arXiv subjects
Publications and source records attributed to K. S. Stelle.
We find new 4-brane and 5-brane solitons in massive gauged $D=6$, $N=2$ and $D=7$, $N=1$ supergravities. In each case, the solutions preserve half of the original supersymmetry. These solutions make use of the metric and dilaton fields only. We also present more general dilatonic $(D-2)$-branes in $D$ dimensions.
The elementary and solitonic supersymmetric $p$-brane solutions to supergravity theories form families related by dimensional reduction, each headed by a maximal (`stainless') member that cannot be isotropically dimensionally oxidized into higher dimensions. We find several new families, headed by stainless solutions in various dimensions $D\le 9$. In some cases, these occur with dimensions $(D,p)$ that coincide with those of descendants of known families, but since the new solutions are stainless, they are necessarily distinct. The new stainless supersymmetric solutions include a 6-brane and a 5-brane in $D=9$, a string in $D=5$, and particles in all dimensions $5\le D\le 9$.
We investigate new realisations of the $W_3$ algebra with arbitrary central charge, making use of the fact that this algebra can be linearised by the inclusion of a spin-1 current. We use the new realisations with $c=102$ and $c=100$ to build non-critical and critical $W_3$ BRST operators. Both of these can be converted by local canonical transformations into a BRST operator for the Virasoro string with $c=28-2$, together with a Kugo-Ojima topological term. Consequently, these new realisations provide embeddings of the Virasoro string into non-critical and critical $W_3$ strings.
We review the origin of anomaly-induced dynamics in theories of $d=2$ gravity from a BRST viewpoint and show how quantum canonical transformations may be used to solve the resulting Liouville or Toda models for the anomalous modes.
We reformulate the BRST quantisation of chiral Virasoro and $W_3$ worldsheet gravities. Our approach follows directly the classic BRST formulation of Yang-Mills theory in employing a derivative gauge condition instead of the conventional conformal gauge condition, supplemented by an introduction of momenta in order to put the ghost action back into first-order form. The consequence of these simple changes is a considerable simplification of the BRST formulation, the evaluation of anomalies and the expression of Wess-Zumino consistency conditions. In particular, the transformation rules of all fields now constitute a canonical transformation generated by the BRST operator $Q$, and we obtain in this reformulation a new result that the anomaly in the BRST Ward identity is obtained by application of the anomalous operator $Q^2$, calculated using operator products, to the gauge fermion.
We consider, for $p$ odd, a $p$--brane coupled to a $(p+1)$th rank background antisymmetric tensor field and to background Yang-Mills (YM) fields {\it via} a Wess-Zumino term. We obtain the generators of antisymmetric tensor and Yang-Mills gauge transformations acting on $p$--brane wavefunctionals (functions on `$p$-loop space'). The Yang-Mills generators do not form a closed algebra by themselves; instead, the algebra of Yang-Mills and antisymmetric tensor generators is a $U(1)$ extension of the usual algebra of Yang-Mills gauge transformations. We construct the $p$-brane's Hamiltonian and thereby find gauge-covariant functional derivatives acting on $p$--brane wavefunctionals that commute with the YM and $U(1)$ generators.
We investigate the spectrum of physical states in the $W_3$ string theory, up to level 2 for a multi-scalar string, and up to level 4 for the two-scalar string. The (open) $W_3$ string has a photon as its only massless state. By using screening charges to study the null physical states in the two-scalar $W_3$ string, we are able to learn about the gauge symmetries of the states in the multi-scalar $W_3$ string.
We construct the low-lying discrete states of the two-scalar $W_3$ string. This includes states that correspond to the analogues of the ground ring generators of the ordinary two-dimensional string. These give rise to infinite towers of discrete states at higher levels.
The nonlinear scalar-field realisation of $w_{1+\infty}$ symmetry in $d=2$ dimensions is studied in analogy to the nonlinear realisation of $d=4$ conformal symmetry $SO(4,2)$. The $w_{1+\infty}$ realisation is derived from a coset-space construction in which the divisor group is generated by the non-negative modes of the Virasoro algebra, with subsequent application of an infinite set of covariant constraints. The initial doubly-infinite set of Goldstone fields arising in this construction is reduced by the covariant constraints to a singly-infinite set corresponding to the Cartan-subalgebra generators $v^\ell_{-(\ell+1)}$. We derive the transformation rules of this surviving set of fields, finding a triangular structure in which fields transform into themselves or into lower members of the set only. This triangular structure gives rise to finite-component subrealisations, including the standard one for a single scalar. We derive the Maurer-Cartan form and discuss the construction of invariant actions.
We present a unified group-theoretical framework for superparticle theories. This explains the origin of the ``twistor-like'' variables that have been used in trading the superparticle's $κ$-symmetry for worldline supersymmetry. We show that these twistor-like variables naturally parametrise the coset space ${\cal G}/{\cal H}$, where $\cal G$ is the Lorentz group $SO^\uparrow(1,d-1)$ and $\cal H$ is its maximal subgroup. This space is a compact manifold, the sphere $S^{d-2}$. Our group-theoretical construction gives the proper covariantisation of a fixed light-cone frame and clarifies the relation between target-space and worldline supersymmetries.
We study the spectrum of $W_3$ strings. In particular, we show that for appropriately chosen space-time signature, one of the scalar fields is singled out by the spin-3 constraint and is ``frozen'': no creation operators from it can appear in physical states and the corresponding momentum must assume a specific fixed value. The remaining theory is unitary and resembles an ordinary string theory in $d\ne26$ with anomalies cancelled by appropriate background charges. In the case of the $W_3$ string, however, the spin-two ``graviton'' is massive.