Integrability of the holomorphic anomaly equations
We show that modularity and the gap condition make the holomorphic anomaly equation completely integrable for non-compact Calabi-Yau manifolds. This leads to a very efficient formalism to solve the topological string on these geometries in terms of almost holomorphic modular forms. The formalism provides in particular holomorphic expansions everywhere in moduli space including large radius points, the conifold loci, Seiberg-Witten points and the orbifold points. It can be also viewed as a very efficient method to solve higher genus closed string amplitudes in the 1/N2 expansion of matrix models with more then one cut.

title: Direct integration and non-perturbative effects in matrix models
abstract: We show how direct integration can be used to solve the closed amplitudes of multicut matrix models with polynomial potentials. In the case of the cubic matrix model, we give explicit expressions for the ring of nonholomorphic modular objects that are needed to express all closed matrix model amplitudes. This allows us to integrate the holomorphic anomaly equation up to holomorphic modular terms that we fix by the gap condition up to genus four. There is an onedimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the nonholomorphic modular ring of the group Γ(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. We use these results to make precision tests of the connection between the large order behavior of the 1/N expansion and nonperturbative effects due to instantons. Finally, we argue that a full understanding of the large genus asymptotics in the multicut case requires a new class of nonperturbative sectors in the matrix model.

title: Wall-Crossing Holomorphic Anomaly and Mock Modularity of Multiple M5-Branes
abstract: Using wall-crossing formulae and the theory of mock modular forms we derive a holomorphic anomaly equation for the modified elliptic genus of two M5-branes wrapping a rigid divisor inside a Calabi–Yau manifold. The anomaly originates from restoring modularity of an indefinite theta-function capturing the wall-crossing of BPS invariants associated to D4-D2-D0 brane systems. We show the compatibility of this equation with anomaly equations previously observed in the context of $${{\mathcal{N}}=4}$$N=4 topological Yang–Mills theory on $${{\mathbbm{P}}^2}$$P2 and E-strings obtained from wrapping M5-branes on a del Pezzo surface. The non-holomorphic part is related to the contribution originating from bound-states of singly wrapped M5-branes on the divisor. We show in examples that the information provided by the anomaly is enough to compute the BPS degeneracies for certain charges. We further speculate on a natural extension of the anomaly to higher D4-brane charge.

title: A Measurement of the Temperature-Density Relation in the Intergalactic Medium Using a New Lyα Absorption-Line Fitting Method
abstract: The evolution of the temperature in the intergalactic medium is related to the reionization of hydrogen and helium and has important consequences for our understanding of the Lyα forest and of galaxy formation. We measure the temperature-density relation of intergalactic gas from Lyα forest observations of eight quasar spectra, using a new line fitting technique to obtain a lower cutoff on the distribution of line widths from which the temperature is derived. Using a numerical simulation, we examine the details of this kind of measurement at different densities, finding that the temperature may be difficult to measure for gas with Δg 1 (Δg is the density of the gas in units of the mean density) because the velocities due to expansion always dominate the widths of the corresponding weak lines, and that the temperature measurement is increasingly ambiguous for gas with Δg 5 because the dispersion in temperature at fixed density is high. From our observed spectra, the temperature is most precisely determined at densities slightly above the mean: T* = (20,200 ± 2700, 20,200 ± 1300, 22,600 ± 1900) K (statistical error bars) for gas densities Δ* = (1.42 ± 0.08, 1.37 ± 0.11, 1.66 ± 0.11) at redshift = (3.9, 3.0, 2.4). Systematic errors in T* should be less than 2000 K. The power-law index of the temperature-density relation, defined by T = T*(Δg/Δ*)γ-1, is γ - 1 = (0.43 ± 0.45, 0.29 ± 0.30, 0.52 ± 0.14) for the same three redshifts. The temperature at fixed overdensity Δ = 1.4 is T1.4 = (20,100 ± 2800, 20,300 ± 1400, 20,700 ± 1900) K. This unchanging temperature is higher than expected for photoionized gas in ionization equilibrium with a cosmic background. If the heat from the He II reionization is responsible for the high measured temperature, then the temperature should not be constant but should have a maximum at the end of the reionization epoch. We update the lower limit to the baryon density implied by the observed mean flux decrement.

title: Measuring extended Higgs sectors as a consistent free couplings model
abstract: A bstractExtended Higgs sectors appear in many models for physics beyond the Standard Model. Current Higgs measurements at the LHC are starting to significantly constrain them. We study their Higgs coupling patterns at tree level as well as including quantum corrections. Our benchmarks include a dark singlet-doublet extension and several twodoublet setups. Using SFitter we translate the current Higgs coupling measurements for one light Higgs state into their respective parameter spaces. Finally, we show how twoHiggs-doublet models can serve as a consistent ultraviolet completion of an assumed single Standard-Model-like Higgs boson with free couplings.

title: The thermal history of the intergalactic medium
abstract: At redshifts z≳2, most of the baryons reside in the smooth intergalactic medium which is responsible for the low column density Lyα forest. This photoheated gas follows a tight temperature–density relation which introduces a cut-off in the distribution of widths of the Lyα absorption lines (b-parameters) as a function of column density. We have measured this cut-off in a sample of nine high-resolution, high signal-to-noise ratio quasar spectra and determined the thermal evolution of the intergalactic medium in the redshift range 2.0–4.5. At a redshift z∼3, the temperature at the mean density shows a peak and the gas becomes nearly isothermal. We interpret this as evidence for the reionization of He ii.

title: News from FormCalc and LoopTools
abstract: The FormCalc package automates the computation of FeynArts amplitudes up to one loop including the generation of a Fortran code for the numerical evaluation of the squared matrix element. Major new or enhanced features in Version 5 are: iterative build-up of essentially arbitrary phase-spaces including cuts, convolution with density functions, and uniform treatment of kinematical variables. The LoopTools library supplies the one-loop integrals necessary for evaluating the squared matrix element. Its most significant extensions in Version 2.2 are the five-point family of integrals, and complex and alternate versions.

title: A Population of Faint Extended Line Emitters and the Host Galaxies of Optically Thick QSO Absorption Systems
abstract: We have conducted a long-slit search for low surface brightness Lyα emitters at redshift 2.67 < z < 3.75. A 92 hr long exposure with the ESO VLT FORS2 instrument down to a 1σ surface brightness detection limit of 8 × 10^(−20) erg cm^(−2) s^(−1) arcsec^(−2) per arcsec^2 aperture yielded a sample of 27 single line emitters with fluxes of a few × 10^(−18) erg s^(−1) cm^(−2). We present arguments that most objects are indeed Lyα. The large comoving number density, 3 × 10^(−2) h^3_(70) Mpc^(−3), the large covering factor, dN/dz ~ 0.2–1, and the often extended Lyα emission suggest that the emitters can be identified with the elusive host population of damped Lyα systems (DLAS) and high column density Lyman limit systems (LLS). A small inferred star formation rate, perhaps supplemented by cooling radiation, appears to energetically dominate the Lyα emission, and is consistent with the low metallicity, low dust content, and theoretically inferred low masses of DLAS, and with the relative lack of success of earlier searches for their optical counterparts. Some of the line profiles show evidence for radiative transfer in galactic outflows. Stacking surface brightness profiles, we find emission out to at least 4". The centrally concentrated emission of most objects appears to light up the outskirts of the emitters (where LLS arise) down to a column density where the conversion from UV to Lyα photon becomes inefficient. DLAS, high column density LLS, and the emitter population discovered in this survey appear to be different observational manifestations of the same low-mass, protogalactic building blocks of present-day L_* galaxies.