One-Loop BPS amplitudes as BPS-state sums

Journal of High Energy Physics (Impact Factor: 6.22). 03/2012; 2012(6). DOI: 10.1007/JHEP06(2012)070
Source: arXiv

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 Poincar\'e 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.

  • Source
    • "+ n relevant for the expansion (3.15), the summand in (3.20) can be rewritten in terms of elementary functions [19]. "
    [Show abstract] [Hide abstract]
    ABSTRACT: After integrating over supermoduli and vertex operator positions, scattering amplitudes in superstring theory at genus $h\leq 3$ are reduced to an integral of a Siegel modular function of degree $h$ on a fundamental domain of the Siegel upper half plane. A direct computation is in general unwieldy, but becomes feasible if the integrand can be expressed as a sum over images under a suitable subgroup of the Siegel modular group: if so, the integration domain can be extended to a simpler domain at the expense of keeping a single term in each orbit -- a technique known as the Rankin-Selberg method. Motivated by applications to BPS-saturated amplitudes, Angelantonj, Florakis and I have applied this technique to one-loop modular integrals where the integrand is the product of a Siegel-Narain theta function times a weakly, almost holomorphic modular form. I survey our main results, and take some steps in extending this method to genus greater than one.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We determine threshold corrections to the gauge couplings in local models of N=2 smooth heterotic compactifications with torsion, given by the direct product of a warped Eguchi-Hanson space and a two-torus, together with a line bundle. Using the worldsheet CFT description previously found and by suitably regularising the infinite target space volume divergence, we show that threshold corrections to the various gauge factors are governed by the non-holomorphic completion of the Appell-Lerch sum. While its holomorphic Mock-modular component captures the contribution of states that localise on the blown-up two-cycle, the non-holomorphic correction originates from non-localised bulk states. We infer from this analysis universality properties for N=2 heterotic local models with flux, based on target space modular invariance and the presence of such non-localised states. We finally determine the explicit dependence of these one-loop gauge threshold corrections on the moduli of the two-torus, and by S-duality we extract the corresponding string-loop and E1-instanton corrections to the Kaehler potential and gauge kinetic functions of the dual type I model. In both cases, the presence of non-localised bulk states brings about novel perturbative and non-perturbative corrections, some features of which can be interpreted in the light of analogous corrections to the effective theory in compact models.
    Journal of High Energy Physics 10/2012; 2013(3). DOI:10.1007/JHEP03(2013)049 · 6.22 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We compute one-loop corrections to five-dimensional gauge and gravitational Chern-Simons terms induced by integrating out charged massive fields. The considered massive fields are spin-1/2 and spin-3/2 fermions, as well as complex two-forms with first order kinetic terms. Consistency with six-dimensional gravitational anomalies of (1,0) and (2,0) theories is shown by interpreting the massive fields as excited Kaluza-Klein modes in a circle compactification. The results are in accordance with the geometric predictions of the M-theory to F-theory duality as well as the comparison with an explicit one-loop computation in heterotic string theory compactified on K3 x S^1.
    Journal of High Energy Physics 02/2013; 2013(7). DOI:10.1007/JHEP07(2013)043 · 6.22 Impact Factor
Show more


Available from