A note on topological amplitudes in hybrid string theory

We study four-dimensional compactifications of type II superstrings on Calabi-Yau spaces using the formalism of hybrid string theory. Chiral and twisted-chiral interactions are rederived, which involve the coupling of the compactification moduli to two powers of the Weyl-tensor and of the derivative of the universal tensor field-strength

A New Lower Bound on the Maximum Number of Satisfied Clauses in Max-SAT and its Algorithmic Applications

A pair of unit clauses is called conflicting if it is of the form $(x)$, $(\bar{x})$. A CNF formula is unit-conflict free (UCF) if it contains no pair of conflicting unit clauses. Lieberherr and Specker (J. ACM 28, 1981) showed that for each UCF CNF formula with $m$ clauses we can simultaneously satisfy at least \pp m clauses, where \pp =(\sqrt{5}-1)/2. We improve the Lieberherr-Specker bound by showing that for each UCF CNF formula $F$ with $m$ clauses we can find, in polynomial time, a subformula $F'$ with $m'$ clauses such that we can simultaneously satisfy at least \pp m+(1-\pp)m'+(2-3\pp)n"/2 clauses (in $F$), where $n"$ is the number of variables in $F$ which are not in $F'$. We consider two parameterized versions of MAX-SAT, where the parameter is the number of satisfied clauses above the bounds $m/2$ and $m(\sqrt{5}-1)/2$. The former bound is tight for general formulas, and the later is tight for UCF formulas. Mahajan and Raman (J. Algorithms 31, 1999) showed that every instance of the first parameterized problem can be transformed, in polynomial time, into an equivalent one with at most $6k+3$ variables and $10k$ clauses. We improve this to $4k$ variables and $(2\sqrt{5}+4)k$ clauses. Mahajan and Raman conjectured that the second parameterized problem is fixed-parameter tractable (FPT). We show that the problem is indeed FPT by describing a polynomial-time algorithm that transforms any problem instance into an equivalent one with at most $(7+3\sqrt{5})k$ variables. Our results are obtained using our improvement of the Lieberherr-Specker bound above

Asymptotic degeneracy of dyonic N=4 string states and black hole entropy

It is shown that the asymptotic growth of the microscopic degeneracy of BPS dyons in four-dimensional N=4 string theory captures the known corrections to the macroscopic entropy of four-dimensional extremal black holes. These corrections are subleading in the limit of large charges and originate both from the presence of interactions in the effective action quadratic in the Riemann tensor and from non-holomorphic terms. The presence of the non-holomorphic corrections and their contribution to the thermodynamic free energy is discussed. It is pointed out that the expression for the microscopic entropy, written as a function of the dilaton field, is stationary at the horizon by virtue of the attractor equations.Comment: 16 pages Late

A well-balanced scheme for the simulation tool-kit A-MaZe: implementation, tests, and first applications to stellar structure

This is the final version. Available on open access from EDP Sciences via the DOI in this recordCharacterizing stellar convection in multiple dimensions is a topic at the forefront of stellar astrophysics. Numerical simulations are an essential tool for this task. We present an extension of the existing numerical tool-kit A-MaZe that enables such simulations of stratified flows in a gravitational field. The finite-volume based, cell-centered, and time-explicit hydrodynamics solver of A-MaZe was extended such that the scheme is now well-balanced in both momentum and energy. The algorithm maintains an initially static balance between gravity and pressure to machine precision. Quasi-stationary convection in slab-geometry preserves gas energy (internal plus kinetic) on average despite strong local up- and down-drafts. By contrast, a more standard numerical scheme is demonstrated to result in substantial gains of energy within a short time on purely numerical grounds. The test is further used to point out the role of dimensionality, viscosity, and Rayleigh number for compressible convection. Applications to a young sun in 2D and 3D, covering a part of the inner radiative zone as well as the outer convective zone, demonstrate that the scheme meets its initial design goal. Comparison with results obtained for a physically identical setup with a time-implicit code show qualitative agreement.European Research Council (ERC)French National Program for High Energies PNH

Black hole partition functions and duality

The macroscopic entropy and the attractor equations for BPS black holes in four-dimensional N=2 supergravity theories follow from a variational principle for a certain `entropy function'. We present this function in the presence of R^2-interactions and non-holomorphic corrections. The variational principle identifies the entropy as a Legendre transform and this motivates the definition of various partition functions corresponding to different ensembles and a hierarchy of corresponding duality invariant inverse Laplace integral representations for the microscopic degeneracies. Whenever the microscopic degeneracies are known the partition functions can be evaluated directly. This is the case for N=4 heterotic CHL black holes, where we demonstrate that the partition functions are consistent with the results obtained on the macroscopic side for black holes that have a non-vanishing classical area. In this way we confirm the presence of a measure in the duality invariant inverse Laplace integrals. Most, but not all, of these results are obtained in the context of semiclassical approximations. For black holes whose area vanishes classically, there remain discrepancies at the semiclassical level and beyond, the nature of which is not fully understood at present.Comment: 36 pages, Late

Core-collapse supernova explosions triggered by a quark-hadron phase transition during the early post-bounce phase

We explore explosions of massive stars, which are triggered via the quark-hadron phase transition during the early post bounce phase of core-collapse supernovae. We construct a quark equation of state, based on the bag model for strange quark matter. The transition between the hadronic and the quark phases is constructed applying Gibbs conditions. The resulting quark-hadron hybrid equations of state are used in core-collapse supernova simulations, based on general relativistic radiation hydrodynamics and three flavor Boltzmann neutrino transport in spherical symmetry. The formation of a mixed phase reduces the adiabatic index, which induces the gravitational collapse of the central protoneutron star. The collapse halts in the pure quark phase, where the adiabatic index increases. A strong accretion shock forms, which propagates towards the protoneutron star surface. Due to the density decrease of several orders of magnitude, the accretion shock turns into a dynamic shock with matter outflow. This moment defines the onset of the explosion in supernova models that allow for a quark-hadron phase transition, where otherwise no explosions could be obtained. The shock propagation across the neutrinospheres releases a burst of neutrinos. This serves as a strong observable identification for the structural reconfiguration of the stellar core. The ejected matter expands on a short timescale and remains neutron-rich. These conditions might be suitable for the production of heavy elements via the r-process. The neutron-rich material is followed by proton-rich neutrino-driven ejecta in the later cooling phase of the protoneutron star where the vp-process might occur.Comment: 29 pages, 24 figures, submitted to Ap

Gravitational waves from supernova matter

We have performed a set of 11 three-dimensional magnetohydrodynamical core collapse supernova simulations in order to investigate the dependencies of the gravitational wave signal on the progenitor's initial conditions. We study the effects of the initial central angular velocity and different variants of neutrino transport. Our models are started up from a 15 solar mass progenitor and incorporate an effective general relativistic gravitational potential and a finite temperature nuclear equation of state. Furthermore, the electron flavour neutrino transport is tracked by efficient algorithms for the radiative transfer of massless fermions. We find that non- and slowly rotating models show gravitational wave emission due to prompt- and lepton driven convection that reveals details about the hydrodynamical state of the fluid inside the protoneutron stars. Furthermore we show that protoneutron stars can become dynamically unstable to rotational instabilities at T/|W| values as low as ~2 % at core bounce. We point out that the inclusion of deleptonization during the postbounce phase is very important for the quantitative GW prediction, as it enhances the absolute values of the gravitational wave trains up to a factor of ten with respect to a lepton-conserving treatment.Comment: 10 pages, 6 figures, accepted, to be published in a Classical and Quantum Gravity special issue for MICRA200

In Macrophages, Caspase-1 Activation by SopE and the Type III Secretion System-1 of S. Typhimurium Can Proceed in the Absence of Flagellin

The innate immune system is of vital importance for protection against infectious pathogens. Inflammasome mediated caspase-1 activation and subsequent release of pro-inflammatory cytokines like IL-1β and IL-18 is an important arm of the innate immune system. Salmonella enterica subspecies 1 serovar Typhimurium (S. Typhimurium, SL1344) is an enteropathogenic bacterium causing diarrheal diseases. Different reports have shown that in macrophages, S. Typhimurium may activate caspase-1 by at least three different types of stimuli: flagellin, the type III secretion system 1 (T1) and the T1 effector protein SopE. However, the relative importance and interdependence of the different factors in caspase-1 activation is still a matter of debate. Here, we have analyzed their relative contributions to caspase-1 activation in LPS-pretreated RAW264.7 macrophages. Using flagellar mutants (fliGHI, flgK) and centrifugation to mediate pathogen-host cell contact, we show that flagellins account for a small part of the caspase-1 activation in RAW264.7 cells. In addition, functional flagella are of key importance for motility and host cell attachment which is a prerequisite for mediating caspase-1 activation via these three stimuli. Using site directed mutants lacking several T1 effector proteins and flagellin expression, we found that SopE elicits caspase-1 activation even when flagellins are absent. In contrast, disruption of essential genes of the T1 protein injection system (invG, sipB) completely abolished caspase-1 activation. However, a robust level of caspase-1 activation is retained by the T1 system (or unidentified T1 effectors) in the absence of flagellin and SopE. T1-mediated inflammasome activation is in line with recent work by others and suggests that the T1 system itself may represent the basic caspase-1 activating stimulus in RAW264.7 macrophages which is further enhanced independently by SopE and/or flagellin