A Study of Two-/One-form Superfields

We study two supersymmetric toy models of a k-form superfield, k=2,1 separately. By ``solving'' Jacobi identities, we show that each model is completely solvable at off-shell level, possesses a severely constrained kinematics, and gives a rigid representation of the supersymmetry algebra. This study of the toy models is motivated by our reanalysis on supersymmetry algebras in gauge theories where we discuss internal symmetry generators carrying spacetime/spinor indices.Comment: 1+35 pages, No figur

Superform formulation for vector-tensor multiplets in conformal supergravity

The recent papers arXiv:1110.0971 and arXiv:1201.5431 have provided a superfield description for vector-tensor multiplets and their Chern-Simons couplings in 4D N = 2 conformal supergravity. Here we develop a superform formulation for these theories. Furthermore an alternative means of gauging the central charge is given, making use of a deformed vector multiplet, which may be thought of as a variant vector-tensor multiplet. Its Chern-Simons couplings to additional vector multiplets are also constructed. This multiplet together with its Chern-Simons couplings are new results not considered by de Wit et al. in hep-th/9710212.Comment: 28 pages. V2: Typos corrected and references updated; V3: References updated and typo correcte

Towards the complete N=2 superfield Born-Infeld action with partially broken N=4 supersymmetry

We propose a systematic way of constructing $N=2, d=4$ superfield Born-Infeld action with a second nonlinearly realized N=2 supersymmetry. The latter, together with the manifest N=2 supersymmetry, form a central-charge extended $N=4, d=4$ supersymmetry. We embed the Goldstone-Maxwell N=2 multiplet into an infinite-dimensional off-shell supermultiplet of this N=4 supersymmetry and impose an infinite set of covariant constraints which eliminate all extra N=2 superfields through the Goldstone-Maxwell one. The Born-Infeld superfield Lagrangian density is one of these composite superfields. The constraints can be solved by iterations to any order in the fields. We present the sought N=2 Born-Infeld action up to the 10th order. It encompasses the action found earlier by Kuzenko and Theisen to the 8th order from a self-duality requirement. This is a strong indication that the complete N=2 Born-Infeld action with partially broken N=4 supersymmetry is also self-dual.Comment: 12 pages, LaTeX, typos corrected, version to appear in Phys. Rev.

BRS Cohomology of the Supertranslations in D=4

Supersymmetry transformations are a kind of square root of spacetime translations. The corresponding Lie superalgebra always contains the supertranslation operator $\delta = c^{\alpha} \sigma^{\mu}_{\alpha \dot \beta} {\overline c}^{\dot \beta} (\epsilon^{\mu})^{\dag}$. We find that the cohomology of this operator depends on a spin-orbit coupling in an SU(2) group and has a quite complicated structure. This spin-orbit type coupling will turn out to be basic in the cohomology of supersymmetric field theories in general.Comment: 14 pages, CTP-TAMU-13/9

Non-Perturbative Green's Functions in Theories with Extended Superconformal Symmetry

The multiplets that occur in four dimensional rigidly supersymmetric theories can be described either by chiral superfields in Minkowski superspace or analytic superfields in harmonic superspace. The superconformal Ward identities for Green's functions of gauge invariant operators of these types are derived. It is shown that there are no chiral superconformal invariants. It is further shown that the Green's functions of analytic operators are severely restricted by the superconformal Ward when analyticity is taken into account.Comment: 17 pages, plain tex. Some conjectures that were in the original paper are clarifed in the light of more recent work to which we give references. See Note added for detail

Supersymmetric Lorentz-Covariant Hyperspaces and self-duality equations in dimensions greater than (4|4)

We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel SO(3,1)-covariant superspaces, which we call hyperspaces, having dimensionality greater than (4|4) of traditional super-Minkowski space. As an application, we consider gauge fields on complexifications of these superspaces; and extending the concept of self-duality, we obtain classes of completely solvable equations analogous to the four-dimensional self-duality equations.Comment: 29 pages, late

QCD sum rules with finite masses

The concept of QCD sum rules is extended to bound states composed of particles with finite mass such as scalar quarks or strange quarks. It turns out that mass corrections become important in this context. The number of relevant corrections is analyzed in a systematic discussion of the IR- and UV-divergencies, leading in general to a finite number of corrections. The results are demonstrated for a system of two massless quarks and two heavy scalar quarks.Comment: 15 pages, including two pictures to be found in an extra file. Latex neads epsf.st

A TOPOLOGICAL LAGRANGIAN FOR MONOPOLES ON FOUR-MANIFOLDS

We present a topological quantum field theory which corresponds to the moduli problem associated to Witten's monopole equations for four-manifolds. The construction of the theory is carried out in purely geometrical terms using the Mathai-Quillen formalism, and the corresponding observables are described. These provide a rich set of new topological quantites.Comment: the date has been correcte

Ultraviolet dependence of Kaluza-Klein effects on electroweak observables

In extensions of the standard model (SM) with d extra dimensions at the TeV scale the virtual exchange of Kaluza-Klein (KK) excitations of the gauge bosons gives contributions that change the SM relations between electroweak observables. These corrections are finite only for d=1; for d\ge 2 the infinite tower of KK modes gives a divergent contribution that has to be regularized introducing a cutoff (the string scale). However, the ultraviolet dependence of the KK effects is completely different if the running of the couplings with the scale is taken into account. We find that for larger d the number of excitations at each KK level increases, but their larger number is compensated by the smaller value of the gauge coupling at that scale. As a result, for any number of extra dimensions the exchange of the complete KK tower always gives a finite contribution. We show that (i) for d=1 the running of the gauge coupling decreases an 14% the effect of the KK modes on electroweak observables; (ii) in all cases more than 90% of the total effect comes from the excitations in the seven lowest KK levels and is then independent of ultraviolet physics.Comment: 8 pages, to appear in Phys. Rev.

Auxiliary Fields for Super Yang-Mills from Division Algebras

Division algebras are used to explain the existence and symmetries of various sets of auxiliary fields for super Yang-Mills in dimensions $d=3,4,6,10$. (Contribution to G\"ursey Memorial Conference I: Strings and Symmetries)Comment: 7 pages, plain TeX, CERN-TH.7470/9