Perturbation theory in terms of superfields and its application to gauge theories

We formulate a perturbation theory in terms of superfields for Lagrangian field theories which are expressable by chiral or general scalar superfields. Especially we consider the generalized QED model of Wess and Zumino where an additional local gauge symmetry is present. Our calculations are manifestly covariant with respect to supersymmetry and local gauge transformations.     

Dynamically Broken Supergauge Symmetries

The dynamical breaking of the supergauge symmetries in the massless supergauge Wess Zumino model isdiscussed without adding the Fayet-Iliopoulos term to the Lagrangian. It is shown, in terms of the Nambu-Jona-Lasiniomechanism, that the supersymmetry breaking and the gauge symmetry breaking can be realized dynamically. It is alsoshown that the dynamical breaking moves the vacuum expectation values of two scalar fields away from zero. In order torestore the symmetry of the vacuum, one of the two scalar fields is translated and at the same time the mass spectrumis changed too.     

The spinorial charges of supersymmetry and twisters

We investigate the precise connection between the spinorial charges of the original supersymmetry algebra of Wess and Zumino and the twisters of Penrose.     

The structure of the new superspace

The new superspace of Wess and Zumino is generalized to the unconstrainedN-extendedD-dimensional case, it amounts actually to a reparametrization of the old superspace. Recurrence relations for the transformation law and for the covariant derivatives of the superfields defined in the new superspace are obtained. The definition of the component fields as local Lorentz covariant fields has the consequence that the gauge covariant expressions obtained for the vielbein and the connection of the new superspace don't contain the terms dropped out in the Wess-Zumino gauge of supergravity.     

Solution to constraints in Wess-Zumino supergravity formalism

We explicitly solve the constraints of the superfield supergravity formalism of Wess and Zumino, for an arbitrary gauge, in terms of superfields. Wess and Zumino's action turns out to be identical to one of a class of actions found earlier by the author: the one with the minimal set of auxiliary fields. We also show how to write chiral Lagrangians, including the cosmological term and the Lagrangian for conformal supergravity.     

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.     

Edge states for quantum Hall droplets in higher dimensions and a generalized WZW model

We consider quantum Hall droplets on complex projective spaces with a combination of Abelian and non-Abelian background magnetic fields. Carrying out an analysis similar to what was done for Abelian backgrounds, we show that the effective action for the edge excitations is given by a chiral, gauged Wess–Zumino–Witten (WZW) theory generalized to higher dimensions.     

BRS cohomology of the chiral superfield

As a start in a search for possible undiscovered anomalies which might break supersymmetry, a general calculation of BRS cohomology for the Wess Zumino chiral multiplet is performed. The calculation is done using spectral sequences in Fock space. It encompasses the vector space of all integrated local polynomials in the fields and their derivatives. This calculation shows that the BRS cohomology space contains an infinite number of polynomials with ghost charge one. Examples of these polynomials are given. All presently known examples possess uncontracted Lorentz spinor (and possibly vector) indices. A simple extension of these results to super Yang Mills theory indicates that there may be previously unnoticed anomalies in that theory.Research supported in part by the Robert A. Welch Foundation and NSF Grant PHY9009850     

The Geometric Construction of WZW Effective Action in Noncommutative Manifold

By constructing close-one-cochain density Ω^12n in the gauge group space we get the Wess-Zumino-Witten (WZW) effective Lagrangian on high-dimensional noncommutative space.Especially consistent anomalies derived from this WZW effective action in noncommutative four-dimensional space coincide with those obtained by L.Bonora etc.(het-th/0002210).     

Light-Front Quantization of Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an U(1) Gauge Field

Light-front quantization of the conformally gauge-fixed Polyakov D1 brane action in the presence of a constant background scalar axion field C(τ, σ) and an U(1) gauge field A _α (τ, σ) is studied. The axion field C and the U(1) gauge field A _α , are seen to behave like the Wess–Zumino (WZ) fields and the term involving these fields is seen to behave like a WZ term for this action.     

Kac–Moody theories for colored phase space (quantum Hall) droplets

We derive the canonical structure and Hamiltonian for arbitrary deformations of a higher-dimensional (quantum Hall) droplet of fermions with spin or color on a general phase space manifold. Gauge fields are introduced via a Kaluza–Klein construction on the phase space. The emerging theory is a nonlinear higher-dimensional generalization of the gauged Kac–Moody algebra. To leading order in ℏ this reproduces the edge state chiral Wess–Zumino–Witten action of the droplets.     

Approximations of Strongly Continuous Families of Unbounded Self-Adjoint Operators

In this paper we analyze supergeometric locally covariant quantum field theories. We develop suitable categories SLoc of super-Cartan supermanifolds, which generalize Lorentz manifolds in ordinary quantum field theory, and show that, starting from a few representation theoretic and geometric data, one can construct a functor \({{\mathfrak{A}}}\) : SLoc\({\to}\)S*Alg to the category of super-*-algebras, which can be interpreted as a non-interacting super-quantum field theory. This construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small. We then solve this problem by using techniques from enriched category theory, which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints. We construct super-quantum field theories in terms of enriched functors \({{\mathfrak{e}\mathfrak{A}}}\) : eSLoc\({\to}\)eS*Alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework. As examples we analyze the superparticle in 1|1-dimensions and the free Wess–Zumino model in 3|2-dimensions.     

Absence of the anomalous magnetic moment in a supersymmetric abelian gauge theory

We give a general argument for the vanishing of the anomalous magnetic moment in a supersymmetric Abelian gauge theory recently constructed by Wess and Zumino, provided in such a model the appropriate Ward identities are consistent with renormalized perturbation theory. Our conclusion is in fact confirmed by explicit one-loop calculation, thus providing a new example of cancellation of Feynman graphs in supersymmetric theories.     

A Duffin-Kemmer-Petiau formulation of supersymmetry

The simple supersymmetric model of Wess and Zumino is reconstructed using the first-order Duffin-Kemmer-Petiau formulation for the Bose fields. In spite of hopes to the contrary, our formulation is more complicated than the standard second-order one.     

Out of equilibrium dynamics of supersymmetry at high energy density

We investigate the out of equilibrium dynamics of global chiral supersymmetry at finite energy density. We concentrate on two specific models. The first is the massive Wess–Zumino model which we study in a self-consistent one-loop approximation. We find that for energy densities above a certain threshold, the fields are driven dynamically to a point in field space at which the fermionic component of the superfield is massless. The state, however, is found to be unstable, indicating a breakdown of the one-loop approximation. To investigate further, we consider an O(N) massive chiral model which is solved exactly in the large N limit. For sufficiently high energy densities, we find that for late times the fields reach a nonperturbative minimum of the effective potential degenerate with the perturbative minimum. This minimum is a true attractor for O(N) invariant states at high energy densities, and this provides a mechanism for determining which of the otherwise degenerate vacua is chosen by the dynamics. The final state for large energy density is a cloud of massless particles (both bosons and fermions) around this new nonperturbative supersymmetric minimum. By introducing boson masses which softly break the supersymmetry, we demonstrate a see-saw mechanism for generating small fermion masses. We discuss some of the cosmological implications of our results.     

Wess-Zumino model in the causal approach

The Wess–Zumino model is analysed in the framework of the causal approach of Epstein–Glaser. The condition of invariance with respect to supersymmetry transformations is similar to gauge invariance in the Zürich formulation. We prove that this invariance condition can be implemented in all orders of perturbation theory, i.e. the anomalies are absent in all orders. This result is of a purely algebraic nature. We work consistently in the quantum framework based on the Bogoliubov axioms of perturbation theory, so no Grassmann variables are necessary. Received: 30 April 2001 / Revised version: 19 July 2001 / Published online: 31 August 2001     

The relationship between four-dimensional θ=π Yang－Mills theory and the two-dimensional Wess－Zumino－Novikov－Witten model

Used the dimensional reduction in the sense of Parisi and Sourlas, the gauge fixing term of the four-dimensional Yang－Mills field without the theta term is reduced to a two-dimensional principal chiral model. By adding the θ term (θ=π), the two-dimensional principal chiral model changes into the two-dimensional level 1 Wess－Zumino－Novikov－Witten model. The non-trivial fixed point indicates that Yang－Mills theory at θ=π is a critical theory without mass gap and confinement.     

Twisted WZW branes from twisted REA's

Quantum geometry of twisted Wess–Zumino–Witten branes is formulated in the framework of twisted reflection equation algebras. It is demonstrated how the representation theory of these algebras leads to the correct classification of branes. A semiclassical formula for quantised brane positions is derived and shown to be consistent with earlier string-theoretic analyses.     

Gauge-theoretic invariants for topological insulators: a bridge between Berry,Wess–Zumino,and Fu–Kane–Mele

We establish a connection between two recently proposed approaches to the understanding of the geometric origin of the Fu–Kane–Mele invariant \(\mathrm {FKM}\in \mathbb {Z}_2\), arising in the context of two-dimensional time-reversal symmetric topological insulators. On the one hand, the \(\mathbb {Z}_2\) invariant can be formulated in terms of the Berry connection and the Berry curvature of the Bloch bundle of occupied states over the Brillouin torus. On the other, using techniques from the theory of bundle gerbes, it is possible to provide an expression for \(\mathrm {FKM}\) containing the square root of the Wess–Zumino amplitude for a certain U(N)-valued field over the Brillouin torus. We link the two formulas by showing directly the equality between the above-mentioned Wess–Zumino amplitude and the Berry phase, as well as between their square roots. An essential tool of independent interest is an equivariant version of the adjoint Polyakov–Wiegmann formula for fields \(\mathbb {T}^2 \rightarrow U(N)\), of which we provide a proof employing only basic homotopy theory and circumventing the language of bundle gerbes.