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Register a new userTwo-Point Functions of Chiral Fields at One Loop in Type II
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We compute the two-point functions for chiral matter states in toroidal intersecting D6-brane models. In particular, we provide the techniques to calculate Moebius strip diagrams including the worldsheet instanton contribution.
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This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by this method. It directly proceeds in terms of the quantities driving algebraic reduction methods. It applies to the four-point functions in the same way as to the three-point functions. Lastly, it extends to kinematics more general than the one of physical e.g. collider processes relevant at one loop.
In the previous paper, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond-Ramond background from the viewpoint of symmetry and spectrum. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. In order to investigate the correspondence further, in this paper we compute correlation functions to all order of genus expansion in the double scaling limit of the matrix model. One-point functions of operators protected by supersymmetry terminate at some finite order, whereas those of unprotected operators yield non-Borel summable series. The behavior of the latter is characteristic in string perturbation series, providing further evidence that the matrix model describes a string theory. Moreover, instanton corrections to the planar one-point functions are also computed, and universal logarithmic scaling behavior is found for non-supersymmetric operators.
In the previous papers, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond-Ramond background. This was confirmed by agreement between planar correlation functions in the matrix model and tree-level amplitudes in the superstring theory. Furthermore, in the matrix model we computed one-point functions of single-trace operators to all orders of genus expansion in its double scaling limit, and found that the large-order behavior of this expansion is stringy and not Borel summable. In this paper, we discuss resurgence structure of these one-point functions and see cancellations of ambiguities in their trans-series. More precisely, we compute both series of ambiguities arising in a zero-instanton sector and in a one-instanton sector, and confirm how they cancel each other. In case that the original integration contour is a finite interval not passing through a saddle point, we have to choose an appropriate integration path in order for resurgence to work.
Inspired by the topological sign-flip definition of the Amplituhedron, we introduce similar, but distinct, positive geometries relevant for one-loop scattering amplitudes in planar $mathcal{N}=4$ super Yang-Mills theory. The simplest geometries are those with the maximal number of sign flips, and turn out to be associated with chiral octagons previously studied in the context of infrared (IR) finite, pure and dual conformal invariant local integrals. Our result bridges two different themes of the modern amplitudes program: positive geometry and Feynman integrals.
We compute the one-loop beta-functions for renormalisable quantum gravity coupled to scalars using the co-ordinate space approach and generalised Schwinger De Witt technique. We resolve apparent contradictions with the corresponding momentum space calculations, and indicate how our results also resolve similar inconsistencies in the fermion case.
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