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Register a new userOne-loop matrix elements of effective superstring interactions: $alpha$-expanding loop integrands
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In the low-energy effective action of string theories, non-abelian gauge interactions and supergravity are augmented by infinite towers of higher-mass-dimension operators. We propose a new method to construct one-loop matrix elements with insertions of operators $D^{2k} F^n$ and $D^{2k} R^n$ in the tree-level effective action of type-I and type-II superstrings. Inspired by ambitwistor string theories, our method is based on forward limits of moduli-space integrals using string tree-level amplitudes with two extra points, expanded in powers of the inverse string tension $alpha$. Similar to one-loop ambitwistor computations, intermediate steps feature non-standard linearized Feynman propagators which eventually recombine to conventional quadratic propagators. With linearized propagators the loop integrand of the matrix elements obey one-lo
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We consider the probability for a colour-singlet qqbar pair to emit a gluon, in strongly and smoothly ordered antenna showers. We expand to second order in alphaS and compare to the second-order QCD matrix elements for Z -> 3 jets, neglecting terms suppressed by 1/NC^2. We give a prescription that corrects the shower to the matrix-element result at this order for both soft and hard emissions, thereby explicitly reducing its dependence on evolution- and renormalization-scale choices. We confirm that the choice of pT for both of these scales absorbs all logarithms through order alphaS^2, and contrast this with various alternatives. We include these corrections in the VINCIA shower generator and study the impact on LEP event-shape and fragmentation observables. An uncertainty estimate is provided for each event, in the form of a vector of alternative weights.
We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of `power-counting for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all `leading-(transcendental-)weight contributions of any four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent all scattering amplitude integrands in the theory---for generic helicities and arbitrary multiplicity.
In this final part of a series of three papers, we will assemble supersymmetric expressions for one-loop correlators in pure-spinor superspace that are BRST invariant, local, and single valued. A key driving force in this construction is the generalization of a so far unnoticed property at tree level; the correlators have the symmetry structure akin to Lie polynomials. One-loop correlators up to seven points are presented in a variety of representations manifesting different subsets of their defining properties. These expressions are related via identities obeyed by the kinematic superfields and worldsheet functions spelled out in the first two parts of this series and reflecting a duality between the two kinds of ingredients. Interestingly, the expression for the eight-point correlator following from our method seems to capture correctly all the dependence on the worldsheet punctures but leaves undetermined the coefficient of the holomorphic Eisenstein series ${rm G}_4$. By virtue of chiral splitting, closed-string correlators follow from the double copy of the open-string results.
In this paper we describe how representation theory of groups can be used to shorten the derivation of two loop partition functions in string theory, giving an intrinsic description of modular forms appearing in the results of DHoker and Phong [1]. Our method has the advantage of using only algebraic properties of modular functions and it can be extended to any genus g.
In type II superstring theory, the vacuum amplitude at a given loop order $g$ can receive contributions from the boundary of the compactified, genus $g$ supermoduli space of curves $overline{mathfrak M}_g$. These contributions capture the long distance or infrared behaviour of the amplitude. The boundary parametrises degenerations of genus $g$ super Riemann surfaces. A holomorphic projection of the supermoduli space onto its reduced space would then provide a way to integrate the holomorphic, superstring measure and thereby give the superstring vacuum amplitude at $g$-loop order. However, such a projection does not generally exist over the bulk of the supermoduli spaces in higher genera. Nevertheless, certain boundary divisors in $partialoverline{mathfrak M}_g$ may holomorphically map onto a bosonic space upon composition with universal morphisms, thereby enabling an integration of the holomorphic, superstring measure here. Making use of ansatz factorisations of the superstring measure near the boundary, our analysis shows that the boundary contributions to the three loop vacuum amplitude will vanish in closed oriented type II superstring theory with unbroken spacetime supersymmetry.
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