Higher genus correlators for tensionless AdS3\rm{AdS}_3 strings

It was recently shown in arXiv:2009.11306 that tree-level correlation functions in tensionless string theory on $\rm{AdS}_3\times\rm{S}^3\times\mathbb{T}^4$ match the expected form of correlation functions in the symmetric orbifold CFT on $\mathbb{T}^4$ in the large $N$ limit. This analysis utilized the free-field realization of the $\mathfrak{psu}(1,1|2)_1$ Wess-Zumino-Witten model, along with a surprising identity directly relating these correlation functions to a branched covering of the boundary of $\rm{AdS}_3$. In particular, this identity implied the unusual feature that the string theory correlators localize to points in the moduli space for which the worldsheet covers the boundary of $\rm{AdS}_3$ with specified branching near the insertion points. In this work we generalize this analysis past the tree-level approximation, demonstrating its validity to higher genus worldsheets, and in turn providing strong evidence for this incarnation of the $\rm{AdS}/\rm{CFT}$ correspondence at all orders in perturbation theory.Comment: JHEP versio

The Lion, the Witch, and the Wormhole: Ensemble averaging the symmetric product orbifold

We consider the ensemble average of two dimensional symmetric product orbifold CFTs $\text{Sym}^N(\mathbb{T}^D)$ over the Narain moduli space. We argue for a bulk dual given by $N$ copies of an abelian Chern-Simons theory coupled to topological gravity, endowed with a discrete gauge symmetry exchanging the $N$ copies. As a check of this proposal, we calculate the ensemble average of various partition and correlation functions of the symmetric product orbifold theory and compare the resulting expressions to gauge theory quantities in the bulk. We comment on the ensemble average of the tensionless string partition function on $\text{AdS}_3 \times \text{S}^3 \times \mathbb T^4$ by considering the specific case of $D=4$ with the addition of supersymmetry.Comment: 84 pages, 25 figure

Free field world-sheet correlators for AdS3{\rm AdS}_3

We employ the free field realisation of the $\mathfrak{psu}(1,1|2)_1$ world-sheet theory to constrain the correlators of string theory on ${\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary ${\rm S}^2$ by the (genus zero) world-sheet -- this is the key property which makes the equivalence to the dual symmetric orbifold manifest. In our approach, this feature follows from a remarkable `incidence relation' obeyed by the correlators, which is reminiscent of a twistorial string description. We also illustrate our results with explicit computations in various special cases.Comment: 42 page

Care processes in people in remission from type 2 diabetes:A cohort study using the National Diabetes Audit

Aims: People with type 2 diabetes can enter remission but may relapse or develop legacy complications. This analysis assesses whether people with remission from type 2 diabetes continue receiving annual care processes recommended in national guidelines and the potential impacts of formal recognition of remission. Methods: People with type 2 diabetes with and without formal recognition (diagnostic code) of remission, and with and without evidence of remission (HbA1c < 48 mmol/mol without prescription for glucose-lowering drugs in preceding 26 weeks), included in the 2018/19 National Diabetes Audit (NDA) for England and Wales were followed up to identify care processes received between 1 January 2019 and 31 March 2020. Results: Of the 2,822,145 people with type 2 diabetes in the cohort, 16,460 (0.58%) were coded with remission in the 2018/19 NDA. After adjustment for age, sex, socioeconomic deprivation and ethnicity, people coded with remission were less likely to receive each care process than those without such coding irrespective of HbA1c measurements (relative risk (RR) of receiving all 8 care processes 0.70 (95% CI 0.69–0.72)). For the 339,235 people with evidence of remission, irrespective of diagnostic coding compared to those without such evidence, the RR for receiving all 8 care processes was 0.94 (95% CI 0.93–0.94). Conclusions: People coded with remission of type 2 diabetes were less likely to receive diabetes care processes than those without such coding. People with evidence of remission had only a slightly reduced likelihood of receiving care processes. Formal recognition of remission may affect the provision or uptake of care processes

Risk factors for COVID-19-related mortality in people with type 1 and type 2 diabetes in England: a population-based cohort study

Background: Diabetes has been associated with increased COVID-19-related mortality, but the association between modifiable risk factors, including hyperglycaemia and obesity, and COVID-19-related mortality among people with diabetes is unclear. We assessed associations between risk factors and COVID-19-related mortality in people with type 1 and type 2 diabetes. Methods: We did a population-based cohort study of people with diagnosed diabetes who were registered with a general practice in England. National population data on people with type 1 and type 2 diabetes collated by the National Diabetes Audit were linked to mortality records collated by the Office for National Statistics from Jan 2, 2017, to May 11, 2020. We identified the weekly number of deaths in people with type 1 and type 2 diabetes during the first 19 weeks of 2020 and calculated the percentage change from the mean number of deaths for the corresponding weeks in 2017, 2018, and 2019. The associations between risk factors (including sex, age, ethnicity, socioeconomic deprivation, HbA1c, renal impairment [from estimated glomerular filtration rate (eGFR)], BMI, tobacco smoking status, and cardiovascular comorbidities) and COVID-19-related mortality (defined as International Classification of Diseases, version 10, code U07.1 or U07.2 as a primary or secondary cause of death) between Feb 16 and May 11, 2020, were investigated by use of Cox proportional hazards models. Findings: Weekly death registrations in the first 19 weeks of 2020 exceeded the corresponding 3-year weekly averages for 2017–19 by 672 (50·9%) in people with type 1 diabetes and 16 071 (64·3%) in people with type 2 diabetes. Between Feb 16 and May 11, 2020, among 264 390 people with type 1 diabetes and 2 874 020 people with type 2 diabetes, 1604 people with type 1 diabetes and 36 291 people with type 2 diabetes died from all causes. Of these total deaths, 464 in people with type 1 diabetes and 10 525 in people with type 2 diabetes were defined as COVID-19 related, of which 289 (62·3%) and 5833 (55·4%), respectively, occurred in people with a history of cardiovascular disease or with renal impairment (eGFR <60 mL/min per 1·73 m2). Male sex, older age, renal impairment, non-white ethnicity, socioeconomic deprivation, and previous stroke and heart failure were associated with increased COVID-19-related mortality in both type 1 and type 2 diabetes. Compared with people with an HbA1c of 48–53 mmol/mol (6·5–7·0%), people with an HbA1c of 86 mmol/mol (10·0%) or higher had increased COVID-19-related mortality (hazard ratio [HR] 2·23 [95% CI 1·50–3·30, p<0·0001] in type 1 diabetes and 1·61 [1·47–1·77, p<0·0001] in type 2 diabetes). In addition, in people with type 2 diabetes, COVID-19-related mortality was significantly higher in those with an HbA1c of 59 mmol/mol (7·6%) or higher than in those with an HbA1c of 48–53 mmol/mol (HR 1·22 [95% CI 1·15–1·30, p<0·0001] for 59–74 mmol/mol [7·6–8·9%] and 1·36 [1·24–1·50, p<0·0001] for 75–85 mmol/mol [9·0–9·9%]). The association between BMI and COVID-19-related mortality was U-shaped: in type 1 diabetes, compared with a BMI of 25·0–29·9 kg/m2, a BMI of less than 20·0 kg/m2 had an HR of 2·45 (95% CI 1·60–3·75, p<0·0001) and a BMI of 40·0 kg/m2 or higher had an HR of 2·33 (1·53–3·56, p<0·0001); the corresponding HRs for type 2 diabetes were 2·33 (2·11–2·56, p<0·0001) and 1·60 (1·47–1·75, p<0·0001). Interpretation: Deaths in people with type 1 and type 2 diabetes rose sharply during the initial COVID-19 pandemic in England. Increased COVID-19-related mortality was associated not only with cardiovascular and renal complications of diabetes but, independently, also with glycaemic control and BMI

Associations of type 1 and type 2 diabetes with COVID-19-related mortality in England: a whole-population study

Background: Although diabetes has been associated with COVID-19-related mortality, the absolute and relative risks for type 1 and type 2 diabetes are unknown. We assessed the independent effects of diabetes status, by type, on in-hospital death in England in patients with COVID-19 during the period from March 1 to May 11, 2020. Methods: We did a whole-population study assessing risks of in-hospital death with COVID-19 between March 1 and May 11, 2020. We included all individuals registered with a general practice in England who were alive on Feb 16, 2020. We used multivariable logistic regression to examine the effect of diabetes status, by type, on in-hospital death with COVID-19, adjusting for demographic factors and cardiovascular comorbidities. Because of the absence of data on total numbers of people infected with COVID-19 during the observation period, we calculated mortality rates for the population as a whole, rather than the population who were infected. Findings: Of the 61 414 470 individuals who were alive and registered with a general practice on Feb 16, 2020, 263 830 (0·4%) had a recorded diagnosis of type 1 diabetes, 2 864 670 (4·7%) had a diagnosis of type 2 diabetes, 41 750 (0·1%) had other types of diabetes, and 58 244 220 (94·8%) had no diabetes. 23 698 in-hospital COVID-19-related deaths occurred during the study period. A third occurred in people with diabetes: 7434 (31·4%) in people with type 2 diabetes, 364 (1·5%) in those with type 1 diabetes, and 69 (0·3%) in people with other types of diabetes. Unadjusted mortality rates per 100 000 people over the 72-day period were 27 (95% CI 27–28) for those without diabetes, 138 (124–153) for those with type 1 diabetes, and 260 (254–265) for those with type 2 diabetes. Adjusted for age, sex, deprivation, ethnicity, and geographical region, compared with people without diabetes, the odds ratios (ORs) for in-hospital COVID-19-related death were 3·51 (95% CI 3·16–3·90) in people with type 1 diabetes and 2·03 (1·97–2·09) in people with type 2 diabetes. These effects were attenuated to ORs of 2·86 (2·58–3·18) for type 1 diabetes and 1·80 (1·75–1·86) for type 2 diabetes when also adjusted for previous hospital admissions with coronary heart disease, cerebrovascular disease, or heart failure. Interpretation: The results of this nationwide analysis in England show that type 1 and type 2 diabetes were both independently associated with a significant increased odds of in-hospital death with COVID-19

Classical geometry from the tensionless string

Abstract Tensionless string theory on AdS3 × S3 × M $$\mathcal{M}$$ is explored in the limit that the strings wind the asymptotic boundary a large number of times. Although the worldsheet is usually thought to be localised to the AdS boundary, we argue that the string can actually probe the bulk geometry in this limit. In particular, we show that correlation functions can be expressed in terms of a minimal-area worldsheet propagating in AdS3. We then relate the classical motion of the string to the twistor-like free field description of the tensionless worldsheet theory. Finally, we consider a particular dimensional reduction of AdS3 to AdS2, and show that the effective action of the worldsheet formally resembles the one-dimensional Schwarzian theory of JT gravity with conical defects

D-branes in AdS₃ x S³ x ⁴ at k = 1 and their holographic duals

String theory on AdS₃ × S³ × ⁴ with minimal k = 1 NS-NS flux can be described in terms of a free field worldsheet theory in the hybrid formalism. We construct various D-branes of this string theory and calculate their associated cylinder amplitudes. We find that these amplitudes match with the cylinder correlators of certain boundary states of the dual symmetric orbifold CFT Sym(⁴), thus suggesting a direct correspondence between these boundary conditions. We also show that the disk amplitudes of these D-branes localise to those points in the worldsheet moduli space where the worldsheet disk holomorphically covers the spacetime disk.ISSN:1126-6708ISSN:1029-847

Spectral flow and localisation in AdS3 string theory

Acknowledgements: We thank Andrea Dei, Yasuaki Hikida, Matthias Gaberdiel, Sylvain Lacriox, Nathan McStay, Kiarash Naderi, Beat Nairz, Ron Reid-Edwards, Volker Schomerus, and David Skinner for useful discussions. We also thank Andrea Dei, Lorenz Eberhardt, Matthias Gaberdiel, Ron Reid-Edwards and David Skinner for useful comments on an early version of the draft. We further thank Yasuaki Hikida and Volker Schomerus for sharing a preliminary version of their recent paper [32]. The work of VS is supported by a grant from the Swiss National Science Foundation. VS also acknowledges the support by the NCCR SwissMAP that is also supported by the Swiss National Science Foundation. The work of BK and SS is supported by STFC consolidated grants ST/T000694/1 and ST/X000664/1. The work of SS is also supported by the Trinity Internal Graduate studentship.Abstract We study string theory in three-dimensional Anti-de Sitter spacetime in the path integral formalism. We derive expressions for generic spectrally-flowed near-boundary vertex operators in the Wakimoto representation, and relate their correlation functions to covering maps from the worldsheet to the target space boundary. We show that the path integral structurally reproduces correlation functions of the dual symmetric orbifold theory. By rephrasing spectral flow as the introduction of a background gauge field, we provide a path integral derivation of the localisation property of the near boundary theory. We then focus on the case of IIB string theory on AdS3 × S3 × 4 with k = 1 units of NS-NS flux, where the relationship between correlation functions and covering maps can be made sharp. We also comment on the relation of the k = 1 theory and twistor theory.</jats:p