Wall-Crossing Holomorphic Anomaly and Mock Modularity of Multiple M5-Branes
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: 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: Helmholtz Alliance Linear Collider Forum
abstract: Supersymmetric scenarios with a very weakly interacting lightest superpartner (LSP) - like the gravitino or axino - naturally give rise to a long-lived next-to-LSP (NLSP). If the NLSP is a charged slepton it leaves a very distinct signature in a collider experiment. At the ILC/CLIC it will be possible to capture a significant fraction of the produced charged sleptons and observe their decays. These decays potentially reveal the nature of the LSP and thus provide a unique possibility to measure the properties of a very weakly interacting LSP which otherwise is most likely hidden from any other observation, like direct or indirect dark matter searches. We review the proposals that have been made to measure the LSP properties at the ILC/CLIC and compare its potential to the capability of the LHC.

title: LHC: Standard Higgs and Hidden Higgs
abstract: Interpretations of Higgs searches critically involve production cross sections and decay probabilities for different analysis channels. Mixing effects can reduce production rates, while invisible decays can reduce decay probabilities. Both effects may transparently be quantified in Higgs systems where a visible Higgs boson is mixed with a hidden sector Higgs boson. Recent experimental exclusion bounds can be re-interpreted in this context as a sign for non-standard Higgs properties. Should a light Higgs boson be discovered, then our analysis will quantify how closely it may coincide with the Standard Model.

title: AN HST SEARCH FOR SUPERNOVAE ACCOMPANYING X-RAY FLASHES
abstract: We present the results from a Hubble Space Telescope ACS search for supernovae associated with X-ray flashes 020903, 040701, 040812, and 040916. We find strong evidence that XRF 020903 (z = 0.25) was associated with a SN 1998bw-like supernova and confirm this using optical spectroscopy at t ~ 25 days. We find no evidence, however, for SN 1998bw-like supernovae associated with the other three events. In the case of XRF 040701 (z = 0.21), we rule out even a faint supernova similar to SN 2002ap, using template light curves for several local Type Ic supernovae. For the two cases in which the redshift is not known, XRFs 040812 and 040916, we derive robust redshift limits, assuming that they were accompanied by supernovae similar to SN 1998bw, and compare these limits with photometric redshift constraints provided by their host galaxies. We supplement this analysis with results for three additional events (XRFs 011030, 020427, and 030723) and discuss the observed diversity of supernovae associated with X-ray flashes and gamma-ray bursts. We conclude that XRF-SNe exist but can be significantly fainter than SN 1998bw, possibly consistent with the observed spread in local Type Ibc supernovae.

title: The metal line systems in hs1700+6416: evidence for inhomogeneities
abstract: We present a high S/N ratio optical spectrum of the bright quasar HS1700+6416. These data usefully complement the UV HST data from Vogel and Reimers (1995). We analyse the metal line systems using photo-ionization models allowing for inhomogeneities in the gas. The models are able to reproduce within a factor of two the large N(HeI)/N(HI) ratio together with the mean column densities of the heavy element species observed in the z=2 systems. The density contrast between low and high density regions is of the order of 30. Although the [O/C] abundance ratio seems slighly larger than solar, firm conclusion should await higher spectral resolution data. A break at the HeII ionization limit of a factor of ten is acceptable in the ionizing spectrum. Abundances are found to be about 0.08 solar. This together with other determinations from the literature indicates that there is evolution in the metal content of metal line systems with redshift: [Mg/H] is slighly below solar at z=0.7 and [C/H]=0.1-0.01 at z=2. We detect an associated CIV system at z=2.7126 in which there is some evidence for the presence of NeVIII, probably NeVI, NeVII, and possibly SiXII.

title: SFitter : Determining Supersymmetric Parameters
abstract: If supersymmetry (or similar complex models) is found at the LHC, the goal for all colliders over the coming decades will be to extract its fundamental parameters from the measurements. Dedicated state–of–the–art tools will be necessary to link a wealth of measurements to an e.g. 20–dimensional MSSM parameter space. Starting from a general log–likelihood function of this hig hdimensional parameter space we show how we can find the best–fit paramete r values and determine their errors. Beyond a single best–fit point we illustra te how distinct secondary minima occur in complex parameter spaces. In cases where there are flat dimensions in the likelihood we comment on the benefits and limitations of marginalizing over additional dimensions.