Clockworked VEVs and Neutrino Mass

In this paper we present an augmented version of the Abelian scalar clockwork model to generate geometrically suppressed vacuum expectation values (vev) of the pseudo Nambu-Goldstone bosons, that we call the clockworked vevs. We briefly comment on generalization of the setup and possible 5D UV realizations. We demonstrate how tiny neutrino mass can be generated by clockworking a weak scale vev.Comment: 13 pages, 2 captioned figures, 1 table, further clarifications added in text, references updated, matches version published in JHE

Heavily separable functors of the second kind and applications

We introduce heavily separable functors of the second kind and study them in three different situations. The first of these is with restrictions and extensions of scalars for modules over small preadditive categories. The second is with free functors taking values in Eilenberg-Moore categories associated to a monad or a comonad. Finally, we consider entwined modules and give if and only if conditions for heavy separability of the second kind for functors forgetting either the comodule action or the module action

Hilbert spaces over C∗C^*-tensor categories, Fredholm modules and cyclic cohomology

We construct Fredholm modules over an algebra taking values in generalized Hilbert spaces over a rigid $C^*$-tensor category. Using methods of Connes, we obtain Chern characters taking values in cyclic cohomology. These Chern characters are well behaved with respect to the periodicity operator, and depend only on the homotopy class of the Fredholm module

The Elusive member of the Ti-Al-C MAX family- Ti4AlC3

We report here perhaps the first successful synthesis and structural characterization of the n=3 family member of Tin+1AlCn, i. e. Ti4AlC3. X-ray Powder diffraction (XRD) data shows characteristic reflections of from corresponding to reflections from the (002), (004), (006), (008), (100), (102), (104), (0010), (105), (106), (0012), (1011) and (1012) planes at 2{\theta} =7.640, 15.170, 22.760, 30.50, 350, 37.40 38.30, 39.20, 41.30, 46.220, 55.240, 58.620 and 60.780 (double structure) respectively. Rietveld refinement of the XRD data reveals a phase purity of about 79 % for alpha-Ti4AlC3, 15 % for beta-Ti4AlC3 and the rest mostly that of cubic TiC (6 %). The primary crystal symmetry of the two dominant phases is the hexagonal P63/mmc. The precursors chosen were TiH2, Al metal powder and Carbon powder in a molar ratio of 3:1.2:2, which build the case for an Al-deficient condition. We adopted the pressureless sintering technique at 13500 C with a dwelling time of 4 hours under ultra-high vacuum of 10-7 mbar. The co-existence of trace amount of Ti2AlC at 1350 deg C is proven by the small structure at 2{\theta}=13.130. No trace of oxides like Al2O3 or TiO2 was found in the end product. The line profile width of XRD data indicates average grain size of the order of micro meter. The Scanning Electron Microscopy images show highly lamellar stacked growth of almost a pure MAX (alpha or beta) phase and grain size of micron order, agreeing well with the XRD data