We show how to systematically construct higher-derivative terms in effective actions in harmonic superspace despite the infinite redundancy in their description due to the infinite number of auxiliary fields. Making an assumption about the absence of certain superspace Chern-Simons-like terms involving vector multiplets, we write all 3-and 4-derivative terms on Higgs, Coulomb, and mixed branches. Among these terms are several with only holomorphic dependence on fields, and at least one satisfies a non-renormalization theorem. These holomorphic terms include a novel 3-derivative term on mixed branches given as an integral over 3/4 of superspace. As an illustration of our method, we search for Wess-Zumino terms in the low energy effective action of N = 2 supersymmetric QCD. We show that such terms occur only on mixed branches. We also present an argument showing that the combination of space-time locality with supersymmetry implies locality in the anticommuting superspace coordinates of for unconstrained superfields.
We show that the sheets for a connected reductive algebraic group G over an algebraically closed field in good characteristic acting on itself by conjugation are in bijection with G-conjugacy classes of tripleswhere M is the connected centralizer of a semisimple element in G, Z(M ) • t is a suitable coset in Z(M )/Z(M ) • and O is a rigid unipotent conjugacy class in M . Any semisimple element is contained in a unique sheet S and S corresponds to a triple with O = {1}. The sheets in G containing a unipotent conjugacy class are precisely those corresponding to triples for which M is a Levi subgroup of a parabolic subgroup of G and such a class is unique.
We consider positive singular solutions to semilinear elliptic problems with possibly singular nonlinearity. We deduce symmetry and monotonicity properties of the solutions via the moving plane procedure.
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