BRST operators for higher-spin algebras
In this paper, we construct non-critical BRST operators for matter and Liouville systems whose currents generate two different W algebras. At the classical level, we construct the BRST operators for W 2,s m ⊗ W 2,s′ l . The construction is possible for s = s ′ or s ≥ s ′ + 2. We also obtain the BRST operator for W 2,4 m ⊗ W 4 l at the classical level. We use free scalar realisations for the matter currents in the above constructions. At the full quantum level, we obtain the BRST operators for W 2,s m ⊗ W 2 l with s = 4,5,6, where W 2 denotes the Virasoro algebra. For the first and last cases, the BRST operators are expressed in terms of abstract matter and Liouville currents. As a by-product, we obtain the W 2,4 algebra at c = −24 and the W 2,6 algebra at c = −2 and −286 3 , at which values the algebras were previously believed not to exist.

title: The complete spectrum of the WN string
abstract: We obtain the complete physical spectrum of the W N string, for arbitrary N . The W N constraints freeze N −2 coordinates, while the remaining coordinates appear in the currents only via their energy-momentum tensor. The spectrum is then effectively described by a set of ordinary Virasoro-like string theories, but with a non-critical value for the central charge and a discrete set of non-standard values for the spin-2 intercepts. In particular, the physical spectrum of the W N string includes the usual massless states of the Virasoro string. By looking at the norms of low-lying states, we find strong indications that all the W N strings are unitary.

title: Classification of p-branes, NUTs, Waves and Intersections
abstract: We give a full classification of the multi-charge supersymmetric p-brane solutions in the massless and massive maximal supergravities in dimensions D ≥ 2 obtained from the toroidal reduction of eleven-dimensional supergravity. We derive simple universal rules for determining the fractions of supersymmetry that they preserve. By reversing the steps of dimensional reduction, the p-brane solutions become intersections of p-branes, NUTs and waves in D = 10 or D = 11. Having classified the lower-dimensional p-branes, this provides a classification of all the intersections in D = 10 and D = 11 where the harmonic functions depend on the space transverse to all the individual objects. We also discuss the structure of U-duality multiplets of p-brane solutions, and show how these translate into multiplets of harmonic and non-harmonic intersections.

title: Embedding of the bosonic string into the W3 string
abstract: 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 f - 2, together with a Kugo-Ojima topological term. Consequently, these realisations provide embeddings of the Virasoro string into non-critical and critical W 3 strings.

title: SYMMETRY IN TWO-DIMENSIONAL GRAVITY
abstract: We study the symmetry of two-dimensional gravity by choosing a generic gauge. A local action is derived which reduces to either the Liouville action or the Polyakov one by reducing to the conformal or light-cone gauge respectively. The theory is also solved classically. We show that an SL(2, R) covariant gauge can be chosen so that the two-dimensional gravity has a manifest Virasoro and the sl(2, R)-current symmetry discovered by Polyakov. The symmetry algebra of the light-cone gauge is shown to be isomorphic to the Beltrami algebra. By using the contour integration method we construct the BRST charge QB corresponding to this algebra following the Fradkin-Vilkovisky procedure and prove that the nilpotence of QB requires c=28 and α0=1. We give a simple interpretation of these conditions.

title: QUANTIZING HIGHER-SPIN STRING THEORIES
abstract: In this paper, we examine the conditions under which a higher-spin string theory can be quantized. The quantizability is crucially dependent on the way in which the matter currents are realized at the classical level. In particular, we construct classical realizations for the W2,s algebra, which is generated by a primary spin-s current in addition to the energy-momentum tensor, and discuss the quantization for s≤8. From these examples we see that quantum BRST operators can exist even when there is no quantum generalization of the classical W2,s algebra. Moreover, we find that there can be several inequivalent ways of quantizing 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 generalizations lead us to examine whether classical BRST operators for (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.

title: POWERFUL HIGH-VELOCITY DISPERSION MOLECULAR HYDROGEN ASSOCIATED WITH AN INTERGALACTIC SHOCK WAVE IN STEPHAN'S QUINTET
abstract: We present the discovery of strong mid-infrared emission lines of molecular hydrogen of apparently high-velocity dispersion (~870 km s-1) originating from a group-wide shock wave in Stephan's Quintet. These Spitzer Space Telescope observations reveal emission lines of molecular hydrogen and little else. This is the first time an almost pure H2 line spectrum has been seen in an extragalactic object. Along with the absence of PAH-dust features and very low excitation ionized gas tracers, the spectra resemble shocked gas seen in Galactic supernova remnants, but on a vast scale. The molecular emission extends over 24 kpc along the X-ray-emitting shock front, but it has 10 times the surface luminosity as the soft X-rays and about one-third the surface luminosity of the IR continuum. We suggest that the powerful H2 emission is generated by the shock wave caused when a high-velocity intruder galaxy collides with filaments of gas in the galaxy group. Our observations suggest a close connection between galaxy-scale shock waves and strong broad H2 emission lines, like those seen in the spectra of ultraluminous infrared galaxies where high-speed collisions between galaxy disks are common.

title: SHOCK-ENHANCED C+ EMISSION AND THE DETECTION OF H2O FROM THE STEPHAN'S QUINTET GROUP-WIDE SHOCK USING HERSCHEL
abstract: We present the first Herschel spectroscopic detections of the [OI]63µm and [CII]158µm fine-structure transitions, and a single para-H_2O line from the 35 x 15 kpc^2 shocked intergalactic filament in Stephan's Quintet. The filament is believed to have been formed when a high-speed intruder to the group collided with clumpy intergroup gas. Observations with the PACS spectrometer provide evidence for broad (> 1000 km s^(-1)) luminous [CII] line profiles, as well as fainter [OI]63µm emission. SPIRE FTS observations reveal water emission from the p-H_2O (1_(11)-0_(00)) transition at several positions in the filament, but no other molecular lines. The H_2O line is narrow, and may be associated with denser intermediate-velocity gas experiencing the strongest shock-heating. The [CII]/PAH_(tot) and [CII]/FIR ratios are too large to be explained by normal photo-electric heating in PDRs.  
region excitation or X-ray/Cosmic Ray heating can also be ruled out. The observations lead to the conclusion that a large fraction the molecular gas is diffuse and warm. We propose that the [CII], [OI] and warm H_2 line emission is powered by a turbulent cascade in which kinetic energy from the galaxy collision with the IGM is dissipated to small scales and low-velocities, via shocks and turbulent eddies. 
Low-velocity magnetic shocks can help explain both the [CII]/[OI] ratio, and the relatively high [CII]/H_2 ratios observed. The discovery that [CII] emission can be enhanced, in large-scale turbulent regions in collisional environments has implications for the interpretation of [CII] emission in high-z galaxies.