Theory of gauge supersymmetry in superspace

A new theory of gravity in Bose space is extended to a local gauge group of arbitrary coordinate transformations in superspace. We find that global supersymmetry can be recovered from the curved non-Riemannian superspace theory.Supported in part by the Natural Science and Engineering Research Council of Canada.     

Dynamical symmetry breaking in SYM theories as a non-semiclassical effect

We study supersymmetry breaking effects in N=1 SYM from the point of view of quantum effective actions. Restrictions on the geometry of the effective potential from superspace are known to be problematic in quantum effective actions, where explicit supersymmetry breaking can and must be studied. On the other hand the true ground state can be determined from this effective action, only. We study the problem whether some parts of superspace geometry are still relevant for the effective potential and discuss whether the ground states found this way justify a low energy approximation based on this geometry. The answer to both questions is negative. Essentially non-semiclassical effects change the behavior of the auxiliary fields completely and lead to the demand of a new interpretation of superspace geometry. These non-semiclassical effects can break supersymmetry. Received: 10 January 2002 / Revised version: 13 April 2002 / Published online: 18 October 2002 RID="*" ID="*" Work supported in part by the Schweizerischer Nationalfonds RID="a" ID="a" e-mail: bergamin@tph.tuwien.ac.at     

Explicit Construction of Supercharges of Supersymmetric Nonlinear Sigma Models in 1 + 1 Spacetime Dimensions

Considering the N = 1 supersymmetry transformations of supersymmetric nonlinear sigma models in 1 + 1 dimensions we construct explicitly conserved Noether currents associated with supersymmetry transformations and derive the associated conserved charges in terms of the basic fields. We compare this result with superspace calculations. Finally we review the connection between extended supersymmetry and the geometry of the target space and derive an explicit form of the supercharges for extended supersymmetry.     

Superspace formulation of supergravity

A geometrical interpretation of supergravity is given in terms of the differential geometry of superspace. Starting from a general affine superspace, the geometry is specified in such a way as to contain as a special case the superspace of a global supersymmetry. Covariant equations are given which are equivalent to those of supergravity in four-space. The question of finding a suitable Lagrangian is discussed.     

Superspace formulation of the dynamical symmetries of the Dirac magnetic monopole

The superspace formulation for the dynamical supersymmetry of the Pauli system in the presence of a Dirac magnetic monopole is presented. It is used to prove that Osp(1, 1) is the largest dynamical invariance group of this system. The action of finite transformations on the parameters of superspace and on the supervariables is given.     

Consistency condition calculations of supersymmetry anomalies

Using differential geometry in superspace it is shown how consistency conditions are solved for coupled supersymmetry, gauge and Lorentz anomalies in normal space-time. Anomaly cancellation mechanisms in d = 10 are shown to remove possible supersymmetry anomalies as well as gauge and Lorentz anomalies.     

Superspace,dimensional reduction,and stochastic quantization

The equivalence between a 6-dimensional stochastic classical scalar field theory and the corresponding 4-dimensional quantum field theory has been shown to stem from a hidden supersymmetry of the former. This has led to a formulation of quantum field theory in a superspace of 6 commuting and 2 anticommuting dimensions. We study gauge and spinor field theories defined on this superspace, showing that the dimensional reduction is a consequence of the geometry of the superspace, and that the stochastic formalism for gauge theories is a natural consequence of the structure of the superspace theory. This allows us to extend the stochastic formalism to include spinors.     

Supercurrent anomaly in non-abelian supersymmetric theories

A method for regularizing the supercurrent, preserving both gauge invariance and supersymmetry is developed, using point-splitting regularization and path-dependent phase factors in superspace. The supercurrent anomaly for general non-abelian supersymmetric theories is obtained on the mass-shell in the one-loop approximation.     

Supersymmetry and Superfields in Three Euclidean Dimensions

The simplest supersymmetry algebra and superspace in three-dimensional Euclidean (3dE) space is examined. Representations of the algebra are considered and the implications of restricting the space of states to states with positive definite norm are determined. A superspace is defined and superfields are introduced. Supersymmetric field theory models in 3dE are described in both superfield and component field forms. The relationship between these models and similar models in four-dimensional Minkowski space is described.     

Supersymmetry anomalies and some aspects of renormalization

We show how the $\text{L}$-matrix elements avoid the problem of supersymmetry breaking by the gauge fixing and ghost terms for renormalization in the Wess-Zumino gauge. Possible origins of supersymmetry anomalies are discussed. Gauge and gravitational anomalies induce a supersymmetry anomaly which has two distinct terms, one of which is gauge invariant. We give the expression for the noninvariant term for 2n-dimensional spacetime and for the invariant part in four dimensions. This anomaly, although cohomologically nontrivial, is still consistent with result that in superspace no supersymmetry anomaly is generated.     

Superspace geometry and N = 1 non-minimal supergravity

We investigate superspace geometry for supergravity with non-minimal auxilliary fields. We find that the kinematic constraints and the superspace Bianchi identities are sufficient to obtain complete component expansions of all superspace quantities, including the vielbein and connection superfields. We include a detailed pedagogical discussion on the analysis of constrained superspace Bianchi identities, demonstrating how these are used to derive component field content and transformation laws. We also note that local, chiral supersymmetry representations which form arbitrary representations of the Lorentz group can exist only within the context of supergravity with non-minimal auxilliary fields.     

The one-loop effective action of the supersymmetric CP(N-1) model

Using superfields we evaluate the superspace one-loop effective action for the supersymmetric CP(N - 1) model and investigate whether there is supersymmetry breaking and confinement.     

Ward Takahashi identities and fluctuation-dissipation theorem in a superspace formulation of the Langevin equation

A class of Langevin equations is formulated as a field theory in superspace. The Ward Takahashi identities associated with the hidden supersymmetry are derived which in turn are shown to lead to the fluctuation dissipation theorems.     

Superspace as a fibre space

Starting from the vector space of anticommuting elements and using the theory of fibre space, the superspace and supersymmetry theory is obtained from a geometrical point of view.     

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.     

Towards Higher-N Superextensions of Born–Infeld Theory

We give a brief account of supersymmetric Born–Infeld theories with extended supersymmetry, including those with partially broken supersymmetry. Some latest developments in this area are presented. One of them is N = 3 supersymmetric Born–Infeld theory which admits a natural off-shell formulation in N = 3 harmonic superspace.     

Superspace analysis of local Lorentz and gauge anomalies in the heterotic string theory

Local Lorentz and gauge anomalies in the sigma model describing the propagation of the heterotic string in an arbitrary background field are discussed in the superspace formulation. An expression for these anomalies is written down in terms of the superfields, and is shown to cancel against an anomalous variation of the antisymmetric tensor field. World-sheet supersymmetry is manifest throughout this analysis.     

Supergraphs extended to broken supersymmetries

Supergraph techniques are generalized to the case of broken supersymmetry. The modified superpropagators for the O'Raifeartaigh model are obtained: they are used for the superspace renormalization and the derivation of the effective potential.     

The one-loop N = 2 supercurrent anomaly

A one-loop superspace calculation of the N = 2 supercurrent anomaly is performed. The method preserves explicitly both N = 2 supersymmetry and gauge invariance.