Supersymmetry Variations Research Articles

Non-renormalization theorems without supergraphs: the Wess–Zumino model

The non-renormalization theorems of chiral vertex functions are derived on the basis of an algebraic analysis. The property, that the interaction vertex is a second supersymmetry variation of a lower dimensional field monomial, is used to relate chiral Green functions to superficially convergent Green functions by extracting the two supersymmetry variations from an internal vertex and transforming them to derivatives acting on external legs. The analysis is valid in the massive as well as in the massless model and can be performed irrespective of properties of the superpotential at vanishing momentum.

Anti-de Sitter BPS black holes in N=2 gauged supergravity

Electrically charged solutions breaking half of the supersymmetry in Anti-de Sitter four dimensional N=2 supergravity coupled to vector supermultiplets are constructed. These static black holes live in an asymptotic AdS 4 space time. The Killing spinor, i.e., the spinor for supersymmetry variation is explicitly constructed for these solutions.

New canonical variables for d=11 supergravity

A set of new canonical variables for $d=11$ supergravity is proposed which renders the supersymmetry variations and the supersymmetry constraint polynomial. The construction is based on the $SO(1,2)\times SO(16)$ invariant reformulation of $d=11$ supergravity given in previous work, and has some similarities with Ashtekar's reformulation of Einstein's theory. The new bosonic variables fuse the gravitational degrees of freedom with those of the three-index photon $A_{MNP}$ in accordance with the hidden symmetries of the dimensionally reduced theory. Although $E_8$ is not a symmetry of the theory, the bosonic sector exhibits a remarkable $E_8$ structure, hinting at the existence of a novel type of ``exceptional geometry''.

N = 2 supergravity and N = 2 super Yang-Mills theory on general scalar manifolds: Symplectic covariance gaugings and the momentum map

The general form of N = 2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets, with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows to cover theories difficult to formulate within superspace or tensor calculus approach. We provide the complete Lagrangian and supersymmetry variations with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Lagrangians for rigid theories are also written in this general setting and the connection with local theories elucidated. The derivation of these results using geometrical techniques is briefly summarized.

D-branes, moduli, and supersymmetry

We study toroidal compactifications of type II string theory with $D$-branes and nontrivial antisymmetric tensor moduli and show that turning on these fields modifies the supersymmetry projections imposed by $D$-branes. These modifications are seen to be necessary for the consistency of $T$ duality. We also show the existence of unusual BPS configurations of branes at angles that are supersymmetric because of conspiracies between moduli fields. Analysis of the problem from the point of view of the effective field theory of massless modes shows that the presence of a two-form background must modify the realization of supersymmetry on the brane. In particular, the appropriate supersymmetry variation of the physical gaugino vanishes in any constant field strength background. These considerations are relevant for the ${E}_{7(7)}$-symmetric counting of states of four-dimensional black holes in type II string theory compactified on ${T}^{6}$.

General matter coupled N = 2 supergravity

The general form of N = 2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in that we use a coordinate independent and manifestly symplectic covariant formalism which allows us to cover theories difficult to formulate within a superspace or tensor calculus approach. We provide the complete lagrangian and supersymmetry variations with all fermionic terms, and the form of the scalar potential for arbitrary quaternionic manifolds and special geometry, not necessarily in special coordinates. Our results can be used to explore properties of theories admitting N = 2 supergravity as low energy limit.

First-order higher curvature supergravities and effective theories of strings

A first-order formulation of higher curvature supergravities in the group manifold approach leads to non-trivial torsion equations. In second-order form the resulting Lagrangians exhibit a non-polynomial structure in the curvatures of the basic fields, as well as in the supersymmetry variations. The relevance of these results for the search of superstring compactification is pointed out. The Chapline-Manton Lagrangian is recovered in first-order form and the supersymmetric completion of Chern-Simons terms in five and ten dimensions is considered.

σ-models, duality transformations and scalar potentials in extended supergravities

We develop a technique to compute scalar potentials in extended supergravities in any dimension on a pure group-theoretical basis. The fermionic supersymmetry variations, which determine the potential, only depend on boosted structure constants of a gauge subgroup K ⊂ G of the isometry group G of the scalar manifold G/H. These variations follow from the Bianchi identities of the underlying gauge superalgebra. We apply this method to construct the coupling of N = 3 matter to supergravity.

Globally supersymmetric multiplets without local extensions

Locally supersymmetric scalar multiplets with an additional external spinor index are constructed. It is shown which other global multiplets with spinor indices cannot be made local in such a way as to give the correct local commutator algebra. A global vector multiplet with spinor index, formed as a spinor derivative of a scalar multiplet, is also given. A formula for commuting supercovariant derivatives and supersymmetry variations is presented.

Massless field supermultiplets with arbitrary spin

Lagrangians for massless free fields with arbitrary spins are derived by postulating gauge transformations for these fields. Global supersymmetry field variations are then exhibited for a massless system involving the pair of spins (S,S+12), and the supersymmetry algebra is explicitly shown to close on-shell. The linear representation theorem for this algebra is used to prove these massless systems are suitably free of intermediate helicity modes. Local coupling of higher-spin fermions to gravity is briefly discussed.

Superconformal Unified Field Theory

We present the gauge theory of the graded conformal group. It contains four real fields with spins 2, $\frac{3}{2}$, 1, and \textonehalf{}. The theory is invariant under local proper conformal, scale, chiral, gravitational, and supersymmetry transformations. This is the first of a class of superunified field theories, possessing $\mathrm{U}(n)$ rather than $\mathrm{O}(n)$ internal gauge symmetries and without a cosmological constant. Unitarity, renormalizability, and asymptotic states and the cancellation of some complicated higher-order terms in one of the two supersymmetry variations remain to be investigated.