A generalisation of (very) special geometry

We construct non-Abelian on-shell vector multiplets in five and in four dimensions. Closing of the supersymmetry algebra imposes dynamical constraints on the fields, and these constraints should be interpreted as equations of motion. If these field equations should not be derivable from an action, we find that supersymmetry allows a broader class of target-space geometries than the familiar rigid (very) special manifolds. These theories, moreover, have more general potentials due to the possibility of including Fayet–Iliopoulos terms in the non-Abelian case. We show that by introducing an action, we recover the standard results. Finally, we relate the five- and four-dimensional theories through dimensional reduction and discuss the corresponding generalised r-map.     

Two-loop QCD amplitude for gg-->h, H in the minimal supersymmetric standard model

We present the two-loop QCD amplitude for the interaction of two gluons and a CP-even Higgs boson in the minimal supersymmetric standard model (MSSM). We apply a novel numerical method for the evaluation of Feynman diagrams with infrared, ultraviolet, and threshold singularities. We discuss subtleties in the ultraviolet renormalization of the amplitude with conventional dimensional regularization, dimensional reduction, and the four dimensional helicity scheme. Finally, we show numerical results for scenarios of supersymmetry breaking with a rather challenging phenomenology in which the Higgs signal in the MSSM is suppressed in comparison to the standard model.     

Supersymmetric quantum hall liquid with a deformed supersymmetry

We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore—Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudopotential Hamiltonian whose groundstate is exactly the parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY pseudopotential Hamiltonian is parameter-dependent and non-Hermitian, its eigenvalues are parameter-independent and real.     

Gauge symmetry and supersymmetry in the Higgsless standard model

The group SO(6) ⊗ SO(5) is shown to be the gauge group as well as supersymmetry group of a four dimensional superstring model. Here, we discuss how supersymmetry is realised in 4-dimensions and further, we successfully reproduce the gauge symmetry results. Using the SO(6) ⊗ SO(5) group, all the known aspects of the string theory are obtained. The model reduces to the Standard Model which has the capability of containing the ingredients of a successful theory of the present day physics. However, there are no Higgs in the model.     

The two-loop renormalization of the gauge coupling and the scalar potential for an arbitrary renormalizable field theory

For any renormalize field theory in four dimensions we obtain the two-loop counterterms for the gauge coupling and the scalar potential, using the background-field method. The calculation was performed in two different subtraction schemes: one is the ordinary dimensional regularization, the other is the so-called dimensional reduction scheme. We show that already at the two-loop level differences occur for the scalar coupling-constants. Only dimensional reduction preserves supersymmetry up to this level.     

Time-dependent supergravity solutions in null dilaton background

A class of time dependent pp-waves with NS–NS flux in type IIA string theory is considered. The background preserves 1/4 supersymmetry and may provide a toy model of Big Bang cosmology with nontrivial flux. At the Big Bang singularity in early past, the string theory is strongly coupled and matrix string model can be used to describe the dynamics. We also construct some time dependent supergravity solutions for D-branes and analyze their supersymmetry properties.     

Renormalization and symmetry conditions in supersymmetric QED

For supersymmetric gauge theories a consistent regularization scheme that preserves supersymmetry and gauge invariance is not known. In this article we tackle this problem for supersymmetric QED within the framework of algebraic renormalization. For practical calculations, a non-invariant regularization scheme may be used together with counterterms from all power-counting renormalizable interactions. From the Slavnov–Taylor identity, expressing gauge invariance, supersymmetry and translational invariance, simple symmetry conditions are derived that are important in a twofold respect: they establish exact relations between physical quantities that are valid to all orders, and they provide a powerful tool for the practical determination of the counterterms. We perform concrete one-loop calculations in dimensional regularization, where supersymmetry is spoiled at the regularized level, and show how the counterterms necessary to restore supersymmetry can be read off easily. In addition, a specific example is given how the supersymmetry transformations in one-loop order are modified by non-local terms. Received: 23 July 1999 / Published online: 14 October 1999     

Dimensional regularization and supersymmetry

We examine in detail the techniques of supersymmetric dimensional regularization. A peculiar complementarity is found to be inherent in the regularization: its manifestly supersymmetric version is contradictory, while the removal of inconsistencies costs a lossof supersymmetry in higher orders. We analyse this phenomenon at the level of Feynman diagrams and discover an explicit example of supersymmetry breakdown in the three-loop approximation. In the light of this result, we reconsider the status of dimensional regularization in globally supersymmetric gauge theories.     

Spontaneous breaking of supersymmetry and gauge invariance in supergravity

Using the new minimal auxiliary fields of N = 1 supergravity it is found possible to construct a model of local supersymmetry which spontaneously breaks both supersymmetry and gauge invariance. The status of the cosmological constant resulting from this breaking is discussed.     

Spontaneous supersymmetry breaking in large-N matrix models with slowly varying potential

We construct a class of matrix models, where supersymmetry (SUSY) is spontaneously broken at the matrix size N infinite. The models are obtained by dimensional reduction of matrix-valued SUSY quantum mechanics. The potential of the models is slowly varying, and the large-N limit is taken with the slowly varying limit.     

Softly broken supersymmetry and the fine-tuning problem

The supersymmetry of the simple Wess-Zumino model is broken, in the tree-approximation, by adding all possible parity-even [mass]-dimension 2 and 3 terms. The model is then renormalized using BPHZ and the normal product algorithm, such that supersymmetry is only softly broken (in the original sense of Schroer and Symanzik).We show that, within the above renormalization scheme, none of the added breaking terms give rise to technical fine-tuning problems (defined in the sense of Gildener) in larger models, with scalar multiplets and hierarchy of mass scales, which is in contrast to what we obtain via analytic schemes such as dimensional renormalization, or supersymmetry extension of which.The discrepancy (which can be shown to persist in more general models) originates in the inherent local ambiguity in the finite parts of subtracted Feynman integrals. Emphasizing that the issue is purely technical (as opposed to physical) in origin, and that all physical properties are scheme-independent (as they should be!), we conclude that the technical fine-tuning problem, in the specific sense used in this paper, being scheme dependent, is not a well-defined issue within the context of renormalized perturbation theory.     

Dynamical breakdown of supersymmetry and chiral symmetry in 1+1 dimensions

Dynamical breakdown of supersymmetry and chiral symmetry is studied through a 1+1 dimensional field theoretical model in the large-N limit in 1/N expansion. The study is based on the calculation of bilinear field condensates in an effective potential approach. It is shown that the condition for supersymmetry breaking is related to the values of the parameters in the model and chiral symmetry breaking exists in most cases.     

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.     

Strings on orientifolds

We construct several examples of compactification of type IIB theory on orientifolds and discuss their duals. In six dimensions we obtain models with N = 1 supersymmetry, multiple tensor multiplets, and different gauge groups. In nine dimensions we obtain a model that is dual to M-theory compactified on a Klein bottle.     

Spontaneous supersymmetry breaking in supersymmetric string theories

A generalization of the dimensional reduction of supersymmetric string theories is introduced which leads to spontaneous breaking of supersymmetry. This supersymmetry breaking has non-trivial consequences for the quantization and dynamics of the theory. The lowest quantum correction to the cosmological constant is calculated and found to be unacceptably large.     

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     

Supersymmetric quantum mechanics in one,two and three dimensions

We discuss a few supersymmetric quantum mechanical models in one, two and three dimensions. In the case of one particle in both two and three dimensions we present some examples where supersymmetry is unbroken and the ground state is many-fold degenerate. Further, we consider the supersymmetric generalization of the nearest neighbour XY model and show that supersymmetry remains unbroken in this case.     

Supersymmetries and BPS configurations on anti-de Sitter space

We study supersymmetry breaking due to the presence of branes on anti-de Sitter space and obtain conditions for brane orientations not to break too many supersymmetries. Using the conditions, we construct a brane configuration corresponding to a baryon in large N gauge theory, and it is shown that the baryon is a marginal bound state of quarks, as is expected from supersymmetry.     

两类新的条件精确可解势及其非线性谱生成代数

从平移的谐振子势出发,利用超对称量子力学构造出两类新的条件精确可解势,其中一类同时出现超对称性和空间对称性的破缺．此外,还构造出了这两类新可解势的非线性谱生成代数. 关键词：     

Non-supersymmetric orientifolds of Gepner models

Starting from a previously collected set of tachyon-free closed strings, we search for N=2$N=2$ minimal model orientifold spectra which contain the standard model and are free of tachyons and tadpoles at lowest order. For each class of tachyon-free closed strings – bulk supersymmetry, automorphism invariants or Klein bottle projection – we do indeed find non-supersymmetric and tachyon free chiral brane configurations that contain the standard model. However, a tadpole-cancelling hidden sector could only be found in the case of bulk supersymmetry. Although about half of the examples we have found make use of branes that break the bulk space–time supersymmetry, the resulting massless open string spectra are nevertheless supersymmetric in all cases. Dropping the requirement that the standard model be contained in the spectrum, we find chiral tachyon and tadpole-free solutions in all three cases, although in the case of bulk supersymmetry all massless spectra are supersymmetric. In the other two cases we find truly non-supersymmetric spectra, but a large fraction of them are nevertheless partly or fully supersymmetric at the massless level.