Unextended superfields in extended supersymmetry

In extended supersymmetry, we discuss the advantages of unextended superfields over extended ones and component fields. We show how to derive from the extended formalism the unextended superfields, and their extended supersymmetry transformations in unextended-superfield form.     

Fibre bundles and supersymmetries

By extending the frame bundle of a manifold admitting a spin structure to a principal fibre bundle with group the super-Poincaré group we are able to derive the supergravity Lagrangian and its invariances under supersymmetry and other transformations in a global form.     

BPS States of D=4 ␣N=1 Supersymmetry

We find the combinations of momentum and domain-wall charges corresponding to BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how the supersymmetry algebra implies their stability. These states form the boundary of the convex cone associated with the Jordan algebra of 4× 4 real symmetric matrices, and we explore some implications of the associated geometry. For the Wess–Zumino model we derive the conditions for preservation of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in addition show that this model does not admit any classical configurations with 3/4 supersymmetry. Our analysis also provides information about BPS states of N=1 D=4 anti-de Sitter supersymmetry. Received: 6 April 2000/ Accepted: 10 September 2000     

A two dimensional Lagrangian model with extended supersymmetry and infinitely many constants of motion

The reduction of the supersymmetric gradedSU(2|1) /S(U ₂×U ₁) -model is discussed. If no extra constraint is imposed, one gets a set of two coupled equations (involving two scalar superfields) which generalizes the supersymmetric sine-Gordon equation. It is shown that these equations, which can be derived by a supersymmetric Lagrangian, reproduce in the bosonic limit the reduced version of theO(4) -model (Pohlmeyer, Lund Regge, Getmanov model). Moreover the associate linear set and an infinite set of local conservation laws for this new supersymmetric model are exhibited. It turns out that, beyond the spinorial charge which generates the supersymmetry transformations, another unexpected spinorial charge is conserved; then the model appears to be invariant underN=2 extended supersymmetry.     

Couplings of N=1 chiral spinor multiplets

We derive the action for n_L≥1 chiral spinor multiplets coupled to vector and scalar multiplets. We give the component form of the action, which contains gauge invariant mass terms for the antisymmetric tensors in the spinor superfield and additional Green–Schwarz couplings to vector fields. We observe that supersymmetry provides mass terms for the scalars in the spinor multiplet that do not arise from eliminating an auxiliary field. We construct the dual action by explicitly performing the duality transformations in superspace and give its component form.     

Supergravity as a gauge theory of supersymmetry

In a new approach to supergravity we consider the gauge theory of the 14-dimensional supersymmetry group. The theory is constructed from 14×4 gauge fields, 4 gauge fields being associated with each of the 14 generators of supersymmetry. The gauge fields corresponding to the 10 generators of the Poincaré subgroup are those normally associated with general relativity, and the gauge fields corresponding to the 4 generators of supersymmetry transformations are identified with a Rarita-Schwinger spinor. The transformation laws of the gauge fields and the Lagrangian of lowest degree are uniquely constructed from the supersymmetry algebra. The resulting action is shown to be invariant under these gauge transformations if the translation associated field strength vanishes. It is shown that the second-order form of the action, which is the same as that previously proposed, is invariant without constraint.     

Use of compensators to break supersymmetry in an N = 1 supergravity theory

We consider an N = 1 supergravity theory with multiple compensators and show that supersymmetry is broken by a solution to the equation of motion of a compensator. When a chiral scalar superfield is coupled to supergravity, we discuss various aspects of supersymmetry breaking and show that the super-Higgs-Kibble effect is operative. Possible applications of this mechanism of supersymmetry breaking in model building and extended supergravity theories are indicated.     

Regularization and supersymmetry-restoring counterterms in supersymmetric QCD

We calculate symmetry-restoring counterterms in supersymmetric QCD at the one-loop level. First we determine loop corrections to the supersymmetry and gauge transformations and find counterterms in such a way that the symmetry algebra holds at the one-loop level. Then these results are used to derive the symmetry-restoring counterterms to all trilinear interactions. In order to obtain unique results it is crucial to use the Slavnov-Taylor identity, which does not only contain supersymmetric and gauge Ward identities but also describes the symmetry algebra. In dimensional regularization this procedure yields unique non-zero values for the counterterms. In contrast, in dimensional reduction we find that no non-symmetric counterterms are needed, neither for the symmetry transformations nor for the physical interactions. For the considered cases this result constitutes a definite test of the supersymmetry and gauge invariance of the scheme. Received: 1 March 2001 / Published online: 25 April 2001     

Local internal supersymmetry of the free Maxwell theory

The free Maxwell theory is shown to possess an extended gauge invariance consisting of local internal supersymmetry transformations in addition to the usual local phase transformations. The Maxwell lagrangian is derived as a particular gauge choice in the extended theory.     

Ableitung einer kontinuierlichen Mannigfaltigkeit von Erhaltungssätzen der modifizierten Korteweg-de-Vries-Gleichung nach dem Noetherschen Satz

Derivation of a Continuous Set of Conservation Laws for the Modified Korteweg-de Vries Equation by Noether's Theorem A method developed recently to derive a continuous set of conservation laws from extended Bäcklund transformations by means of Noether's theorem is applied to the modified Korteweg-de Vries (m. KdV) equation that describes Alfvén waves in a plasma. The corresponding conserved currents are equivalent to those found by WADATI , SANUKI and KONNO . It is shown that the extended Bäcklund transformation B?_α for the m. KdV equation, which coincides with that for the sine-Gordon equation, by MIURA'S transformation becomes the extended Bäcklund transformation β_x for the Korteweg-de Vries equation where x = 1/2α.     

Off-shell N = 8 supersymmetry with central charges

Using a new technique of dimensional reduction by Legendre transformation we derive an off-shell formulation of the N = 8 extended supersymmetry algebra, which is realised in the maximally extended supergravity theory. The theory has an Sp(8) manifest global invariance and some of the fields satisfy differential constraints.     

Anomalous brightness of quasars resolved by supersymmetry

This article expands the development of the concept of reciprocal symmetry (Ref. 1) and points out that it is (by definition) the supersymmetry of nature. First we derive the relation between the supersymmetric, reciprocal spacetime coordinate transformations of Ref. 1 and the standard Lorentz transformations of relativity. Then we demonstrate or prove the assertion in Ref. 1 that the Robertson-Walker and the Schwarzschild metrics map (exactly) reciprocally. Finally, we derive the relativistic cosmic redshift as a function of distance of the source from the observer in the implied pseudo-dynamic Machian observable universe model. This uniquely consistent physical cosmological model is then applied to interpret the redshifts from quasars. In so doing, we find that this new interpretation puts the quasars considerably closer than does the interpretation of the big-bang theory [see Eq. (36)] and seems to remove the brightness or magnitude anomaly for these objects. As discussed in the Appendix, it also explains why the big-bang interpretation (including the inflationary universe model, etc.) gives good results.     

Materializing superghosts

The off-shell Batalin-Vilkovysky (BV) realization has been constructed for N = 1, d = 10 super-Yang-Mills theory with seven auxiliary fields. This becomes possible due to the materialized ghost phenomenon. Namely, supersymmetry ghosts are coordinates on a manifold B of ten-dimensional spinors with the pure spinors cut out. Auxiliary fields are sections of a bundle over B, and supersymmetry transformations are nonlinear in ghosts. By integrating out the auxiliary fields, we obtain an on-shell supersymmetric BV action with quadratic terms in the antifields. Exactly this on-shell BV action was obtained in our previous paper after integration out of auxiliary fields in the framework of a pure spinor superfield formalism. The text was submitted by the authors in English.     

Decoupling in supersymmetric theories

We examine the decoupling of massive states in supergravity theories. Using superspace functional techniques to “integrate out” the massive modes we derive the effective low-energy lagrangian. The technique is extended to the case of large supersymmetry breaking and we show how the effective lagrangian correctly accounts for vacuum expectation values of massive fields. We discuss the structure of effective theories following from the superstring in which the effects of Kaluza-Klein modes and states massive after intermediate scale breaking are included. It is shown in the case of large intermediate scale breaking the theory should possess discrete symmetries to protect light states from large supersymmetry breaking and we list the conditions for viable models.     

D=1 chiral supersymmetry with a central charge

We analyse a model which provides a realisation of Witten'sD=0+1 supersymmetry extended by a central charge, which is interpreted as defining a superselection rule, and study the interactions of its superfields. At the same time, this model allows us to discuss some general properties of extended supersymmetry theories.     

Non-local Conservation Laws and Flow Equations¶ for Supersymmetric Integrable Hierarchies

An infinite series of Grassmann-odd and Grassmann-even flow equations is defined for a class of supersymmetric integrable hierarchies associated with loop superalgebras. All these flows commute with the mutually commuting bosonic ones originally considered to define these hierarchies and, hence, provide extra fermionic and bosonic symmetries that include the built-in N=1 supersymmetry transformation. The corresponding non-local conserved quantities are also constructed. As an example, the particular case of the principal supersymmetric hierarchies associated with the affine superalgebras with a fermionic simple root system is discussed in detail.     

Constructive approach to supergravity

Starting from a first-order formulation of the Lagrangian of noninteracting massless helicity-2 and helicity-3/2 particles, we deduce global supersymmetry transformations. Then, allowing the supersymmetry transformations to become local requires, if supersymmetry is to be maintained, the introduction of a unique primitive interaction through the gravitino stress tensor and torsion. Finally, the imposition of exact supersymmetry invariance leads by a short, constructive process to full supergravity and the complete form of the supersymmetry transformations. In particular, no explicit use is made of general coordinate invariance, and the self-consistency of the gravitational coupling emerges from the local supersymmetry requirement alone.     

The (2+1)-dimensional supersymmetric CPN−1 model and the central charge

The supersymmetry algebra is examined for the (2+1)-dimensional supersymmetric CP^N?1 model, on the basis of the observation of Witten and Olive in (1+1) and (3+1) dimensions. We then demonstrate that also in this (2+1)-dimensional model the usual supersymmetry algebra is modified by the appearance of the topological numbers of the solitons, which are nothing but the instantons in (1+1) dimensions, as central charges. To obtain the model, we begin by constructing the supersymmetric model in (3+1) dimensions. Then it is reduced to (2+1) dimensions by means of the dimensional reduction technique. We observe that the (2+1)-dimensional supersymmetric CP^N?1 model thus obtained admits an O(2) extended supersymmetry.     

Lie symmetry, discrete symmetry and supersymmetry of the Pauli Hamiltonian

Starting from the full group of symmetries of a system we select a discrete subset of transformations which allows to introduce the Clifford algebra of operators generating new supercharges of extended supersymmetry. The system defined by the Pauli Hamiltonian is discussed. Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June 2001 Partially supported by the KBN-Grant # 5 P03B056 20.     

Algebraic properties of extended supergravity theories

Chirality transformations and generalized duality transformations are used to show that the extended O(2) and O(3) supergravity theories in fact have a U(2) and a U(3) invariance respectively. The coupling of these supergravity theories to matter multiplets having global extended supersymmetry is considered. In one case where the matter multiplet has a non-vanishing central charge, one finds a minimal coupling of the vector field of the supergravity multiplet.