Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra

Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate different scales in the spectral fluctuations. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator for staggered fermions from SU(2) lattice gauge theory for different lattice size and gauge couplings. In disordered systems, the Thouless energy sets the universal scale for which RMT applies. This relates to recent theoretical studies which suggest a strong analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with high quality. We find deviations which allows us to give an estimate for this universal scale. Other deviations than these are seen whose possible origin is discussed. Moreover, we work out higher order correlators as well, in particular three--point correlation functions.Comment: 24 pages, 24 figures, all included except one figure, missing eps file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised version, to appear in PRD, minor modifications and corrected typos, Fig.4 revise

BMN operators with vector impurities, Z_2 symmetry and pp-waves

We calculate the coefficients of three-point functions of BMN operators with two vector impurities. We find that these coefficients can be obtained from those of the three-point functions of scalar BMN operators by interchanging the coefficient for the symmetric-traceless representation with the coefficient for the singlet. We conclude that the Z_2 symmetry of the pp-wave string theory is not manifest at the level of field theory three-point correlators.Comment: 25 pages, 7 figures. v1: A reference and a footnote added; v2: New contributions found, Z_2 symmetry lost in 3-point function

Lectures on Chiral Disorder in QCD

I explain the concept that light quarks diffuse in the QCD vacuum following the spontaneous breakdown of chiral symmetry. I exploit the striking analogy to disordered electrons in metals, identifying, among others, the universal regime described by random matrix theory, diffusive regime described by chiral perturbation theory and the crossover between these two domains.Comment: Lectures given at the Cargese Summer School, August 6-18, 200

Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons

We study the bosonic and fermionic zero modes in noncommutative instanton backgrounds based on the ADHM construction. In k instanton background in U(N) gauge theory, we show how to explicitly construct 4Nk (2Nk) bosonic (fermionic) zero modes in the adjoint representation and 2k (k) bosonic (fermionic) zero modes in the fundamental representation from the ADHM construction. The number of fermionic zero modes is also shown to be exactly equal to the Atiyah-Singer index of the Dirac operator in the noncommutative instanton background. We point out that (super)conformal zero modes in non-BPS instantons are affected by the noncommutativity. The role of Lorentz symmetry breaking by the noncommutativity is also briefly discussed to figure out the structure of U(1) instantons.Comment: v3: 24 pages, Latex, corrected typos, references added, to appear in Phys. Rev.

Propagators in Noncommutative Instantons

We explicitly construct Green functions for a field in an arbitrary representation of gauge group propagating in noncommutative instanton backgrounds based on the ADHM construction. The propagators for spinor and vector fields can be constructed in terms of those for the scalar field in noncommutative instanton background. We show that the propagators in the adjoint representation are deformed by noncommutativity while those in the fundamental representation have exactly the same form as the commutative case.Comment: 28 pages, Latex, v2: A few typos correcte

Computation of the winding number diffusion rate due to the cosmological sphaleron

A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in a static Einstein universe is carried out. By examining spectra of the fluctuation operators and applying the zeta function regularization scheme, a closed analytical expression for the transition rate at the one-loop level is derived. This is a unique example of an exact solution for a sphaleron model in $3+1$ spacetime dimensions.Comment: Some style corrections suggested by the referee are introduced (mainly in Sec.II), one reference added. To appear in Phys.Rev.D 29 pages, LaTeX, 3 Postscript figures, uses epsf.st

Planet Hunters Tess I: TOI 813, a subgiant hosting a transiting Saturn-sized planet on an 84-day orbit

We report on the discovery and validation of TOI 813 b (TIC55525572b), a transiting exoplanet identified by citizen scientists in data from NASA's Transiting Exoplanet Survey Satellite (TESS) and the first planet discovered by the Planet Hunters TESS project. The host star is a bright (V = 10.3 mag) subgiant (R* = 1.94 R☉, M☉ = 1.32 M☉). It was observed almost continuously by TESS during its first year of operations, during which time four individual transit events were detected. The candidate passed all the standard light curve-based vetting checks, and ground-based follow-up spectroscopy and speckle imaging enabled us to place an upper limit of 2 MJup (99 per cent confidence) on the mass of the companion, and to statistically validate its planetary nature. Detailed modelling of the transits yields a period of 83.8911+0.0027-0.0031 d, a planet radius of 6.71 ± 0.38 R⊕ and a semimajor axis of 0.423+0031-0.037 AU. The planet's orbital period combined with the evolved nature of the host star places this object in a relatively underexplored region of parameter space. We estimate that TOI 813 b induces a reflex motion in its host star with a semi-amplitude of ∼6 m s−1, making this a promising system to measure the mass of a relatively long-period transiting planet

A hot mini-Neptune in the radius valley orbiting solar analogue HD 110113

We report the discovery of HD 110113 b (TESS object of interest-755.01), a transiting mini-Neptune exoplanet on a 2.5-d orbit around the solar-analogue HD 110113 (Teff = 5730 K). Using TESS photometry and High Accuracy Radial velocity Planet Searcher (HARPS) radial velocities gathered by the NCORES program, we find that HD 110113 b has a radius of 2.05 ± 0.12 R⊕ and a mass of 4.55 ± 0.62 M⊕. The resulting density of $2.90^{+0.75}_{-0.59}$ g cm-3 is significantly lower than would be expected from a pure-rock world; therefore HD 110113 b must be a mini-Neptune with a significant volatile atmosphere. The high incident flux places it within the so-called radius valley; however, HD 110113 b was able to hold on to a substantial (0.1-1 per cent) H-He atmosphere over its ∼4 Gyr lifetime. Through a novel simultaneous Gaussian process fit to multiple activity indicators, we were also able to fit for the strong stellar rotation signal with period 20.8 ± 1.2 d from the RVs and confirm an additional non-transiting planet, HD 110113 c, which has a mass of 10.5 ± 1.2 M⊕ and a period of $6.744^{+0.008}_{-0.009}$ d