A note on higher-derivative actions for free higher-spin fields

Higher-derivative theories of free higher-spin fields are investigated focusing on their symmetries. Generalizing familiar two-derivative constrained formulations, we first construct less-constrained Einstein-like and Maxwell-like higher-derivative actions. Then, we construct Weyl-like actions - the actions admitting constrained Weyl symmetries - with different numbers of derivatives. They are presented in a factorized form making use of Einstein-like and Maxwell-like tensors. The last (highest-derivative) member of the hierarchy of the Weyl-like actions coincides with the Fradkin-Tseytlin conformal higher-spin action in four dimensions.Comment: Version to appear in JHEP, 22 page

Notes on higher-spin algebras: minimal representations and structure constants

The higher-spin (HS) algebras so far known can be interpreted as the symmetries of the minimal representation of the isometry algebra. After discussing this connection briefly, we generalize this concept to any classical Lie algebras and consider the corresponding HS algebras. For sp(2N) and so(N), the minimal representations are unique so we get unique HS algebras. For sl(N), the minimal representation has one-parameter family, so does the corresponding HS algebra. The so(N) HS algebra is what underlies the Vasiliev theory while the sl(2) one coincides with the 3D HS algebra hs[lambda]. Finally, we derive the explicit expression of the structure constant of these algebras --- more precisely, their bilinear and trilinear forms. Several consistency checks are carried out for our results.Comment: minor corrections, references adde

Efros-Shklovskii variable range hopping in reduced graphene oxide sheets of varying carbon sp2 fraction

We investigate the low temperature electron transport properties of chemically reduced graphene oxide (RGO) sheets with different carbon sp2 fractions of 55 to 80 %. We show that in the low bias (Ohmic) regime, the temperature (T) dependent resistance (R) of all the devices follow Efros-Shklovskii variable range hopping (ES-VRH) R ~ exp[(T(ES)/T)^1/2] with T(ES) decreasing from 30976 to 4225 K and electron localization length increasing from 0.46 to 3.21 nm with increasing sp2 fraction. From our data, we predict that for the temperature range used in our study, Mott-VRH may not be observed even at 100 % sp2 fraction samples due to residual topological defects and structural disorders. From the localization length, we calculate a bandgap variation of our RGO from 1.43 to 0.21 eV with increasing sp2 fraction from 55 to 80 % which agrees remarkably well with theoretical prediction. We also show that, in the high bias regime, the hopping is field driven and the data follow R ~ exp[(E(0)/E)^1/2] providing further evidence of ES-VRH.Comment: 13 pages, 6 figures, 1 tabl

RRR Characteristics for SRF Cavities

The first heavy ion accelerator is being constructed by the rare isotope science project (RISP) launched by the Institute of Basic Science (IBS) in South Korea. Four different types of superconducting cavities were designed, and prototypes were fabricated such as a quarter wave resonator (QWR), a half wave resonator (HWR) and a single spoke resonator (SSR). One of the critical factors determining performances of the superconducting cavities is a residual resistance ratio (RRR). The RRR values essentially represent how much niobium is pure and how fast niobium can transmit heat as well. In general, the RRR degrades during electron beam welding due to the impurity incorporation. Thus it is important to maintain RRR above a certain value at which a niobium cavity shows target performance. In this study, RRR degradation related with electron beam welding conditions, for example, welding power, welding speed, and vacuum level will be discussed

Generating functions of (partially-)massless higher-spin cubic interactions

Generating functions encoding cubic interactions of (partially-)massless higher-spin fields are provided within the ambient-space formalism. They satisfy a system of higher-order partial differential equations that can be explicitly solved due to their factorized form. We find that the number of consistent couplings increases whenever the squares of the field masses take some integer values (in units of the cosmological constant) and satisfy certain conditions. Moreover, it is shown that only the supplemental solutions can give rise to non-Abelian deformations of the gauge symmetries. The presence of these conditions on the masses is a distinctive feature of (A)dS interactions that has in general no direct counterpart in flat space.Comment: 29 pages, 2 figures. References adde

An Upper Bound on the Size of Obstructions for Bounded Linear Rank-Width

We provide a doubly exponential upper bound in $p$ on the size of forbidden pivot-minors for symmetric or skew-symmetric matrices over a fixed finite field $\mathbb{F}$ of linear rank-width at most $p$. As a corollary, we obtain a doubly exponential upper bound in $p$ on the size of forbidden vertex-minors for graphs of linear rank-width at most $p$. This solves an open question raised by Jeong, Kwon, and Oum [Excluded vertex-minors for graphs of linear rank-width at most $k$. European J. Combin., 41:242--257, 2014]. We also give a doubly exponential upper bound in $p$ on the size of forbidden minors for matroids representable over a fixed finite field of path-width at most $p$. Our basic tool is the pseudo-minor order used by Lagergren [Upper Bounds on the Size of Obstructions and Interwines, Journal of Combinatorial Theory Series B, 73:7--40, 1998] to bound the size of forbidden graph minors for bounded path-width. To adapt this notion into linear rank-width, it is necessary to well define partial pieces of graphs and merging operations that fit to pivot-minors. Using the algebraic operations introduced by Courcelle and Kant\'e, and then extended to (skew-)symmetric matrices by Kant\'e and Rao, we define boundaried $s$-labelled graphs and prove similar structure theorems for pivot-minor and linear rank-width.Comment: 28 pages, 1 figur