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Diet and lifestyle-related illnesses including functional gastrointestinal disorders (FGIDs) and obesity are rapidly emerging health issues worldwide. Research has focused on addressing FGIDs via in-person cognitive-behavioral therapies, diet modulation and pharmaceutical intervention. Yet, there is paucity of research reporting on digital therapeutics care delivering weight loss and reduction of FGID symptom severity, and on modeling FGID status and symptom severity reduction including personalized genomic SNPs and gut microbiome signals. Our aim for this study was to assess how effective a digital therapeutics intervention personalized on genomic SNPs and gut microbiome signals was at reducing symptomatology of FGIDs on individuals that successfully lost body weight. We also aimed at modeling FGID status and FGID symptom severity reduction using demographics, genomic SNPs, and gut microbiome variables. This study sought to train a logistic regression model to differentiate the FGID status of subjects enrolled in a digital therapeutics care program using demographic, genetic, and baseline microbiome data. We also trained linear regression models to ascertain changes in FGID symptom severity of subjects at the time of achieving 5% or more of body weight loss compared to baseline. For this we utilized a cohort of 177 adults who reached 5% or more weight loss on the Digbi Health personalized digital care program, who were retrospectively surveyed about changes in symptom severity of their FGIDs and other comorbidities before and after the program. Gut microbiome taxa and demographics were the strongest predictors of FGID status. The digital therapeutics program implemented, reduced the summative severity of symptoms for 89.42% (93/104) of users who reported FGIDs. Reduction in summative FGID symptom severity and IBS symptom severity were best modeled by a mixture of genomic and microbiome predictors, whereas reduction in diarrhea and constipation symptom severity were best modeled by microbiome predictors only. This preliminary retrospective study generated diagnostic models for FGID status as well as therapeutic models for reduction of FGID symptom severity. Moreover, these therapeutic models generate testable hypotheses for associations of a number of biomarkers in the prognosis of FGIDs symptomatology., Competing Interests: All authors except JU and PD were employees of Digbi Health. JU did contractual work for Digbi Health. PD was an advisor to Digbi Health. The authors declare that this study received funding from Digbi Health. The funder Digbi Health was not involved in the study design, collection, analysis, interpretation of data, the writing of this article, or the decision to submit it for publication. SK, DA, and RS had a patent-pending concerning this work: US Application No. 63/246,348, Methods and systems for multi-omic interventions as diagnostics for personalized care of functional gastrointestinal disorders. The digital therapeutics program provided to study participants in this work is a commercially available program developed and marketed by Digbi Health., (Copyright © 2022 Kumbhare, Francis-Lyon, Kachru, Uday, Irudayanathan, Muthukumar, Ricchetti, Singh-Rambiritch, Ugalde, Dulai, Almonacid and Sinha.)

Background: The COVID-19 pandemic has highlighted the urgency of addressing an epidemic of obesity and associated inflammatory illnesses. Previous studies have demonstrated that interactions between single-nucleotide polymorphisms (SNPs) and lifestyle interventions such as food and exercise may vary metabolic outcomes, contributing to obesity. However, there is a paucity of research relating outcomes from digital therapeutics to the inclusion of genetic data in care interventions., Objective: This study aims to describe and model the weight loss of participants enrolled in a precision digital weight loss program informed by the machine learning analysis of their data, including genomic data. It was hypothesized that weight loss models would exhibit a better fit when incorporating genomic data versus demographic and engagement variables alone., Methods: A cohort of 393 participants enrolled in Digbi Health's personalized digital care program for 120 days was analyzed retrospectively. The care protocol used participant data to inform precision coaching by mobile app and personal coach. Linear regression models were fit of weight loss (pounds lost and percentage lost) as a function of demographic and behavioral engagement variables. Genomic-enhanced models were built by adding 197 SNPs from participant genomic data as predictors and refitted using Lasso regression on SNPs for variable selection. Success or failure logistic regression models were also fit with and without genomic data., Results: Overall, 72.0% (n=283) of the 393 participants in this cohort lost weight, whereas 17.3% (n=68) maintained stable weight. A total of 142 participants lost 5% bodyweight within 120 days. Models described the impact of demographic and clinical factors, behavioral engagement, and genomic risk on weight loss. Incorporating genomic predictors improved the mean squared error of weight loss models (pounds lost and percent) from 70 to 60 and 16 to 13, respectively. The logistic model improved the pseudo R 2 value from 0.193 to 0.285. Gender, engagement, and specific SNPs were significantly associated with weight loss. SNPs within genes involved in metabolic pathways processing food and regulating fat storage were associated with weight loss in this cohort: rs17300539_G (insulin resistance and monounsaturated fat metabolism), rs2016520_C (BMI, waist circumference, and cholesterol metabolism), and rs4074995_A (calcium-potassium transport and serum calcium levels). The models described greater average weight loss for participants with more risk alleles. Notably, coaching for dietary modification was personalized to these genetic risks., Conclusions: Including genomic information when modeling outcomes of a digital precision weight loss program greatly enhanced the model accuracy. Interpretable weight loss models indicated the efficacy of coaching informed by participants' genomic risk, accompanied by active engagement of participants in their own success. Although large-scale validation is needed, our study preliminarily supports precision dietary interventions for weight loss using genetic risk, with digitally delivered recommendations alongside health coaching to improve intervention efficacy., (©Ranjan Sinha, Dashyanng Kachru, Roshni Ray Ricchetti, Simitha Singh-Rambiritch, Karthik Marimuthu Muthukumar, Vidhya Singaravel, Carmel Irudayanathan, Chandana Reddy-Sinha, Imran Junaid, Garima Sharma, Patricia Alice Francis-Lyon. Originally published in the Journal of Medical Internet Research (https://www.jmir.org), 19.05.2021.)

Digital therapeutics (DTx) are an emerging medical therapy comprising evidence-based interventions that are regulatory approved for patient use, or are under development, for a variety of medical conditions, including hypertension, cancer, substance use disorders and mental disorders. DTx have significant potential to reduce the overall burden on healthcare systems and offer potential economic benefits. There is currently no specific legal regulation on DTx in the EU. Although European countries have similar approaches to digital health solutions, the adoption of DTx varies across the continent. The aim of this narrative review is to discuss the levels of adoption of DTx in Europe, and to explore possible strategies to improve adoption, with the goal of higher rates of adoption, and more consistent use of DTx across the continent. The article discusses the regulatory and reimbursement landscape across Europe; validation requirements for DTx, and the importance of co-design and an ecosystem-centric approach in the development of DTx. Also considered are drivers of adoption and prescription practices for DTx, as well as patient perspectives on these therapeutics. The article explores potential factors that may contribute to low rates of DTx adoption in Europe, including lack of harmonisation in regulatory requirements and reimbursement; sociodemographic factors; health status; ethical concerns; challenges surrounding the use and validation of AI; knowledge and awareness among healthcare professionals (HCPs) and patients, and data standards and interoperability. Efforts to improve rates of access to DTx and adoption of these therapeutics across Europe are described. Finally, a framework for improved uptake of DTx in Europe is proposed. [ABSTRACT FROM AUTHOR]

Personalized nutrition (PN) represents a transformative approach in dietary science, where individual genetic profiles guide tailored dietary recommendations, thereby optimizing health outcomes and managing chronic diseases more effectively. This review synthesizes key aspects of PN, emphasizing the genetic basis of dietary responses, contemporary research, and practical applications. We explore how individual genetic differences influence dietary metabolisms, thus underscoring the importance of nutrigenomics in developing personalized dietary guidelines. Current research in PN highlights significant gene–diet interactions that affect various conditions, including obesity and diabetes, suggesting that dietary interventions could be more precise and beneficial if they are customized to genetic profiles. Moreover, we discuss practical implementations of PN, including technological advancements in genetic testing that enable real-time dietary customization. Looking forward, this review identifies the robust integration of bioinformatics and genomics as critical for advancing PN. We advocate for multidisciplinary research to overcome current challenges, such as data privacy and ethical concerns associated with genetic testing. The future of PN lies in broader adoption across health and wellness sectors, promising significant advancements in public health and personalized medicine. [ABSTRACT FROM AUTHOR]

Autism spectrum disorder (ASD) is a complex neurodevelopmental condition characterized by several core symptoms: restricted interests, communication difficulties, and impaired social interactions. Many ASD children experience gastrointestinal functional disorders, impacting their well-being. Emerging evidence suggests that a gut microbiota imbalance may exacerbate core and gastrointestinal symptoms. Our review assesses the gut microbiota in children with ASD and interventions targeting microbiota modulation. The analysis of forty-four studies (meta-analyses, reviews, original research) reveals insights into the gut microbiota–ASD relationship. While specific microbiota alterations are mixed, some trends emerge. ASD children exhibit increased Firmicutes (36–81%) and Pseudomonadota (78%) and decreased Bacteroidetes (56%). The Bacteroidetes to Firmicutes ratio tends to be lower (56%) compared to children without ASD, which correlates with behavioral and gastrointestinal abnormalities. Probiotics, particularly Lactobacillus, Bifidobacterium, and Streptococcus strains, show promise in alleviating behavioral and gastrointestinal symptoms (66%). Microbiota transfer therapy (MTT) seems to have lasting benefits for the microbiota and symptoms in one longitudinal study. Prebiotics can potentially help with gastrointestinal and behavioral issues, needing further research for conclusive efficacy due to different interventions being used. This review highlights the gut microbiota–ASD interplay, offering potential therapeutic avenues for the gut–brain axis. However, study heterogeneity, small sample sizes, and methodological variations emphasize the need for comprehensive, standardized research. Future investigations may unveil complex mechanisms linking the gut microbiota to ASD, ultimately enhancing the quality of life for affected individuals. [ABSTRACT FROM AUTHOR]

Introduction. Throughout several decades, English has been strengthening its position as lingua franca in international communication. The relevance of the given study is justified by the examination of the English language from the perspective of contact variantology and in the context of gradually emerging new version of English – Euro-English. The aim of the presented work is to consider the socio-political prerequisites for the strengthening of the English language role for intra-European communication, as well as to try to explain the significance of Brussels for this process. Methodology and sources. Scientific publications of domestic and foreign linguists, sociolinguists (D.S. Borodina, Z.G. Proshina, B. Kachru, D. Crystal, E. Edwards), as well as interviews with European politicians and public figures (Michel Guerin, Pascal Smet, Sven Gatz) all comprise the research material. The method of synthesis and analysis, descriptive method, comparative language analysis is used in the process of work on this article. Results and discussion. The widespread usage of English in Europe has led to the creation of several mixed language variants and intra-European communication in English gives the latter the status of a supranational communication language. Belgium is seen as the center for the formation of this new language variant, which is explained by the representation of a significant number of international organizations and corporations in Brussels. In the context of the competition between French and Dutch, the difficult linguistic situation in Belgium finds a peculiar resolution in the regular use of English which some activists propose to make the third official language of the Brussels-Capital Region. Euro-English has already acquired several characteristic lexical, morphosyntactic and phonetical features, whilst the withdrawal of Great Britain from the European Union has provided serious possibilities for Euro-English to continue its formation as an independent language variant free from “care” and control of English native speakers. Conclusion. The existence of the English language variants involves the preservation of uniqueness for each nation where these are used, as well as the enrichment of the language from which these variants are derived from. Gradual formation of Euro-English confirms the presence of high number of professional and everyday communications under which the representatives of various European nations find common language – and that is English.

We consider the quiver Yangians associated to general affine Dynkin diagrams. Although the quivers are generically not toric, the algebras have some similar structures. The odd reflections of the affine Dynkin diagrams should correspond to Seiberg duality of the quivers, and we investigate the relations of the dual quiver Yangians. We also mention the construction of the twisted quiver Yangians. It is conjectured that the truncations of the (twisted) quiver Yangians can give rise to certain 풲-algebras. Incidentally, we give the screening currents of the 풲-algebras in terms of the free field realization in the case of generalized conifolds. Moreover, we discuss the toroidal and elliptic algebras for any general quivers. [ABSTRACT FROM AUTHOR]

We study global anomalies of discrete gauge symmetries in six-dimensional supergravities and their realizations in F-theory. We explicitly construct a discrete Green-Schwarz mechanism that depends on the choice of a coupling constant and on a certain quadratic refinement in differential cohomology. By geometrically engineering theories with G = ℤ3 gauge symmetry and no tensor multiplets, we observe that a particular choice of the quadratic refinement is singled out in F-theory. This implies new Swampland constraints on the discrete charge spectra of 6d supergravities. On the other hand, the discrete Green-Schwarz coupling depends on the geometry of the Calabi-Yau. We use anomaly inflow to relate this to a 't Hooft anomaly of the induced global symmetry in the worldsheet theories of non-critical strings. Using topological symmetry lines, we further relate this anomaly to the modular properties of twisted-twined elliptic genera. We then argue that the latter are encoded in the A-model topological string partition functions on different torus fibrations that are equipped with a flat torsional B-field. This allows us to derive a geometric expression for the global discrete anomaly in terms of the height-pairing of a multi-section on a genus one fibered Calabi-Yau. [ABSTRACT FROM AUTHOR]

We study the massless charged spectrum of U(1) gauge fields in F-theory that arise from flux breaking of a nonabelian group. The U(1) charges that arise in this way can be very large. In particular, using vertical flux breaking, we construct an explicit 4D F-theory model with a U(1) decoupled from other gauge sectors, in which the massless/light fields have charges as large as 657. This result greatly exceeds prior results in the literature. We argue heuristically that this result may provide an upper bound on charges for light fields under decoupled U(1) factors in the F-theory landscape. We also show that the charges can be even larger when the U(1) is coupled to other gauge groups. [ABSTRACT FROM AUTHOR]

We give a general description of gauge symmetry breaking using vertical and remainder fluxes in 4D F-theory models. The fluxes can break a geometric gauge group to a smaller group and induce chiral matter, even when the larger group admits no chiral matter representations. We focus specifically on applications to realizations of the Standard Model gauge group and chiral matter spectrum through breaking of rigid exceptional gauge groups E7, E6, which are ubiquitous in the 4D F-theory landscape. Supplemented by an intermediate SU(5) group, these large classes of models give natural constructions of Standard Model-like theories with small numbers of generations of matter in F-theory. [ABSTRACT FROM AUTHOR]

With the development of 16S rRNA technology, gut microbiome evaluation has been performed in many diseases, including gastrointestinal tumors. Among these cancers, gastric cancer (GC) exhibits high morbidity and mortality and has been extensively studied in its pathogenesis and diagnosis techniques. The current researches have proved that the gut microbiome may have the potential to distinguish GC patients from healthy patients. However, the change of the gut microbiome according to tumor node metastasis classification (TNM) has not been clarified. Besides, the characteristics of gut microbiome in GC patients and their ages of onset are also ambiguous. To address the above shortcomings, we investigated 226 fecal samples and divided them according to their tumor stage and onset age. The findings revealed that surgery and tumor stage can change the characteristic of GC patients' gut microbiota. In specific, the effect of surgery on early gastric cancer (EGC) was greater than that on advanced gastric cancer (AGC), and the comparison of postoperative microflora with healthy people indicated that EGC has more differential bacteria than AGC. Besides, we found that Collinsella, Blautia, Anaerostipes, Dorea, and Lachnospiraceae_ND3007_group expressed differently between EGC and AGC. More importantly, it is the first time revealed that the composition of gut microbiota in GC is different between different onset ages. Key points: •Gut microbiota of gastric cancer (GC) patients are either highly associated with TNM stage and surgery or not. It shows surgery has more significant changes in early gastric cancer (EGC) than advanced gastric cancer (AGC). •There existed specific gut microbiota between EGC and AGC which may have potential to distinguish the early or advanced GC. •Onset age of GC may influence the gut microbiota: the composition of gut microbiota of early-onset gastric cancer (EOGC) and late-onset gastric cancer (LOGC) is significantly different. [ABSTRACT FROM AUTHOR]

In F-theory, if a fiber type of an elliptic fibration involves a condition that requires an exceptional curve to split into two irreducible components, it is called “split” or “non-split” type depending on whether it is globally possible or not. In the latter case, the gauge symmetry is reduced to a non-simply-laced Lie algebra due to monodromy. We show that this split/non-split transition is, except for a special class of models, a conifold transition from the resolved to the deformed side, associated with the conifold singularities emerging where the codimension-one singularity is enhanced to D2k+2 (k ≥ 1) or E7. We also examine how the previous proposal for the origin of non-local matter can be actually implemented in our blow-up analysis. [ABSTRACT FROM AUTHOR]

Neuropsychiatric diseases and obesity are major components of morbidity and health care costs, with genetic, lifestyle, and gut microbiome factors linked to their etiology. Dietary and weight-loss interventions can help improve mental health, but there is conflicting evidence regarding their efficacy; and moreover, there is substantial interindividual heterogeneity that needs to be understood. We aimed to identify genetic and gut microbiome factors that explain interindividual differences in mental health improvement after a dietary and lifestyle intervention for weight loss. We recruited 369 individuals participating in Digbi Health's personalized digital therapeutics care program and evaluated the association of 23 genetic scores, the abundance of 178 gut microbial genera, and 42 bacterial pathways with mental health. We studied the presence/absence of anxiety or depression, or sleep problems at baseline and improvement on anxiety, depression, and insomnia after losing at least 2% body weight. Participants lost on average 5.4% body weight and >95% reported improving mental health symptom intensity. There were statistically significant correlations between: (a) genetic scores with anxiety or depression at baseline, gut microbial functions with sleep problems at baseline, and (b) genetic scores and gut microbial taxa and functions with anxiety, depression, and insomnia improvement. Our results are concordant with previous findings, including the association between anxiety or depression at baseline with genetic scores for alcohol use disorder and major depressive disorder. As well, our results uncovered new associations in line with previous epidemiological literature. As evident from previous literature, we also observed associations of gut microbial signatures with mental health including short-chain fatty acids and bacterial neurotoxic metabolites specifically with depression. Our results also show that microbiome and genetic factors explain self-reported mental health status and improvement better than demographic variables independently. The genetic and microbiome factors identified in this study provide the basis for designing and personalizing dietary interventions to improve mental health. [ABSTRACT FROM AUTHOR]

We investigate infinite distance limits in the complex structure moduli space of F-theory compactified on K3 to eight dimensions. While this is among the simplest possible arenas to test ideas about the Swampland Distance Conjecture, it is nevertheless non-trivial enough to improve our understanding of the physics for these limiting geometries, including phenomena of emergence. It also provides a perspective on infinite distance limits from the viewpoint of open strings. The paper has two quite independent themes. In the main part we show that all degenerations of elliptic K3 surfaces at infinite distance as analysed in the companion paper [1] can be interpreted as (partial) decompactification or emergent string limits in F-theory, in agreement with the Emergent String Conjecture. We present a unified geometric picture of the possible towers of states that can become light and illustrate our general claims via the connection between Kulikov models of degenerating K3 surfaces and the dual heterotic string. As an application we classify the possible maximal non-abelian Lie algebras and their Kac-Moody and loop extensions that can arise in the infinite distance limits. In the second part we discuss the infinite distance behaviour of certain exact quartic gauge couplings. We encounter a tension with the hypothesis that effective couplings should be fully generated by integrating out massive states. We show that by appropriately renormalizing the string coupling, at least partial emergence can be achieved. [ABSTRACT FROM AUTHOR]

We extend the investigation in [1] of special toroidal compactifications of heterotic string theory for which the half-BPS states provide representations of subgroups of the Conway group. We also explore dual descriptions of these theories and find that they are all linked to either F-theory or type IIA string theory on K3 surfaces with symplectic automorphism groups that are the same Conway subgroups as those of the heterotic dual. The matching with type IIA K3 dual theories includes both the matching of symmetry groups and a comparison between the Narain lattice on the heterotic side and the cohomology lattice on the type IIA side. We present twelve examples where we can identify a type IIA dual K3 orbifold theory as the dual description of the heterotic theory. In addition, we include a supplementary Mathematica package that performs most of the computations required for these comparisons. [ABSTRACT FROM AUTHOR]

Many interesting questions about F-theory models, including several concerning the F-theory swampland, involve massless matter charged under U(1) gauge symmetries. It is therefore important to better understand the geometric properties of F-theory models realizing various U(1) charges. We propose that, for F-theory models described by elliptic fibrations in Weierstrass form, the U(1) charge of light matter is encoded in the orders of vanishing of the section components corresponding to the U(1) gauge symmetry. We give specific equations relating the U(1) charges to the orders of vanishing that seem to hold for both U(1)-charged singlets and for matter additionally charged under a simply-laced nonabelian gauge algebra. Our formulas correctly describe properties of F-theory models in the prior literature, and we give an argument that they should describe the orders of vanishing for arbitrarily high U(1) charges. They also resemble formulas for the p-adic valuations of elliptic divisibility sequences developed by Stange [1]. These proposals could serve as a U(1) analogue of the Katz-Vafa method, allowing one to determine U(1) charges without resolution. Additionally, they predict geometric information about F-theory models with general U(1) charges, which may be useful for exploring the F-theory landscape and swampland. [ABSTRACT FROM AUTHOR]

In six-dimensional F-theory/heterotic string theory, half-hypermultiplets arise only when they correspond to particular quaternionic Kähler symmetric spaces, which are mostly associated with the Freudenthal–Tits magic square. Motivated by the intriguing singularity structure previously found in such F-theory models with a gauge group SU (6), SO (12), or E 7, we investigate, as the final magical example, an F-theory on an elliptic fibration over a Hirzebruch surface of the non-split I 6 type, in which the unbroken gauge symmetry is supposed to be Sp (3). We find significant qualitative differences between the previous F-theory models associated with the magic square and the present case. We argue that the relevant half-hypermultiplets arise at the E 6 points, where half-hypermultiplets 20 of SU (6) would have appeared in the split model. We also consider the problem on the non-local matter generation near the D 6 point. After stating what the problem is, we explain why this is so by using the recent result that a split/non-split transition can be regarded as a conifold transition. [ABSTRACT FROM AUTHOR]

We analyze the de Sitter construction of [1] using ten-dimensional supergravity, finding exact agreement with the four-dimensional effective theory. Starting from the fermionic couplings in the D7-brane action, we derive the ten-dimensional stress-energy due to gaugino condensation on D7-branes. We demonstrate that upon including this stress-energy, as well as that due to anti-D3-branes, the ten-dimensional equations of motion require the four-dimensional curvature to take precisely the value determined by the four-dimensional effective theory of [1]. [ABSTRACT FROM AUTHOR]

We prove that, for every 6D supergravity theory that has an F-theory description, the property of charge completeness for the connected component of the gauge group (meaning that all charges in the corresponding charge lattice are realized by massive or massless states in the theory) is equivalent to a standard assumption made in F-theory for how geometry encodes the global gauge theory by means of the Mordell-Weil group of the elliptic fibration. This result also holds in 4D F-theory constructions for the parts of the gauge group that come from sections and from 7-branes. We find that in many 6D F-theory models the full charge lattice of the theory is generated by massless charged states; this occurs for each gauge factor where the associated anomaly coefficient satisfies a simple positivity condition. We describe many of the cases where this massless charge sufficiency condition holds, as well as exceptions where the positivity condition fails, and analyze the related global structure of the gauge group and associated Mordell-Weil torsion in explicit F-theory models. [ABSTRACT FROM AUTHOR]

We construct novel web diagrams with a trivalent or quadrivalent gluing for various 6d/5d theories from certain Higgsings of 6d conformal matter theories on a circle. The theories realized on the web diagrams include 5d Kaluza-Klein theories from circle compactifications of the 6d G2 gauge theory with 4 flavors, the 6d F4 gauge theory with 3 flavors, the 6d E6 gauge theory with 4 flavors and the 6d E7 gauge theory with 3 flavors. The Higgsings also give rise to 5d Kaluza-Klein theories from twisted compactifications of 6d theories including the 5d pure SU(3) gauge theory with the Chern-Simons level 9 and the 5d pure SU(4) gauge theory with the Chern-Simons level 8. We also compute the Nekrasov partition functions of the theories by applying the topological vertex formalism to the newly obtained web diagrams. [ABSTRACT FROM AUTHOR]

We observe that in many F-theory models, tuning a specific gauge group G and matter content M under certain circumstances leads to an automatic enhancement to a larger gauge group G′ ⊃ G and matter content M′ ⊃ M. We propose that this is true for any theory G, M whenever there exists a containing theory G′, M′ that cannot be Higgsed down to G, M. We give a number of examples including non-Higgsable gauge factors, nonabelian gauge factors, abelian gauge factors, and exotic matter. In each of these cases, tuning an F-theory model with the desired features produces either an enhancement or an inconsistency, often when the associated anomaly coefficient becomes too large. This principle applies to a variety of models in the apparent 6D supergravity swampland, including some of the simplest cases with U(1) and SU(N) gauge groups and generic matter, as well as infinite families of U(1) models with higher charges presented in the prior literature, potentially ruling out all these apparent swampland theories. [ABSTRACT FROM AUTHOR]

We extend the dictionary between the BPS spectrum of Heterotic strings and the one of F-/M-theory compactifications on K3 fibered Calabi-Yau 3-folds to cases with higher rank non-Abelian gauge groups and in particular to dual pairs between Heterotic CHL orbifolds and compactifications on Calabi-Yau 3-folds with a compatible genus one fibration. We show how to obtain the new supersymmetric index purely from the Calabi-Yau geometry by reconstructing the Noether-Lefschetz generators, which are vector-valued modular forms. There is an isomorphism between the latter objects and vector-valued lattice Jacobi forms, which relates them to the elliptic genera and twisted-twined elliptic genera of six- and five-dimensional Heterotic strings. The meromorphic Jacobi forms generate the dimensions of the refined cohomology of the Hilbert schemes of symmetric products of the fiber and allow us to refine the BPS indices in the fiber and therefore to obtain, conjecturally, actual state counts. Using the properties of the vector-valued lattice Jacobi forms we also provide a mathematical proof of the non-Abelian weak gravity conjecture for F-/M-theory compactified on this general class of fibered Calabi-Yau 3-folds. [ABSTRACT FROM AUTHOR]

Using topological string techniques, we compute BPS counting functions of 5d gauge theories which descend from 6d superconformal field theories upon circle compactification. Such theories are naturally organized in terms of nodes of Higgsing trees. We demonstrate that the specialization of the partition function as we move from the crown to the root of a tree is determined by homomorphisms between rings of Weyl invariant Jacobi forms. Our computations are made feasible by the fact that symmetry enhancements of the gauge theory which are manifest on the massless spectrum are inherited by the entire tower of BPS particles. In some cases, these symmetry enhancements have a nice relation to the 1-form symmetry of the associated gauge theory. [ABSTRACT FROM AUTHOR]

In this paper, we initiate the study of the 2d F-theory landscape based on compact elliptic Calabi-Yau fivefolds. In particular, we determine the boundary models of the landscape using Calabi-Yau fivefolds with the largest known Hodge numbers h1,1 and h4,1. The former gives rise to the largest geometric gauge group in the currently known 2d (0,2) supergravity landscape, which is E 8 482 632 421 × F 4 3 224 195 728 × G 2 11 927 989 964 × SU 2 25 625 222 180 . Besides that, we systematically study the hypersurfaces in weighted projective spaces with small degrees, and check the gravitational anomaly cancellation. Moreover, we also initiate the study of singular bases in 2d F-theory. We find that orbifold singularities on the base fourfold have non-zero contributions to the gravitational anomaly. [ABSTRACT FROM AUTHOR]

Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively. We study their Coulomb and Higgs branches using crepant resolutions and deformations of the singularities. We propose a relation between the resulting moduli spaces, by compactifying the theories to 3d, followed by 3d N = 4 mirror symmetry and an S-type gauging of an abelian flavor symmetry. In particular, we use this correspondence to determine the Higgs branch of some 5d SCFTs and their magnetic quivers from the geometry. As an application of the general framework, we observe that singularities that engineer Argyres-Douglas theories in Type IIB also give rise to rank-0 5d SCFTs in M-theory. We also compute the higher-form symmetries of the 4d and 5d SCFTs, including the one-form symmetries of generalized Argyres-Douglas theories of type (G, G′). [ABSTRACT FROM AUTHOR]

Glauber-Sudarshan states, sometimes simply referred to as Glauber states, or alternatively as coherent and squeezed-coherent states, are interesting states in the configuration spaces of any quantum field theories, that closely resemble classical trajectories in space-time. In this paper, we identify four-dimensional de Sitter space as a coherent state over a supersymmetric Minkowski vacuum. Although such an identification is not new, what is new however is the claim that this is realizable in full string theory, but only in conjunction with temporally varying degrees of freedom and quantum corrections resulting from them. Furthermore, fluctuations over the de Sitter space is governed by a generalized graviton (and flux)-added coherent state, also known as the Agarwal-Tara state. The realization of de Sitter space as a state, and not as a vacuum, resolves many issues associated with its entropy, zero-point energy and trans-Planckian censorship, amongst other things. [ABSTRACT FROM AUTHOR]

We determine 5d N = 1 SCFTs originating from 6d (En, Em) conformal matter theories with n ≠ m by circle reduction and mass deformations. The marginal geometries are constructed and we derive their combined fiber diagrams (CFDs). The CFDs allow for an enumeration of descendant SCFTs obtained by decoupling matter hypermultiplets and a description of candidate weakly coupled quivers. [ABSTRACT FROM AUTHOR]

We focus on 4D N = 2 string vacua described both by perturbative Heterotic theory and by Type IIA theory; a Calabi-Yau three-fold XIIA in the Type IIA language is further assumed to have a regular K3-fibration. It is well-known that one can assign a modular form Φ to such a vacuum by counting perturbative BPS states in Heterotic theory or collecting Noether-Lefschetz numbers associated with the K3-fibration of XIIA. In this article, we expand the observations and ideas (using gauge threshold correction) in the literature and formulate a modular form Ψ with full generality for the class of vacua above, which can be used along with Φ for the purpose of classification of those vacua. Topological invariants of XIIA can be extracted from Φ and Ψ, and even a pair of diffeomorphic Calabi-Yau's with different Kähler cones may be distinguished by introducing the notion of "the set of Ψ's for Higgs cascades/for curve classes". We illustrated these ideas by simple examples. [ABSTRACT FROM AUTHOR]

We construct a general form for an F-theory Weierstrass model over a general base giving a 6D or 4D supergravity theory with gauge group (SU(3) × SU(2) × U(1))/ℤ6 and generic associated matter, which includes the matter content of the standard model. The Weierstrass model is identified by unHiggsing a model with U(1) gauge symmetry and charges q ≤ 4 previously found by the first author. This model includes two distinct branches that were identified in earlier work, and includes as a special case the class of models recently studied by Cvetič, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing. We develop a systematic methodology for checking that a parameterized class of F-theory Weierstrass models with a given gauge group G and fixed matter content is generic (contains all allowed moduli) and confirm that this holds for the models constructed here. [ABSTRACT FROM AUTHOR]

We examine the proposal in the previous paper to resolve the puzzle in transitions in discrete gauge groups. We focus on a four-section geometry to test the proposal. We observed that a discrete ℤ2 gauge group enlarges and U(1) also forms in F-theory along any bisection geometries locus in the four-section geometry built as the complete intersections of two quadrics in ℙ3 fibered over any base. Furthermore, we demonstrate that giving vacuum expectation values to hypermultiplets breaks the enlarged U(1) × ℤ2 gauge group down to a discrete ℤ4 gauge group via Higgsing. We thus confirmed that the proposal in the previous paper is consistent when a four-section splits into a pair of bisections in the four-section geometry. This analysis may be useful for understanding the Higgsing processes occurring in the transitions in discrete gauge groups in six-dimensional F-theory models. We also discuss the construction of a family of six-dimensional F-theory models in which U(1) × ℤ4 forms. [ABSTRACT FROM AUTHOR]

In this study, we introduce a new class of rational elliptic 3-folds, which we refer to as “1/2 Calabi-Yau 3-folds”. We construct elliptically fibered Calabi-Yau 3-folds by utilizing these rational elliptic 3-folds. The construction yields a novel approach to build elliptically fibered Calabi-Yau 3-folds of various Mordell-Weil ranks. Our construction of Calabi-Yau 3-folds can be considered as a three-dimensional generalization of the operation of gluing pairs of 1/2 K3 surfaces to yield elliptic K3 surfaces. From one to seven U(1)s form in six-dimensional N = 1 F-theory on the constructed Calabi-Yau 3-folds. Seven tensor multiplets arise in these models. [ABSTRACT FROM AUTHOR]

We argue that global F-theory compactifications to four dimensions gener- ally exhibit higher rank Yukawa matrices from multiple geometric contributions known as Yukawa points. The holomorphic couplings furthermore have large hierarchies for generic complex structure moduli. Unlike local considerations, the compact setup realizes these features all through geometry, and requires no instanton corrections. As an example, we consider a concrete toy model with SU(5) × U(1) gauge symmetry. From the geometry, we find two Yukawa points for the 1 0 − 2 5 ¯ 6 5 ¯ − 4 coupling, producing a rank two Yukawa matrix. Our methods allow us to track all complex structure dependencies of the holomorphic couplings and study the ratio numerically. This reveals hierarchies of O (105) and larger on a full-dimensional subspace of the moduli space. [ABSTRACT FROM AUTHOR]

We apply machine learning techniques to solve a specific classification problem in 4D F-theory. For a divisor D on a given complex threefold base, we want to read out the non-Higgsable gauge group on it using local geometric information near D. The input features are the triple intersection numbers among divisors near D and the output label is the non-Higgsable gauge group. We use decision tree to solve this problem and achieved 85%-98% out-of-sample accuracies for different classes of divisors, where the data sets are generated from toric threefold bases without (4,6) curves. We have explicitly generated a large number of analytic rules directly from the decision tree and proved a small number of them. As a crosscheck, we applied these decision trees on bases with (4,6) curves as well and achieved high accuracies. Additionally, we have trained a decision tree to distinguish toric (4,6) curves as well. Finally, we present an application of these analytic rules to construct local base configurations with interesting gauge groups such as SU(3). [ABSTRACT FROM AUTHOR]

Using a one-way Monte Carlo algorithm from several different starting points, we get an approximation to the distribution of toric threefold bases that can be used in four-dimensional F-theory compactification. We separate the threefold bases into 'resolvable' ones where the Weierstrass polynomials ( f, g) can vanish to order (4 , 6) or higher on codimension-two loci and the 'good' bases where these (4 , 6) loci are not allowed. A simple estimate suggests that the number of distinct resolvable base geometries exceeds 10, with over 10 'good' bases, though the actual numbers are likely much larger. We find that the good bases are concentrated at specific 'end points' with special isolated values of h that are bigger than 1,000. These end point bases give Calabi-Yau fourfolds with specific Hodge numbers mirror to elliptic fibrations over simple threefolds. The non-Higgsable gauge groups on the end point bases are almost entirely made of products of E, F, G and SU(2). Nonetheless, we find a large class of good bases with a single non-Higgsable SU(3). Moreover, by randomly contracting the end point bases, we find many resolvable bases with h( B) ∼ 50-200 that cannot be contracted to another smooth threefold base. [ABSTRACT FROM AUTHOR]

We show that F-theory compactifications with abelian gauge factors generally exhibit a non-trivial global gauge group structure. The geometric origin of this structure lies with the Shioda map of the Mordell-Weil generators. This results in constraints on the $$ \mathfrak{u}(1) $$ charges of non-abelian matter consistent with observations made throughout the literature. In particular, we find that F-theory models featuring the Standard Model algebra actually realise the precise gauge group [SU(3) × SU(2) × U(1)]/ ℤ . Furthermore, we explore the relationship between the gauge group structure and geometric (un-)higgsing. In an explicit class of models, we show that, depending on the global group structure, an $$ \mathfrak{s}\mathfrak{u}(2)\oplus \mathfrak{u}(1) $$ gauge theory can either unhiggs into an SU(2) × SU(2) or an SU(3) × SU(2) theory. We also study implications of the charge constraints as a criterion for the F-theory 'swampland'. [ABSTRACT FROM AUTHOR]

Supergravity theories in more than four dimensions with grand unified gauge symmetries are an important intermediate step towards the ultraviolet completion of the Standard Model in string theory. Using toric geometry, we classify and analyze six-dimensional F-theory vacua with gauge group SO(10) taking into account Mordell-Weil U(1) and discrete gauge factors. We determine the full matter spectrum of these models, including charged and neutral SO(10) singlets. Based solely on the geometry, we compute all matter multiplicities and confirm the cancellation of gauge and gravitational anomalies independent of the base space. Particular emphasis is put on symmetry enhancements at the loci of matter fields and to the frequent appearance of superconformal points. They are linked to non-toric Kähler deformations which contribute to the counting of degrees of freedom. We compute the anomaly coefficients for these theories as well by using a base-independent blow-up procedure and superconformal matter transitions. Finally, we identify six-dimensional supergravity models which can yield the Standard Model with high-scale supersymmetry by further compactification to four dimensions in an Abelian flux background. [ABSTRACT FROM AUTHOR]

Using E-strings, we can analyze not only six-dimensional superconformal field theories but also probe vacua of non-perturabative heterotic string. We study strings made of D3-branes wrapped on various two-cycles in the global F-theory setup. We claim that E-strings are elementary in the sense that various combinations of E-strings can form M-strings as well as heterotic strings and new kind of strings, called G-strings. Using them, we show that emissions and combinations of heterotic small instantons generate most of known six-dimensional superconformal theories, their affinizations and little string theories. Taking account of global structure of compact internal geometry, we also show that special combinations of E-strings play an important role in constructing six-dimensional theories of D- and E-types. We check global consistency conditions from anomaly cancellation conditions, both from five-branes and strings, and show that they are given in terms of elementary E-string combinations. [ABSTRACT FROM AUTHOR]

According to a recent classification of 6d (1 , 0) theories within F-theory there are only six 'pure' 6d gauge theories which have a UV superconformal fixed point. The corresponding gauge groups are SU(3) , SO(8) , F , E , E , and E . These exceptional models have BPS strings which are also instantons for the corresponding gauge groups. For G simply-laced, we determine the 2d $$ \mathcal{N}=\left(0,4\right) $$ worldsheet theories of such BPS instanton strings by a simple geometric engineering argument. These are given by a twisted S compactification of the 4d $$ \mathcal{N}=2 $$ theories of type H , D , E , E and E (and their higher rank generalizations), where the 6d instanton number is mapped to the rank of the corresponding 4d SCFT. This determines their anomaly polynomials and, via topological strings, establishes an interesting relation among the corresponding T × S partition functions and the Hilbert series for moduli spaces of G instantons. Such relations allow to bootstrap the corresponding elliptic genera by modularity. As an example of such procedure, the elliptic genera for a single instanton string are determined. The same method also fixes the elliptic genus for case of one F instanton. These results unveil a rather surprising relation with the Schur index of the corresponding 4d $$ \mathcal{N}=2 $$ models. [ABSTRACT FROM AUTHOR]

Starting from 6D superconformal field theories (SCFTs) realized via F-theory, we show how reduction on a circle leads to a uniform perspective on the phase structure of the resulting 5D theories, and their possible conformal fixed points. Using the correspon-dence between F-theory reduced on a circle and M-theory on the corresponding elliptically fibered Calabi-Yau threefold, we show that each 6D SCFT with minimal supersymmetry directly reduces to a collection of between one and four 5D SCFTs. Additionally, we find that in most cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization of a quiver gauge theory. These two reductions of the theory often correspond to different phases in the 5D theory which are in general connected by a sequence of flop transitions in the extended Kähler cone of the Calabi-Yau threefold. We also elaborate on the structure of the resulting conformal fixed points, and emergent flavor symmetries, as realized by M-theory on a canonical singularity. [ABSTRACT FROM AUTHOR]