Nambu Bracket for M Theory

In this article we give a concise review of recent progress in our understanding of the Lie 3-algebra and their application to the Bagger-Lambert-Gustavsson model describing multiple M2-branes in M theory.Comment: 13 pages, prepared for The Fourth International Symposium on Symmetries in Subatomic Physics (SSP 2009), minor modification, references adde

Holographic Superconductors with Ho\v{r}ava-Lifshitz Black Holes

We discuss the phase transition of planar black holes in Ho\v{r}ava-Lifshitz gravity by introducing a Maxwell field and a complex scalar field. We calculate the condensates of the charged operators in the dual CFTs when the mass square of the complex scalar filed is $m^2=-2/L^2$ and $m^2=0$, respectively. We compute the electrical conductivity of the \hl superconductor in the probe approximation. In particular, it is found that there exists a spike in the conductivity for the case of the operator with scaling dimension one. These results are quite similar to those in the case of Schwarzschild-AdS black holes, which demonstrates that the holographic superconductivity is a robust phenomenon associated with asymptotic AdS black holes.Comment: 12 pages, 7 figures,refs adde

Heterotic and type I strings from twisted supermembranes

As shown by Ho\v{r}ava and Witten, there are gravitational anomalies at the boundaries of $M^{10}\times S^1/Z_2$ of 11 dimensional supergravity. They showed that only 10 dimensional vector multiplets belonging to $E_8$ gauge group can be consistently coupled to this theory. Thus, the dimensional reduction of this theory should be the low energy limit of the $E_8\times E_8$ heterotic string. Here we assume that M-theory is a theory of supermembranes which includes twisted supermembranes. We show that for a target space $M^{10}\times S^1/Z_2$, in the limit in which $S^1/Z_2$ is small, the effective action is the $E_8\times E_8$ heterotic string. We also consider supermembranes on $M^{9}\times S^1\times S^1/Z_2$ and find the dualities expected from 11 dimensional supergravity on this manifold. We show that the requirements for worldsheet anomaly cancellations at the boundaries of the worldvolume action are the same requirements imposed on the Ho\v{r}ava-Witten action.Comment: 17 pages, Late

Temperature evolution of magnetic structure of HoFeO3_3 by single crystal neutron diffraction

We have investigated the temperature evolution of the magnetic structures of HoFeO$_3$ by single crystal neutron diffraction. The three different magnetic structures found as a function of temperature for \hfo\ are described by the magnetic groups Pb$'$n$'2_1$, Pbn$2_1$ and Pbn$'2_1'$ and are stable in the temperature ranges $\approx$ 600-55~K, 55-37~K and 35$>T>2$~K respectively. In all three the fundamental coupling between the Fe sub-lattices remains the same and only their orientation and the degree of canting away from the ideal axial direction varies. The magnetic polarisation of the Ho sub-lattices in these two higher temperature regions, in which the major components of the Fe moment lie along $x$ and $y$, is very small. The canting of the moments from the axial directions is attributed to the antisymmetric interactions allowed by the crystal symmetry. They include contributions from single ion anisotropy as well as the Dzyaloshinski antisymmetric exchange. In the low temperature phase two further structural transitions are apparent in which the spontaneous magnetisation changes sign with respect to the underlying antiferromagnetic configuration. In this temperature range the antisymmetric exchange energy varies rapidly as the the Ho sub-lattices begin to order. So long as the ordered Ho moments are small the antisymmetric exchange is due only to Fe-Fe interactions, but as the degree of Ho order increases the Fe-Ho interactions take over whilst at the lowest temperatures, when the Ho moments approach saturation the Ho-Ho interactions dominate. The reversals of the spontaneous magnetisation found in this study suggest that in \hfo\ the sums of the Fe-Fe and Ho-Ho antisymmetric interactions have the same sign as one another, but that of the Ho-Fe terms is opposite

Magnetic Ordering in the Spin-Ice Candidate Ho2_2Ru2_2O7_7

Neutron scattering measurements on the spin-ice candidate material Ho$_2$Ru$_2$O$_7$ have revealed two magnetic transitions at T $\sim$ 95 K and T $\sim$ 1.4 K to long-range ordered states involving the Ru and Ho sublattices, respectively. Between these transitions, the Ho$^{3+}$ moments form short-ranged ordered spin clusters. The internal field provided by the ordered S=1 Ru$^{4+}$ moments disrupts the fragile spin-ice state and drives the Ho$^{3+}$ moments to order. We have directly measured a slight shift in the Ho$^{3+}$ crystal field levels at 95 K from the Ru ordering.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Letter