Analytic Results for Massless Three-Loop Form Factors

We evaluate, exactly in d, the master integrals contributing to massless three-loop QCD form factors. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm. Using our results for the master integrals we obtain analytical expressions for two missing constants in the ep-expansion of the two most complicated master integrals and present the form factors in a completely analytic form.Comment: minor revisions, to appear in JHE

Gravitational physics with antimatter

The production of low-energy antimatter provides unique opportunities to search for new physics in an unexplored regime. Testing gravitational interactions with antimatter is one such opportunity. Here a scenario based on Lorentz and CPT violation in the Standard- Model Extension is considered in which anomalous gravitational effects in antimatter could arise.Comment: 5 pages, presented at the International Conference on Exotic Atoms (EXA 2008) and the 9th International Conference on Low Energy Antiproton Physics (LEAP 2008), Vienna, Austria, September 200

Electromagnetic wave diffraction by periodic planar metamaterials with nonlinear constituents

We present a theory which explains how to achieve an enhancement of nonlinear effects in a thin layer of nonlinear medium by involving a planar periodic structure specially designed to bear a trapped-mode resonant regime. In particular, the possibility of a nonlinear thin metamaterial to produce the bistable response at a relatively low input intensity due to a large quality factor of the trapped-mode resonance is shown. Also a simple design of an all-dielectric low-loss silicon-based planar metamaterial which can provide an extremely sharp resonant reflection and transmission is proposed. The designed metamaterial is envisioned for aggregating with a pumped active medium to achieve an enhancement of quantum dots luminescence and to produce an all-dielectric analog of a 'lasing spaser'.Comment: 18 pages, 13 figure

Isotopic variation of parity violation in atomic ytterbium

We report on measurements of atomic parity violation, made on a chain of ytterbium isotopes with mass numbers A=170, 172, 174, and 176. In the experiment, we optically excite the 6s2 1S0 -> 5d6s 3D1 transition in a region of crossed electric and magnetic fields, and observe the interference between the Stark- and weak-interaction-induced transition amplitudes, by making field reversals that change the handedness of the coordinate system. This allows us to determine the ratio of the weak-interaction-induced electric-dipole (E1) transition moment and the Stark-induced E1 moment. Our measurements, which are at the 0.5% level of accuracy for three of the four isotopes measured, allow a definitive observation of the isotopic variation of the weak-interaction effects in an atom, which is found to be consistent with the prediction of the Standard Model. In addition, our measurements provide information about an additional Z' boson.Comment: 19 pages, 4 figures, 2 table

BKM Lie superalgebras from counting twisted CHL dyons

Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with N=4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, are given in terms of multiplicative eta products with the Mathieu group, M_{24}, playing an important role. These multiplicative eta products enable us to construct Siegel modular forms that count twisted quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a special class of Siegel modular forms, the dd-modular forms, that have been classified by Clery and Gritsenko[arXiv:0812.3962]. We show that each one of these dd-modular forms arise as the Weyl-Kac-Borcherds denominator formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the Weyl chamber are in one-to-one correspondence with the walls of marginal stability in the corresponding CHL model for twisted dyons as well as untwisted ones. This leads to a periodic table of BKM Lie superalgebras with properties that are consistent with physical expectations.Comment: LaTeX, 32 pages; (v2) matches published versio

Unwinding of a cholesteric liquid crystal and bidirectional surface anchoring

We examine the influence of bidirectional anchoring on the unwinding of a planar cholesteric liquid crystal induced by the application of a magnetic field. We consider a liquid crystal layer confined between two plates with the helical axis perpendicular to the substrates. We fixed the director twist on one boundary and allow for bidirectional anchoring on the other by introducing a high-order surface potential. By minimizing the total free energy for the system, we investigate the untwisting of the cholesteric helix as the liquid crystal attempts to align with the magnetic field. The transitions between metastable states occur as a series of pitchjumps as the helix expels quarter or half-turn twists, depending on the relative sizes of the strength of the surface potential and the bidirectional anchoring. We show that secondary easy axis directions can play a significant role in the unwinding of the cholesteric in its transition towards a nematic, especially when the surface anchoring strength is large

Atomic transition frequencies, isotope shifts, and sensitivity to variation of the fine structure constant for studies of quasar absorption spectra

Theories unifying gravity with other interactions suggest spatial and temporal variation of fundamental "constants" in the Universe. A change in the fine structure constant, alpha, could be detected via shifts in the frequencies of atomic transitions in quasar absorption systems. Recent studies using 140 absorption systems from the Keck telescope and 153 from the Very Large Telescope, suggest that alpha varies spatially. That is, in one direction on the sky alpha seems to have been smaller at the time of absorption, while in the opposite direction it seems to have been larger. To continue this study we need accurate laboratory measurements of atomic transition frequencies. The aim of this paper is to provide a compilation of transitions of importance to the search for alpha variation. They are E1 transitions to the ground state in several different atoms and ions, with wavelengths ranging from around 900 - 6000 A, and require an accuracy of better than 10^{-4} A. We discuss isotope shift measurements that are needed in order to resolve systematic effects in the study. The coefficients of sensitivity to alpha-variation (q) are also presented.Comment: Includes updated version of the "alpha line" lis

On AGT description of N=2 SCFT with N_f=4

We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov partition function of N=2 SCFT. We focus our attention on the SU(2) theory with N_f=4 flavor symmetry, whose partition function, according to AGT, is given by the Liouville four-point function on the sphere. The gauge theory with N_f=4 is known to exhibit SO(8) symmetry. We explain how the Weyl symmetry transformations of SO(8) flavor symmetry are realized in the Liouville theory picture. This is associated to functional properties of the Liouville four-point function that are a priori unexpected. In turn, this can be thought of as a non-trivial consistency check of AGT conjecture. We also make some comments on elementary surface operators and WZW theory.Comment: 18 pages. v2, a misinterpretation in the gauge theory side has been corrected; title and introduction were changed accordingl

Pure-glue hidden valleys through the Higgs portal

We consider the possibility that the Higgs boson can act as a link to a hidden sector in the context of pure-glue hidden valley models. In these models the standard model is weakly coupled, through loops of heavy messengers fields, to a hidden sector whose low energy dynamics is described by a pure-Yang-Mills theory. Such a hidden sector contains several metastable hidden glueballs. In this work we shall extend earlier results on hidden valleys to include couplings of the messengers to the standard model Higgs sector. The effective interactions at one-loop couple the hidden gluons to the standard model particles through the Higgs sector. These couplings in turn induce hidden glueball decays to fermion pairs, or cascade decays with multiple Higgs emission. The presence of effective operators of different mass dimensions, often competing with each other, together with a great diversity of states, leads to a great variability in the lifetimes and decay modes of the hidden glueballs. We find that most of the operators considered in this paper are not heavily constrained by precision electroweak physics, therefore leaving plenty of room in the parameter space to be explored by the future experiments at the LHC.Comment: 44 pages, 16 figures. Major revision for JHEP, corrected an error in Eq. 5.1, comments adde

Parafermionic Liouville field theory and instantons on ALE spaces

In this paper we study the correspondence between the $\hat{\textrm{su}}(n)_{k}\oplus \hat{\textrm{su}}(n)_{p}/\hat{\textrm{su}}(n)_{k+p}$ coset conformal field theories and $\mathcal{N}=2$ SU(n) gauge theories on $\mathbb{R}^{4}/\mathbb{Z}_{p}$. Namely we check the correspondence between the SU(2) Nekrasov partition function on $\mathbb{R}^{4}/\mathbb{Z}_{4}$ and the conformal blocks of the $S_{3}$ parafermion algebra (in $S$ and $D$ modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. Studying the structure of the instanton partition function on $\mathbb{R}^4/\mathbb{Z}_p$ we also find some evidence that this correspondence with arbitrary $p$ takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version to appear in JHE