Splitting Extended Supersymmetry

We show how splitting supersymmetry reconciles a class of intersecting brane models with unification. The gauge sector in these models arises in multiplets of extended supersymmetry while matter states are in N=1 representations. A deformation of the angles between the branes gives large masses to squarks and sleptons, as well as supersymmetry breaking contributions to other string states. The latter generate at one-loop heavy Dirac masses for Winos and gluinos and can induce a mass term for the Higgsino doublets. We find that this scenario is compatible with gauge coupling unification at high scale for both cases where the gauge sector is N=2 and N=4 supersymmetric. Moreover a neutralino, combination of neutral Higgsinos and Binos, is a natural candidate for dark matter.Comment: 10 pages, minor chages, version to be published in PL

Extended supersymmetry and its reduction on a circle with point singularities

We investigate $N$-extended supersymmetry in one-dimensional quantum mechanics on a circle with point singularities. For any integer $n$, $N=2n+1$ supercharges are explicitly constructed in terms of discrete transformations, and a class of singularities compatible with supersymmetry is clarified. In our formulation, the supersymmetry can be reduced to $M$-extended supersymmetry for any integer $M<N$. The degeneracy of the spectrum and spontaneous supersymmetry breaking are also studied.Comment: 36 pages, 5 figures, 2 table

Worldsheets with Extended Supersymmetry

We determine the equations which govern the gauge symmetries of worldsheets with local supersymmetry of arbitrary rank $(N,N')$, and their possible anomalies. Both classical and ghost conformally invariant multiplets of the left or right sector are assembled into the components of a single $O(N)$-superfield. The component with ghost number zero of this superfield is the $N$-supersymmetric generalization of the Beltrami differential. In a Lagrangian approach, and after gauge-fixing, it becomes the super-moduli of Riemann surfaces coupled to local supersymmetry of rank $N$. It is also the source of all linear superconformal currents derived from ordinary operator product techniques. The interconnection between BRST invariant actions with different values of $N\geq 3$, and their possible link to topological 2D-gravity coupled to topological sigma models, are shown by straightforward algebraic considerations.Comment: 15 pages, Latex. A section on the connection to topological action is adde

Exact Extended Supersymmetry on a Lattice: Twisted N=2 Super Yang-Mills in Two Dimensions

We propose a lattice action for two dimensional super Yang-Mills theory with a twisted N=2 supersymmetry. The extended supersymmetry is fully and exactly realized on the lattice. The method employed is quite general and its extension to the N=4 supersymmetry in four dimensions is briefly presented. The lattice has a new type of ``fermionic'' links, where odd Grassmann variables, supercharges and fermionic connections sit. The Leibniz rule is preserved on the lattice, although in a modified ``shifted'' form that takes into account the link nature of both derivatives and supercharges. Superfields are semi-local objects and superfield expansion is naturally embedded in the lattice structure. The Dirac-K\"ahler twist generates the extended twisted supersymmetry, turning the multiplicity of species doublers into the multiplicity due to the extended supersymmetry. In this way the balance between bosonic and fermionic degrees of freedom is preserved.Comment: 15 pages, 11 figure

Homology of Lie algebra of supersymmetries and of super Poincare Lie algebra

We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$. For dimensions $D=10,11$ we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry algebra.Comment: New version with some additions and correction

Extended Supersymmetry on Curved Spaces

We study N=2 superconformal theories on Euclidean and Lorentzian four-manifolds with a view toward applications to holography and localization. The conditions for supersymmetry are equivalent to a set of differential constraints including a "generalised" conformal Killing spinor equation depending on various background fields. We solve these equations in the general case and give very explicit expressions for the auxiliary fields that we need to turn on to preserve some supersymmetry. As opposed to what has been observed for the N=1 case, the conditions for unbroken supersymmetry turn out to be almost independent of the signature of spacetime, with the exception of few degenerate cases including the topological twist. Generically, the only geometrical constraint coming from supersymmetry is the existence of a conformal Killing vector on the manifold, all other constraints determine the background auxiliary fields.Comment: 31 pages, v2: minor changes and important references adde

Extended supersymmetry in AdS_3 higher spin theories

We determine the asymptotic symmetry algebra (for fields of low spin) of the $M\times M$ matrix extended Vasiliev theories on AdS$_3$ and find that it agrees with the $\mathcal{W}$-algebra of their proposed coset duals. Previously it was noticed that for $M=2$ the supersymmetry increases from $\mathcal{N}=2$ to $\mathcal{N}=4$. We study more systematically this type of supersymmetry enhancements and find that, although the higher spin algebra has extended supersymmetry for all $M\geq 2$, the corresponding asymptotic symmetry algebra fails to be superconformal except for $M=2$, when it has large $\mathcal{N}=4$ superconformal symmetry. Moreover, we find that the Vasiliev theories based on $shs^E\! \left( \mathcal{N} \vert 2, \mathbb{R} \right)$ are special cases of the matrix extended higher spin theories, and hence have the same supersymmetry properties.Comment: 23 page

Higgs alignment from extended supersymmetry

We consider the effective type-II Two-Higgs doublet model originating from Dirac gaugino models with extended supersymmetry in the gauge sector, which is automatically aligned in the simplest realisations. We show that raising the scale at which the extended supersymmetry is manifest and including quantum corrections actually improves the alignment. Using an effective field theory approach including new threshold corrections and two-loop RGEs, plus two-loop corrections to the Higgs mass in the low-energy theory, we study the implications from the Higgs mass and other experimental constraints on the scale of superpartners. We contrast the results of the minimal Dirac gaugino model, where alignment is automatic, with the hMSSM and the MRSSM, where it is not, also providing an hMSSM-inspired analysis for the new models.Comment: 37 pages, 13 figures. References added. Published versio

Superconformal Invariants and Extended Supersymmetry

The superconformal invariants in analytic superspace are found. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain harmonic superspaces. It is argued that the correlation functions for a class of sufficiently low dimension gauge invariant operators in N=2 and N=4 supersymmetric Yang-Mills theory can be evaluated up to constants.Comment: 10p, late