A few remarks on the zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges

The construction outlined by Henyey is employed to provide examples of normalizable zero modes of the Faddeev-Popov operator in the Landau and maximal Abelian gauges in SU(2) Euclidean Yang-Mills theories in d=3 dimensions. The corresponding gauge configurations have all finite norm ||A||^2 < \infty. In particular, in the case of the Landau gauge, the explicit construction of an infinite class of normalizable zero modes with finite norm ||A||^2 is provided.Comment: 9 pages. Extended discussion in the conclusions. Version accepted for publication in the J. Math. Phy

Long-distance radiative coupling between quantum dots in photonic crystal dimers

We study the mutual interaction between two identical quantum dots coupled to the normal modes of two-site photonic crystal molecules in a planar waveguide geometry, i.e. photonic crystal dimers. We find that the radiative coupling between the two quantum emitters is maximized when they are in resonance with either the bonding or the antibonding modes of the coupled cavity system. Moreover, we find that such effective interdot coupling is sizable, in the meV range, and almost independent from the cavities distance, as long as a normal mode splitting exceeding the radiative linewidth can be established (strong cavity-cavity coupling condition). In realistic and high quality factor photonic crystal cavity devices, such distance can largely exceed the emission wavelength, which is promising for long distance entanglement generation between two qubits in an integrated nanophotonic platform. We show that these results are robust against position disorder of the two quantum emitters within their respective cavities.Comment: 10 pages, 6 figure

Pad\'e approximation and glueball mass estimates in 3d and 4d with N_c = 2,3 colors

A Pad\'e approximation approach, rooted in an infrared moment technique, is employed to provide mass estimates for various glueball states in pure gauge theories. The main input in this analysis are theoretically well-motivated fits to lattice gluon propagator data, which are by now available for both SU(2) and SU(3) in 3 and 4 space-time dimensions. We construct appropriate gauge invariant and Lorentz covariant operators in the (pseudo)scalar and (pseudo)tensor sector. Our estimates compare reasonably well with a variety of lattice sources directly aimed at extracting glueball masses.Comment: 11 pages, 5 .png figures. v2: extra figure, calculational details and references; improved presentation and title. Version to appear in Phys.Lett.

Accessing the topological susceptibility via the Gribov horizon

The topological susceptibility, $\chi^4$, following the work of Witten and Veneziano, plays a key role in identifying the relative magnitude of the $\eta^{\prime}$ mass, the so-called $U(1)_{A}$ problem. A nonzero $\chi^4$ is caused by the Veneziano ghost, the occurrence of an unphysical massless pole in the correlation function of the topological current. In a recent paper (Phys.Rev.Lett.114 (2015) 24, 242001), an explicit relationship between this Veneziano ghost and color confinement was proposed, by connecting the dynamics of the Veneziano ghost, and thus the topological susceptibility, with Gribov copies. However, the analysis is incompatible with BRST symmetry (Phys.Rev.D 93 (2016) no.8, 085010). In this paper, we investigate the topological susceptibility, $\chi^4$, in SU(3) and SU(2) Euclidean Yang-Mills theory using an appropriate Pad\'e approximation tool and a non-perturbative gluon propagator, within a BRST invariant framework and by taking into account Gribov copies in a general linear covariant gauge.Comment: 17 pages, 4 figures. v2: corrected typos, new figures, improved style of presentatio

An all-order proof of the equivalence between Gribov's no-pole and Zwanziger's horizon conditions

The quantization of non-Abelian gauge theories is known to be plagued by Gribov copies. Typical examples are the copies related to zero modes of the Faddeev-Popov operator, which give rise to singularities in the ghost propagator. In this work we present an exact and compact expression for the ghost propagator as a function of external gauge fields, in SU(N) Yang-Mills theory in the Landau gauge. It is shown, to all orders, that the condition for the ghost propagator not to have a pole, the so-called Gribov's no-pole condition, can be implemented by demanding a nonvanishing expectation value for a functional of the gauge fields that turns out to be Zwanziger's horizon function. The action allowing to implement this condition is the Gribov-Zwanziger action. This establishes in a precise way the equivalence between Gribov's no-pole condition and Zwanziger's horizon condition.Comment: 11 pages, typos corrected, version accepted for publication in Phys. Lett.

Mapping quantitative trait loci for performance traits on pig chromosome 6 (SSC6).

The objective of this study was to perform QTL mapping associated with performance traits on swine chromosome 6 (SSC6). The F2 population was produced by outcrossing using two native Brazilian breed Piau sires and 18 commercial dams. A total of 617 F2 animals were genotyped for 13 microsatellite markers. The traits evaluated in the F2 population were teat number (TN), birth weight (BW), weight at 21, 42, 63, 77 and 105 days of age (W21, W42, W63, W77, W105), weight at slaughter (WS), and average daily gain (ADG), feed intake (FI) and feed/gain ratio (FG) from 77 to 105 days of age. Data were analyzed by multiple regression developed for analysis of crosses between outbred lines, using the QTL Express software. A significant QTL was detected for FI at 99 cM. A suggestive QTL was detected for W42 located at 55 cM. A locus located at 100 cM seems to affect the traits FI and ADG. Evidence for loci affecting weight at the other ages not was not found. O objetivo deste estudo foi obter o mapeamento de QTL no cromossomo 6 suíno (SSC6) associado a características de desempenho. A população F2 foi produzida utilizando o cruzamento divergente de dois reprodutores da raça nativa brasileira Piau e 18 fêmeas comerciais. Um total de 617 animais F2 foram genotipados para 13 marcadores microssatélites. As características avaliadas na população F2 foram: número de tetas (TN), peso ao nascimento (BW), peso aos 21, 42, 63, 77 e 105 dias de idade (W21, W42, W63, W77, W105), peso ao abate (WS), e ganho de peso médio diário (ADG), consumo de ração (FI) e conversão alimentar (FG) dos 77 aos 105 dias de idade. Os dados foram analisados usando a metodologia de regressão múltipla desenvolvida para análises de cruzamentos entre linhas divergentes, usando o software QTL Express. Um QTL significativo foi detectado para FI em 99 cM. Um QTL sugestivo foi detectado para W42 localizado em 55cM. As características FI e ADG parecem estar sob a influência de um loco situado em torno de 100 cM no cromossomo estudado. Não foram encontrados QTLs para peso em as outras diferentes idades