 2:58:59 PM

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Carlo Angelantonj, Ioannis Florakis, Boris Pioline. One-Loop BPS amplitudes as BPS-state sums. Journal of High Energy Physics, Springer, 2012, 6, pp.070. 〈10.1007/JHEP06(2012)070〉. 〈hal-00678471〉

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