In the first lecture, we discuss basic aspects of worldsheet and penta-brane instantons as well as (unoriented) D-brane instantons, which is our main focus here, and threshold corrections to BPS-saturated couplings. The second lecture is devoted to non-perturbative superpotentials generated by 'gauge' and 'exotic' instantons living on D3-branes at orientifold singularities. In the third lecture we discuss the interplay between worldsheet and D-string instantons on T 4 /Z 2 . We focus on a 4-fermi amplitude, give Heterotic and perturbative Type I descriptions, and offer a multi D-string instanton interpretation. We conclude with possible interesting developments.
We give a new expression for the supercurrent and its conservation in curved N = 1, D = 4 superspace using the superconformal approach. The first component of the superfield, whose lowest component is the vector auxiliary field gives the (super)Einstein equations. Its trace and couplings to conformal and non-conformal matter are presented. In a suitable dilatational gauge, the conformal gauge, we obtain an update of the CallanColeman-Jackiw improved currents for conformal matter, containing R-symmetry corrections for a new traceless covariantly conserved energy-momentum tensor. We observe that in the Poincaré gauge, where standard Poincaré supergravity is usually formulated, the currents are not improved and then the higher conformal symmetry of the matter sector is obscured. The curvature multiplets are used to find supersymmetric curved backgrounds and some examples are exhibited in agreement with existing results.
In this paper we compute the partition function of 5D supersymmetric U(1) gauge theory with extra adjoint matter in general Ω-background. It is well known that such partition functions encode very rich topological information. We show in particular that unlike the case with no extra matter, the partition function with extra adjoint at some special values of the parameters directly reproduces the generating function for the Poincare polynomial of the moduli space of instantons. Comparing our results with those recently obtained by Iqbal et. al., who used the refined topological vertex method, we present our comments on apparent discrepancies.
We discuss local supercurrents as sources of the super-Einstein equations in the superconformal approach in the old and new minimal (auxiliary fields) formulation. Modifications of the Ward identity giving the covariant divergence of the Einstein multiplet are considered in presence of a Fayet-Iliopoulos term. Curvature multiplets can be used as alternative to the gravitino variation in the search for rigid supersymmetric curved backgrounds.
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