Chern-Simons Gravity and Holographic Anomalies

We present a holographic treatment of Chern-Simons (CS) gravity theories in odd dimensions. We construct the associated holographic stress tensor and calculate the Weyl anomalies of the dual CFT.Comment: Added references, and minor corrections. 21 pages, havmac, no figure

Integrable field theories from Poisson algebras

New integrable 1 + 1 dimensional classical field theories are found that include infinite dimensional analogues of N-particle Toda-and Calogero-Moser systems, as well as non-relativistic theories with an interaction that is polynomial in the first (spatial) derivative of the field. The existence, as well as the involutivity, of an infinite set of independent conserved quantities follows most easily from a 2 + 1 dimensional Lax-pair which uses as its underlying infinite dimensional Lie algebra a Poisson algebra of functions in two variables

New superconformal multiplets and higher derivative invariants in six dimensions

Within the framework of six-dimensional ${\cal N}=(1,0)$ conformal supergravity, we introduce new off-shell multiplets ${\cal O}{}^{*}(n)$, where $n=3,4,\dots,$ and use them to construct higher-rank extensions of the linear multiplet action. The ${\cal O}{}^{*}(n)$ multiplets may be viewed as being dual to well-known superconformal ${\cal O}(n)$ multiplets. We provide prepotential formulations for the ${\cal O}(n)$ and ${\cal O}{}^{*}(n)$ multiplets coupled to conformal supergravity. For every ${\cal O}{}^{*}(n)$ multiplet, we construct a higher derivative invariant which is superconformal on arbitrary superconformally flat backgrounds. We also show how our results can be used to construct new higher derivative actions in supergravity.Comment: 17 pages; V2: comments and reference adde

The conformal supercurrents in diverse dimensions and conserved superconformal currents

Given a conserved and traceless energy-momentum tensor and a conformal Killing vector, one obtains a conserved current. We generalise this construction to superconformal theories in three, four, five and six dimensions with various amounts of supersymmetry by working in the appropriate superspaces.Comment: 23 page

Anisotropy in the orbital susceptibilities of hcp metals

Calculations of the magnetic susceptibility of the hcp transition metals Sc and Zr are carried out. The major contributions to the susceptibility are found to be the Van Vleck orbital and Pauli spin terms. Other smaller yet significant contributions are the Landau-Peierls and core diamagnetic terms. Particular attention is given the Van Vleck contribution in order to advance the understanding of orbital paramagnetism in transition metals;The required energy bands and wavefunctions are determined^from the augmented plane wave (APW) method, and the Kubo-^Obata formula (1) is used to obtain a value for the Van Vleck orbital^susceptibility. Estimates of the spin and diamagnetic terms are made^and the sum of the various contributions is computed to obtain the^bulk susceptibility. Our calculations yielded the values (chi)(,(PARLL)) = 362 x^10(\u27-6) emu/mole and (chi)(,(PERP)) = 384 x 10(\u27-6) emu/mole for the susceptibility^of Sc and the values (chi)(,(PARLL)) = 159 x 10(\u27-6) emu/mole and (chi)(,(PERP)) = 164 x^10(\u27-6) emu/mole for the susceptibility of Zr. These calculated resultsfor Sc and Zr are then compared to the measurements of Speddingand Croat (2) and Collings and Ho (3), respectively. The calculatedand measured values of the susceptibility in Sc are found to agreequite well with one another. On the other hand, for Zr we find amarked disagreement between the calculated and measuredsusceptibilities. Attempts are made to understand this disagreement;and suggestions are made for additional calculations to expedite the solution of this and related problems; *DOE Report IS-T-1050. This work was performed under Contract No. W-7405-eng-82 with the U.S. Department of Energy.(1) R. Kubo and Y. Obata, J. Phys. Soc. Japan 11, 547 (1956).(2) F. H. Spedding and J. J. Croat, J. Chem. Phys. 58, 5514 (1973).(3) E. W. Collings and J. C. Ho, Phys. Rev. B 4, 349 (1971)

Analyticity Properties of Graham-Witten Anomalies

Analytic properties of Graham-Witten anomalies are considered. Weyl anomalies according to their analytic properties are of type A (coming from $\delta$-singularities in correlators of several energy-momentum tensors) or of type B (originating in counterterms which depend logarithmically on a mass scale). It is argued that all Graham-Witten anomalies can be divided into 2 groups: internal and external, and that all external anomalies are of type B, whereas among internal anomalies there is one term of type A and all the rest are of type B. This argument is checked explicitly for the case of a free scalar field in a 6-dimensional space with a 2-dimensional submanifold.Comment: 2 typos correcte

The Third Way to Interacting p-form Theories

We construct a class of interacting $(d-2)$-form theories in $d$ dimensions that are `third way' consistent. This refers to the fact that the interaction terms in the $p$-form field equations of motion neither come from the variation of an action nor are they off-shell conserved on their own. Nevertheless the full equation is still on-shell consistent. Various generalizations, e.g. coupling them to $(d-3)$-forms, where 3-algebras play a prominent role, are also discussed. The method to construct these models also easily recovers the modified 3$d$ Yang-Mills theory obtained earlier and straightforwardly allows for higher derivative extensions

Higher Spin Black Holes in Three Dimensions: Comments on Asymptotics and Regularity

In the context of (2+1)--dimensional SL(N,R)\times SL(N,R) Chern-Simons theory we explore issues related to regularity and asymptotics on the solid torus, for stationary and circularly symmetric solutions. We display and solve all necessary conditions to ensure a regular metric and metric-like higher spin fields. We prove that holonomy conditions are necessary but not sufficient conditions to ensure regularity, and that Hawking conditions do not necessarily follow from them. Finally we give a general proof that once the chemical potentials are turn on -- as demanded by regularity -- the asymptotics cannot be that of Brown-Henneaux