Interplay of structural distortions, dielectric effects and magnetic order in multiferroic GdMnO3

Multiferroic materials are characterized by simultaneous magnetic and ferroelectric ordering making them good candidates for magneto-electrical applications. We conducted thermal expansion and magnetostriction measurements in magnetic fields up to 14 T on perovskitic GdMnO3 by highresolution capacitive dilatometry in an effort to determine all longitudinal and transversal components of the magnetostriction tensor. Below the ordering temperature T (N) = 42 K, i.e., within the different complex (incommensurate or complex) antiferromagnetic phases, lattice distortions of up to 100 ppm have been found. Although no change of the lattice symmetry occurs, the measurements reveal strong magneto-structural phenomena, especially in the incommensurate sinusoidal antiferromagnetic phase. A strong anisotropy of the magnetoelastic properties was found, in good agreement with the type and propagation vector of the magnetic structure. We demonstrate that our capacitive dilatometry can detect lattice expansion effects and changes of the dielectric permittivity simultaneously because the sample is housed inside the capacitor. A separation of both effects is possible by shielding the sample. Dielectric transitions could be detected by this method and compared to the critical values of H and T in the magnetic phase diagram. Dielectric changes measured at 1 kHz excitation frequency are detected in GdMnO3 at about 180 K, and between 10 K and 25 K in the canted antiferromagnetic structure which is characterized by a complex magnetic order on both the Gd- and Mn-sites.

Higher spin resolution of a toy big bang

Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three-dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS(3)-gravity can be written as an SL(2, C) Chern-Simons theory, we investigate SL(3, C) Chern-Simons theory as a higher-spin context in which these singularities might get resolved. As in the case of higher spin black holes in AdS(3), the solutions are invariantly characterized by their holonomies. We show that the dS(3) quotient singularity can be desingularized by an SL(3, C) gauge transformation that preserves the holonomy: this is a higher spin resolution the cosmological singularity. Our work deals exclusively with the bulk theory, and is independent of the subtleties involved in defining a CFT2 dual to dS(3) in the sense of dS/CFT.

Black holes in higher spin supergravity

We study black hole solutions in Chern-Simons higher spin supergravity based on the superalgebra sl(3 vertical bar 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 vertical bar 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.

Entanglement entropy from the holographic stress tensor

We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero, the timetime component of the Brown-York stress tensor evaluated on the co-dimension 1 entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that the Euclidean actionmethods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription.

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.

Relative entropy in higher spin holography

We examine relative entropy in the context of the higher spin/CFT duality. We consider 3D bulk configurations in higher spin gravity which are dual to the vacuum and a high temperature state of a CFT with W-algebra symmetries in the presence of a chemical potential for a higher spin current. The relative entropy between these states is then evaluated using the Wilson line functional for holographic entanglement entropy. In the limit of small entangling intervals, the relative entropy should vanish for a generic quantum system. We confirm this behavior by showing that the difference in the expectation values of the modular Hamiltonian between the states matches with the difference in the entanglement entropy in the short-distance regime. Additionally, we compute the relative entropy of states corresponding to smooth solutions in the SL(2, Z) family with respect to the vacuum.

A Variant of the Hadwiger-Debrunner (p, q)-Problem in the Plane

Let X be a convex curve in the plane (say, the unit circle), and let be a family of planar convex bodies such that every two of them meet at a point of X. Then has a transversal of size at most . Suppose instead that only satisfies the following ``(p, 2)-condition'': Among every p elements of , there are two that meet at a common point of X. Then has a transversal of size . For comparison, the best known bound for the Hadwiger-Debrunner (p, q)-problem in the plane, with , is . Our result generalizes appropriately for if is, for example, the moment curve.

epsilon-expansions near three dimensions from conformal field theory

We formally extend the CFT techniques introduced in arXiv: 1505.00963, to phi(2d0/d0-2) theory in d = d(0) dimensions and use it to compute anomalous dimensions near d(0) = 3, 4 in a unified manner. We also do a similar analysis of the O(N) model in three dimensions by developing a recursive combinatorial approach for OPE contractions. Our results match precisely with low loop perturbative computations. Finally, using 3-point correlators in the CFT, we comment on why the phi(3) theory in d(0) = 6 is qualitatively different.

Analytic bootstrap at large spin

We use analytic conformal bootstrap methods to determine the anomalous dimensions and OPE coefficients for large spin operators in general conformal field theories in four dimensions containing a scalar operator of conformal dimension Delta(phi). It is known that such theories will contain an in finite sequence of large spin operators with twists approaching 2 Delta(phi) + 2n for each integer n. By considering the case where such operators are separated by a twist gap from other operators at large spin, we analytically determine the n, Delta(phi) dependence of the anomalous dimensions. We find that for all n, the anomalous dimensions are negative for Delta(phi) satisfying the unitarity bound. We further compute the first subleading correction at large spin and show that it becomes universal for large twist. In the limit when n is large, we find exact agreement with the AdS/CFT prediction corresponding to the Eikonal limit of a 2-2 scattering with dominant graviton exchange.