Invariant Wess-Zumino Research Articles

P-Brane superalgebras via integrability

It has long been appreciated that superalgebras with bosonic and fermionic generators additional to those in the super-Poincare algebra underlie p-brane and D-brane actions in superstring theory. These algebras have been revealed via “bottom up” approaches, involving consideration of Noether charges, and by “top down” approaches, involving the construction of manifestly supersymmetry invariant Wess–Zumino actions. In this paper, we give an alternative derivation of these algebras based on integrability of supersymmetry transformations assigned to fields in order to solve a cohomology problem related to the construction of Wess–Zumino terms for p-brane and D-brane actions.

SU (2|1) mechanics and harmonic superspace

We define the worldline harmonic superspace and its analytic subspace as a deformation of the flat harmonic superspace. The harmonic superfield description of the two mutually mirror off-shell supermultiplets is developed and the corresponding invariant actions are presented, as well as the relevant classical and quantum supercharges. Whereas the σ-model actions exist for both types of the multiplet, the invariant Wess–Zumino term can be defined only for one of them, thus demonstrating non-equivalence of these multiplets in the case as opposed to the flat supersymmetry. A superconformal subclass of general actions invariant under the trigonometric-type realizations of the supergroup is singled out. The superconformal Wess–Zumino actions are shown to possess an infinite-dimensional supersymmetry forming the centerless super Virasoro algebra. We solve a few simple instructive examples of the supersymmetric quantum mechanics of the multiplets and reveal the representation contents of the corresponding sets of the quantum states.

Wess-Zumino term in the $ \mathcal{N} = 4 $ SYM effective action revisited

The low-energy effective action for the N=4 super Yang-Mills on the Coulomb branch is known to include an SO(6)-invariant Wess-Zumino (WZ) term for the six scalar fields. For each maximal, non-anomalous subgroup of the SU(4) R-symmetry, we find a four-dimensional form of the WZ term with this subgroup being manifest. We then show that a recently proposed expression for the four-derivative part of the effective action in N=4 USp(4) harmonic superspace yields the WZ term with manifest SO(5) R-symmetry subgroup. The N=2 SU(2) harmonic superspace form of the effective action produces the WZ term with manifest SO(4) x SO(2). We argue that there is no four-dimensional form of the WZ term with manifest SU(3) R-symmetry, which is relevant for N=1 and N=3 superspace formulations of the effective action.

Spacetime scale-invariant super- p-brane actions on enlarged superspaces and the geometry of κ-symmetry

We use the additional variables of suitably enlarged superspaces to write new actions for extended objects, with κ-symmetry, in such a way that the tension emerges from them as an integration constant. Our actions correspond to the spacetime scale-invariant ones previously considered by Bergshoeff et al. once the worldvolume forms introduced there are reinterpreted in terms of fields associated with the coordinates of the enlarged superspaces. It is shown that the κ-symmetry of the new actions is given by a certain type of right local transformations of the extended superspace groups. Further, we also show that the enlarged superspaces that allow for strictly invariant Wess–Zumino terms also lead to strict κ-invariance, i.e., the Lagrangian itself (not only the action) is both supersymmetry- and κ-invariant.

CANONICAL QUANTIZATION OF THE DEGENERATE WESS–ZUMINO ACTION INCLUDING CHIRAL INTERACTION WITH GAUGE FIELDS

A consistent quantization procedure for the chiral SU(3) gauge model in the presence of the SO(3)-invariant Wess–Zumino action is constructed. The physical content of the model is analyzed. As a simple example the 2D SU(2) gauge model with the degenerate Wess–Zumino action is also considered.

SO(N) invariant Wess-Zumino action and its quantization

A consistent quantization procedure of anomalous chiral models is discussed. It is based on the modification of the classical action by adding Wess-Zumino terms. The $SO(3)$ invariant WZ action for the $SO(3)$ model is constructed. Quantization of the corresponding modified theory is considered in details.

CHERN-SIMONS COCHAIN AND ANOMALY

In this paper, we define a coboundary operator acting on the cochain in gauge potential space and establish a formula about Chern-Simons coboundary. The result can be employed to obtain the non-abelian anomaly, the gauge invariant Wess-Zumino effec-tive action and the Schwinger term etc. We show that the present approach covers Fad-deev's, Song's, and Zumino's approaches.

Anomalies, Cohomology and Chiern-Simons Cochains

We present a concept of cohomology of the gauge transformations, establish the homomorphic relation between this cohomology group and the Chern-Simons type characteristic class sequence, and analyse their applications to the non-Abelian anomaly, the gauge invariant Wess-Zumino effective action and the Schwinger term etc. We show that the present approach includes faddeev's song's and zumino's approaches.

The Gauge Invariant Wess-Zumino Action Functional, Chiral Anomalies and Topology

The gauge invariant Wess-Zumino action functional in dimensional space is obtained by properly constructing the manifestly gauge invariant -forms which satisfy the Abelian anomalous Ward identity in dimensional space. Apart from its simplicity, directness, the construction clearly embodies the connections between the gauge invariant Wess-Zumino action functional, chiral anomalies and topology.

Soft fermionic modes in chiral- and super-symmetries at positive temperature

The conformally invariant Wess-Zumino model is studied at various levels of approximation at positive temperature. It is found that the bosons acquire a mass of order gT, whereas due to chiral symmetry the fermion exhibits the soft dispersion relation ω = 1 3 k for momenta much less than g 2 T. Weak-coupling but non-perturbative methods are needed to obtain this result.