Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local CP2

The holomorphic anomaly equations describe B-model closed topological strings in Calabi-Yau geometries. Having been used to construct perturbative expansions, it was recently shown that they can also be extended past perturbation theory by making use of resurgent transseries. These yield formal nonperturbative solutions, showing integrability of the holomorphic anomaly equations at the nonperturbative level. This paper takes such constructions one step further by working out in great detail the specific example of topological strings in the mirror of the local CP2 toric Calabi-Yau background, and by addressing the associated (resurgent) large-order analysis of both perturbative and multi-instanton sectors. In particular, analyzing the asymptotic growth of the perturbative free energies, one finds contributions from three different instanton actions related by Z_3 symmetry, alongside another action related to the Kahler parameter. Resurgent transseries methods then compute, from the extended holomorphic anomaly equations, higher instanton sectors and it is shown that these precisely control the asymptotic behavior of the perturbative free energies, as dictated by resurgence. The asymptotic large-order growth of the one-instanton sector unveils the presence of resonance, i.e., each instanton action is necessarily joined by its symmetric contribution. The structure of different resurgence relations is extensively checked at the numerical level, both in the holomorphic limit and in the general nonholomorphic case, always showing excellent agreement with transseries data computed out of the nonperturbative holomorphic anomaly equations. The resurgence relations further imply that the string free energy displays an intricate multi-branched Borel structure, and that resonance must be properly taken into account in order to describe the full transseries solution.Comment: 63 pages, 54 images in 24 figures, jheppub-nosort.sty; v2: corrected figure, minor changes, final version for CM

Resurgent Transseries and the Holomorphic Anomaly

The gauge theoretic large N expansion yields an asymptotic series which requires a nonperturbative completion in order to be well defined. Recently, within the context of random matrix models, it was shown how to build resurgent transseries solutions encoding the full nonperturbative information beyond the 't Hooft genus expansion. On the other hand, via large N duality, random matrix models may be holographically described by B-model closed topological strings in local Calabi-Yau geometries. This raises the question of constructing the corresponding holographically dual resurgent transseries, tantamount to nonperturbative topological string theory. This paper addresses this point by showing how to construct resurgent transseries solutions to the holomorphic anomaly equations. These solutions are built upon (generalized) multi-instanton sectors, where the instanton actions are holomorphic. The asymptotic expansions around the multi-instanton sectors have both holomorphic and anti-holomorphic dependence, may allow for resonance, and their structure is completely fixed by the holomorphic anomaly equations in terms of specific polynomials multiplied by exponential factors and up to the holomorphic ambiguities -- which generalizes the known perturbative structure to the full transseries. In particular, the anti-holomorphic dependence has a somewhat universal character. Furthermore, in the nonperturbative sectors, holomorphic ambiguities may be fixed at conifold points. This construction shows the nonperturbative integrability of the holomorphic anomaly equations, and sets the ground to start addressing large-order analysis and resurgent nonperturbative completions within closed topological string theory.Comment: 59 pages, jheppub-nosort.sty; v2: small additions, minor changes, refs updated; v3: more minor corrections, final version for AH

Compressibility and structural stability of ultra-incompressible bimetallic interstitial carbides and nitrides

We have investigated by means of high-pressure x-ray diffraction the structural stability of Pd2Mo3N, Ni2Mo3C0.52N0.48, Co3Mo3C0.62N0.38, and Fe3Mo3C. We have found that they remain stable in their ambient-pressure cubic phase at least up to 48 GPa. All of them have a bulk modulus larger than 330 GPa, being the least compressible material Fe3Mo3C, B0 = 374(3) GPa. In addition, apparently a reduction of compressibility is detected as the carbon content increased. The equation of state for each material is determined. A comparison with other refractory materials indicates that interstitial nitrides and carbides behave as ultra-incompressible materials.Comment: 14 pages, 3 figures, 1 tabl

Locally Most Powerful Invariant Tests for Correlation and Sphericity of Gaussian Vectors

In this paper we study the existence of locally most powerful invariant tests (LMPIT) for the problem of testing the covariance structure of a set of Gaussian random vectors. The LMPIT is the optimal test for the case of close hypotheses, among those satisfying the invariances of the problem, and in practical scenarios can provide better performance than the typically used generalized likelihood ratio test (GLRT). The derivation of the LMPIT usually requires one to find the maximal invariant statistic for the detection problem and then derive its distribution under both hypotheses, which in general is a rather involved procedure. As an alternative, Wijsman's theorem provides the ratio of the maximal invariant densities without even finding an explicit expression for the maximal invariant. We first consider the problem of testing whether a set of $N$-dimensional Gaussian random vectors are uncorrelated or not, and show that the LMPIT is given by the Frobenius norm of the sample coherence matrix. Second, we study the case in which the vectors under the null hypothesis are uncorrelated and identically distributed, that is, the sphericity test for Gaussian vectors, for which we show that the LMPIT is given by the Frobenius norm of a normalized version of the sample covariance matrix. Finally, some numerical examples illustrate the performance of the proposed tests, which provide better results than their GLRT counterparts

Pattern formation from consistent dynamical closures of uniaxial nematic liquid crystals

Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation for the single-particle non-homogeneous distribution function of particle orientations and the evolution equations for the second and fourth order orientational tensor parameters. Afterwards, two dynamic closure approximations are discussed, one of them considering the relaxation of the fourth order orientational parameter and leading to a novel expression for the free-energy like function in terms of the scalar order parameter. Considering the evolution equation of the density of the system and values of the interaction parameter for which isotropic and nematic phases coexist, our analysis predicts that patterns and traveling waves can be produced in lyotropic uniaxial nematics even in the absence of external driving.Comment: 34 pages, 7 figure

XMM-Newton observations of the first unidentified TeV gamma-ray source TeV J2032+4130

(abridged) The first unidentified very high energy gamma ray source (TeV J2032+4130) in the Cygnus region has been the subject of intensive search for a counterpart source at other wavelengths. A deep ($\approx 50$ ksec) exposure of TeV J2032+4130 with \textit{XMM-Newton} has been obtained. The contribution of point sources to the observed X-ray emission from TeV J2032+4130 is subtracted from the data. The point-source subtracted X-ray data are analyzed using blank sky exposures and regions adjacent to the position of TeV J2032+4130 in the field of view covered by the XMM-Newton telescopes to search for diffuse X-ray emission. An extended X-ray emission region with a full width half maximum (FWHM) size of $\approx 12$ arc min is found. The centroid of the emission is co-located with the position of TeV J2032+4130.The energy spectrum of the emission coinciding with the position and extension of TeV J2032+4130 can be modeled by a power-law model with a photon index $\Gamma=1.5\pm0.2_\mathrm{stat}\pm0.3_\mathrm{sys}$ and an energy flux integrated between 2 and 10 keV of $f_{2-10 \mathrm{keV}} \approx 7\cdot 10^{-13}$ ergs/(cm$^2$ s) which is lower than the very high energy gamma-ray flux observed from TeV J2032+4130. We conclude that the faint extended X-ray emission discovered in this observation is the X-ray counterpart of TeV J2032+4130. Formally, it can not be excluded that the extended emission is due to an unrelated population of faint, hot ($k_BT\approx 10$ keV) unresolved point-sources which by chance coincides with the position and extension of TeV J2032+4130. We discuss our findings in the frame of both hadronic and leptonic gamma-ray production scenarios.Comment: 5 Pages, 3 Figures, accepted for publication in A&

Zircon to monazite phase transition in CeVO4

X-ray diffraction and Raman-scattering measurements on cerium vanadate have been performed up to 12 and 16 GPa, respectively. Experiments reveal that at 5.3 GPa the onset of a pressure-induced irreversible phase transition from the zircon to the monazite structure. Beyond this pressure, diffraction peaks and Raman-active modes of the monazite phase are measured. The zircon to monazite transition in CeVO4 is distinctive among the other rare-earth orthovanadates. We also observed softening of external translational Eg and internal B2g bending modes. We attributed it to mechanical instabilities of zircon phase against the pressure-induced distortion. We additionally report lattice-dynamical and total-energy calculations which are in agreement with the experimental results. Finally, the effect of non-hydrostatic stresses on the structural sequence is studied and the equations of state of different phases are reported.Comment: 45 pages, 8 figures, 8 table

X-ray diffraction measurements of Mo melting to 119 GPa and the high pressure phase diagram

In this paper, we report angle-dispersive X-ray diffraction data of molybdenum melting, measured in a double-sided laser-heated diamond-anvil cell up to a pressure of 119 GPa and temperatures up to 3400 K. The new melting temperatures are in excellent agreement with earlier measurements up to 90 GPa that relied on optical observations of melting and in strong contrast to most theoretical estimates. The X-ray measurements show that the solid melts from the bcc structure throughout the reported pressure range and provide no evidence for a high temperature transition from bcc to a close-packed structure, or to any other crystalline structure. This observation contradicts earlier interpretations of shock data arguing for such a transition. Instead, the values for the Poisson ratios of shock compressed Mo, obtained from the sound speed measurements, and the present X-ray evidence of loss of long-range order suggest that the 210 GPa ( ∼ 4100 K) transition in the shock experiment is from the bcc structure to a new, highly viscous, structured [email protected]

On the complementarity of pulsar timing and space laser interferometry for the individual detection of supermassive black hole binaries

Gravitational waves coming from Super Massive Black Hole Binaries (SMBHBs) are targeted by both Pulsar Timing Array (PTA) and Space Laser Interferometry (SLI). The possibility of a single SMBHB being tracked first by PTA, through inspiral, and later by SLI, up to merger and ring down, has been previously suggested. Although the bounding parameters are drawn by the current PTA or the upcoming Square Kilometer Array (SKA), and by the New Gravitational Observatory (NGO), derived from the Laser Interferometer Space Antenna (LISA), this paper also addresses sequential detection beyond specific project constraints. We consider PTA-SKA, which is sensitive from 10^(-9) to p x 10^(-7) Hz (p=4, 8), and SLI, which operates from s x 10^(-5) up to 1 Hz (s = 1, 3). A SMBHB in the range 2x 10^(8) - 2 x 10^(9) solar masses (the masses are normalised to a (1+z) factor, the red shift lying between z = 0.2 and z=1.5) moves from the PTA-SKA to the SLI band over a period ranging from two months to fifty years. By combining three Super Massive Black Hole (SMBH)-host relations with three accretion prescriptions, nine astrophysical scenarios are formed. They are then related to three levels of pulsar timing residuals (50, 5, 1 ns), generating twenty-seven cases. For residuals of 1 ns, sequential detection probability will never be better than 4.7 x 10^(-4) y^(-2) or 3.3 x 10^(-6) y^(-2) (per year to merger and per year of survey), according to the best and worst astrophysical scenarios, respectively; put differently this means one sequential detection every 46 or 550 years for an equivalent maximum time to merger and duration of the survey. The chances of sequential detection are further reduced by increasing values of the s parameter (they vanish for s = 10) and of the SLI noise, and by decreasing values of the remnant spin. REST OF THE ABSTRACT IN THE PDF FILE.Comment: To appear in the Astrophysical Journa