Renyi entropies of free bosons on the torus and holography

We analytically evaluate the Renyi entropies for the two dimensional free boson CFT. The CFT is considered to be compactified on a circle and at finite temperature. The Renyi entropies S_n are evaluated for a single interval using the two point function of bosonic twist fields on a torus. For the case of the compact boson, the sum over the classical saddle points results in the Riemann-Siegel theta function associated with the A_{n-1} lattice. We then study the Renyi entropies in the decompactification regime. We show that in the limit when the size of the interval becomes the size of the spatial circle, the entanglement entropy reduces to the thermal entropy of free bosons on a circle. We then set up a systematic high temperature expansion of the Renyi entropies and evaluate the finite size corrections for free bosons. Finally we compare these finite size corrections both for the free boson CFT and the free fermion CFT with the one-loop corrections obtained from bulk three dimensional handlebody spacetimes which have higher genus Riemann surfaces as its boundary. One-loop corrections in these geometries are entirely determined by quantum numbers of the excitations present in the bulk. This implies that the leading finite size corrections contributions from one-loop determinants of the Chern-Simons gauge field and the Dirac field in the dual geometry should reproduce that of the free boson and the free fermion CFT respectively. By evaluating these corrections both in the bulk and in the CFT explicitly we show that this expectation is indeed true.Comment: Published version. 56 pages. 6 figures. Argument for the agreement of the leading finite size corrections evaluated from CFT and gravity has been adde

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N|N-1). The algebra for the N=3 case is written down explicitly using the fact that it arises as the global part of the super conformal W_3 superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N-1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N\geq 4, the sl(N|N-1) theory admits smooth supersymmetric conical defects.Comment: 40 pages, includes discussion of conical defects for N\geq 4, typos corrected and presentation improve

The Deconfinement Transition in SO(3) Gauge Theory

The SO(3) lattice gauge theory with a Villain form of action was investigated by Monte Carlo techniques on asymmetric lattices with Nt = 2 and 4, where Nt is the number of sites in the temporal extent. Unlike the results for higher Nt, only one transition of second order was found for Nt = 2 . An extended action with an irrelevant term to suppress Z_2 monopoles enabled us to get a better view of the deconfinement transition as the effects of bulk transition could be suppressed as well. Although the action has no global Z_2 symmetry for the SO(3) theory, unlike the SU(2) theory at finite temperature, our study revealed a second order deconfinement transition, with properties similar to the deconfinement transition of SU(2).Comment: 19 pages latex, incl. figure

Black holes in higher spin supergravity

We study black hole solutions in Chern-Simons higher spin supergravity based on the superalgebra sl(3|2). These black hole solutions have a U(1) gauge field and a spin 2 hair in addition to the spin 3 hair. These additional fields correspond to the R-symmetry charges of the supergroup sl(3|2). Using the relation between the bulk field equations and the Ward identities of a CFT with N=2 super-W_3 symmetry, we identify the bulk charges and chemical potentials with those of the boundary CFT. From these identifications we see that a suitable set of variables to study this black hole is in terms of the charges present in three decoupled bosonic sub-algebras of the N=2 super-W_3 algebra. The entropy and the partition function of these R-charged black holes are then evaluated in terms of the charges of the bulk theory as well as in terms of its chemical potentials. We then compute the partition function in the dual CFT and find exact agreement with the bulk partition function.Comment: 27 pages. Published versio

Relation between dispersion lines and conductance of telescoped armchair double-wall nanotubes analyzed using perturbation formulas and first-principles calculations

The Landauer's formula conductance of the telescoped armchair nanotubes is calculated with the Hamiltonian defined by first-principles calculations (SIESTA code). Herein, partially extracting the inner tube from the outer tube is called 'telescoping'. It shows a rapid oscillation superposed on a slow oscillation as a function of discrete overlap length $(L-1/2)a$ with an integer variable $L$ and the lattice constant $a$. Considering the interlayer Hamiltonian as a perturbation, we obtain the approximate formula of the amplitude of the slow oscillation as $|A|^2/(|A|^2+\varepsilon^2)$ where $A$ is the effective interlayer interaction and $\varepsilon$ is the band split without interlayer interaction. The approximate formula is related to the Thouless number of the dispersion lines.Comment: 9 figure

Finite Conductivity in Mesoscopic Hall Bars of Inverted InAs/GaSb Quantum Wells

We have studied experimentally the low temperature conductivity of mesoscopic size InAs/GaSb quantum well Hall bar devices in the inverted regime. Using a pair of electrostatic gates we were able to move the Fermi level into the electron-hole hybridization state, and observe a mini gap. Temperature dependence of the conductivity in the gap shows residual conductivity, which can be consistently explained by the contributions from the free as well as the hybridized carriers in the presence of impurity scattering, as proposed by Naveh and Laikhtman [Euro. Phys. Lett., 55, 545-551 (2001)]. Experimental implications for the stability of proposed helical edge states will be discussed.Comment: 5 pages, 4 figure

Scattering Theory for Quantum Hall Anyons in a Saddle Point Potential

We study the theory of scattering of two anyons in the presence of a quadratic saddle-point potential and a perpendicular magnetic field. The scattering problem decouples in the centre-of-mass and the relative coordinates. The scattering theory for the relative coordinate encodes the effects of anyon statistics in the two-particle scattering. This is fully characterized by two energy-dependent scattering phase shifts. We develop a method to solve this scattering problem numerically, using a generalized lowest Landau level approximation.Comment: 5 pages. Published version, with clarified presentatio