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

A Practical Approach for Biochemical Modeling in the CFD Evaluation of Novel Anaerobic Digester Concepts for Biogas Production

The detailed physics-based description of anaerobic digesters is characterized by their multiscale and multiphysics nature, with Computational Fluid Dynamics (CFD) simulations being the most comprehensive approach. In practice, difficulties in obtaining a detailed characterization of the involved biochemical reactions hinder its application in the design of novel reactor concepts, where all physics interplays in the reactor must be considered. To solve this limitation, a practical approach is introduced where a calibration step using actual process data was applied for the simplified biochemical reactions involved, allowing us to efficiently manage uncertainties arising when characterizing biochemical reactions with lab scale facilities. A complete CFD modeling approach is proposed for the anaerobic digestion of wastewater, including heat transfer and multiphasic flow. The proposed multiphase model was verified using reference data and, jointly with the biochemical modeling approach, applied to a lab-scale non-conventional anaerobic digester for winery wastewater treatment. The results showed qualitative improvement in predicting methane production when the diameter of the particles was reduced, since larger particles tend to move downwards. The biochemistry of the process could be simplified introducing a preexponential factor of 380 (kmol/m3)(1 – n)/s for each considered chemical reaction. In general, the proposed approach can be used to overcome limitations when using CFD to scale-up optimization of non-conventional reactors involving biochemical reactions

Fontes de alimentação de R. pallescens e índice de infecção por Trypanosoma em área endêmica da doença de Chagas em Amador, região central do Panamá

The sylvatic triatomine Rhodnius pallescens is considered to be the most important and widespread vector of Trypanosoma cruzi and Trypanosoma rangeli in Panama. However, its behavior and biological characteristics have only been partially investigated. Thus, to achieve sustainable and efficient control over Chagas disease in Panama, a better understanding of the ecology and biology of R. pallescens is essential. In this study we evaluated R. pallescens host feeding sources using a dot-blot assay, and the trypanosome infection index by PCR analysis in a Chagas disease endemic area of central Panama. It was found that in peridomestic palm trees, 20.3% of the examined bugs had fed on opossums (Didelphis marsupialis). However, we observed an increased anthropophagy (25.4%) for those bugs collected inside houses. Considering the domestic and peridomestic habitats as a whole, the proportion of collected R. pallescens infected with trypanosomes was 87.4%. In the two habitats the predominant infection was with T. cruzi (80-90%). Between 47-51% of the analyzed triatomines were infected with T. rangeli. Mixed infections (40-51%) were also detected. These findings provide a better basis for the implementation of a rational control and surveillance program for Chagas disease in regions where R. pallescens is endemic.O triatomíneo silvestre Rhodnius pallescens é considerado o mais importante vetor do Trypanosoma cruzi e Trypanosoma rangeli no Panamá. Entretanto, seu comportamento e características biológicas são pouco estudados. Para controlar a doença de Chagas no Panamá é necessário melhorar a compreensão dos aspectos eco-biológicos do R. pallescens. Neste estudo, investigaram-se as fontes de alimentação de R. pallescens usando dot-blot e o índice de infecção por Trypanosoma por metodologia molecular, em área endêmica da doença de Chagas na região central do Panamá. Foi observado que 20,3% dos barbeiros coletados em palmeiras peridomésticas se alimentavam de gambás (Didelphis marsupialis). Contudo, barbeiros coletados dentro das residências apresentaram antropofagia aumentada (25,4%). Considerando o ambiente doméstico e peridoméstico juntos, o percentual de R. pallescens infectados com Trypanosoma foi de 87,4 %. Nos ambientes doméstico e peridoméstico, a infecção por T. cruzi foi de 80,4% e 90%; a infecção por T. rangeli foi de 47% e 51%, respectivamente. Observou-se infecção mista em 43% dos triatomíneos coletados em ambiente doméstico e em 51% dos triatomíneos peridomésticos. Estes achados fornecem embasamento para a implementação de um controle adequado e um programa de vigilância para a doença de Chagas em regiões onde o R. pallescens é endêmico

Vacuum Energy for Generalized Dirac Combs at T = 0

The quantum vacuum energy for a hybrid comb of Dirac δ-δ′ potentials is computed by using the energy of the single δ-δ′ potential over the real line that makes up the comb. The zeta function of a comb periodic potential is the continuous sum of zeta functions over the dual primitive cell of Bloch quasi-momenta. The result obtained for the quantum vacuum energy is non-perturbative in the sense that the energy function is not analytical for small couplings