Higher-spin Realisations of the Bosonic String

It has been shown that certain $W$ algebras can be linearised by the inclusion of a spin--1 current. This provides a way of obtaining new realisations of the $W$ algebras. Recently such new realisations of $W_3$ were used in order to embed the bosonic string in the critical and non-critical $W_3$ strings. In this paper, we consider similar embeddings in $W_{2,4}$ and $W_{2,6}$ strings. The linearisation of $W_{2,4}$ is already known, and can be achieved for all values of central charge. We use this to embed the bosonic string in critical and non-critical $W_{2,4}$ strings. We then derive the linearisation of $W_{2,6}$ using a spin--1 current, which turns out to be possible only at central charge $c=390$. We use this to embed the bosonic string in a non-critical $W_{2,6}$ string.Comment: 8 pages. CTP TAMU-10/95

Liouville and Toda Solitons in M-theory

We study the general form of the equations for isotropic single-scalar, multi-scalar and dyonic $p$-branes in superstring theory and M-theory, and show that they can be cast into the form of Liouville, Toda (or Toda-like) equations. The general solutions describe non-extremal isotropic $p$-branes, reducing to the previously-known extremal solutions in limiting cases. In the non-extremal case, the dilatonic scalar fields are finite at the outer event horizon.Comment: Latex, 10 pages. Minor corrections to text and titl

Quantising Higher-spin String Theories

In this paper, we examine the conditions under which a higher-spin string theory can be quantised. The quantisability is crucially dependent on the way in which the matter currents are realised at the classical level. In particular, we construct classical realisations for the $W_{2,s}$ algebra, which is generated by a primary spin-$s$ current in addition to the energy-momentum tensor, and discuss the quantisation for $s\le8$. From these examples we see that quantum BRST operators can exist even when there is no quantum generalisation of the classical $W_{2,s}$ algebra. Moreover, we find that there can be several inequivalent ways of quantising a given classical theory, leading to different BRST operators with inequivalent cohomologies. We discuss their relation to certain minimal models. We also consider the hierarchical embeddings of string theories proposed recently by Berkovits and Vafa, and show how the already-known $W$ strings provide examples of this phenomenon. Attempts to find higher-spin fermionic generalisations lead us to examine the whether classical BRST operators for $W_{2,{n\over 2}}$ ($n$ odd) algebras can exist. We find that even though such fermionic algebras close up to null fields, one cannot build nilpotent BRST operators, at least of the standard form.Comment: CTP TAMU-24/94, KUL-TF-94/11, SISSA-135/94/E

Observation of long range magnetic ordering in pyrohafnate Nd2Hf2O7: A neutron diffraction study

We have investigated the physical properties of a pyrochlore hafnate Nd2Hf2O7 using ac magnetic susceptibility \chi_ac(T), dc magnetic susceptibility \chi(T), isothermal magnetization M(H) and heat capacity C_p(T) measurements, and determined the magnetic ground state by neutron powder diffraction study. An upturn is observed below 6 K in C_p(T)/T, however both C_p(T) and \chi(T) do not show any clear anomaly down to 2 K. The \chi_ac(T) shows a well pronounced anomaly indicating an antiferromagnetic transition at T_N = 0.55 K. The long range antiferromagnetic ordering is confirmed by neutron diffraction. The refinement of neutron diffraction pattern reveals an all-in/all-out antiferromagnetic structure, where for successive tetrahedra, the four Nd3+ magnetic moments point alternatively all-into or all-out-of the tetrahedron, with an ordering wavevector k = (0, 0, 0) and an ordered state magnetic moment of m = 0.62(1) \mu_B/Nd at 0.1 K. The ordered moment is strongly reduced reflecting strong quantum fluctuations in ordered state.Comment: 10 pages, 9 figures and 2 tables; to appear in Phys. Rev.