Higher spin de Sitter quasinormal modes

We construct higher spin quasinormal modes algebraically in $D$-dimensional de Sitter spacetime using the ambient space formalism. The quasinormal modes fall into two nonunitary lowest-weight representations of $\mathfrak{so}(1, D)$. From a local QFT point of view, the lowest-weight quasinormal modes of massless higher spin fields are produced by gauge-invariant boundary conserved currents and boundary higher-spin Weyl tensors inserted at the southern pole of the past boundary. We also show that the quasinormal spectrum of a massless/massive spin-$s$ field is precisely encoded in the Harish-Chandra character corresponding to the unitary massless/massive spin-$s$ $\text{SO}(1, D)$ representation.Comment: 38 pages, 1 figur

Higher Spin de Sitter Hilbert Space

We propose a complete microscopic definition of the Hilbert space of minimal higher spin de Sitter quantum gravity and its Hartle-Hawking vacuum state. The fundamental degrees of freedom are $2N$ bosonic fields living on the future conformal boundary, where $N$ is proportional to the de Sitter horizon entropy. The vacuum state is normalizable. The model agrees in perturbation theory with expectations from a previously proposed dS-CFT description in terms of a fermionic Sp(N) model, but it goes beyond this, both in its conceptual scope and in its computational power. In particular it resolves the apparent pathologies affecting the Sp(N) model, and it provides an exact formula for late time vacuum correlation functions. We illustrate this by computing probabilities for arbitrarily large field excursions, and by giving fully explicit examples of vacuum 3- and 4-point functions. We discuss bulk reconstruction and show the perturbative bulk QFT canonical commutations relations can be reproduced from the fundamental operator algebra, but only up to a minimal error term $\sim e^{-\mathcal{O}(N)}$, and only if the operators are coarse grained in such a way that the number of accessible "pixels" is less than $\mathcal{O}(N)$. Independent of this, we show that upon gauging the higher spin symmetry group, one is left with $2N$ physical degrees of freedom, and that all gauge invariant quantities can be computed by a $2N \times 2N$ matrix model. This suggests a concrete realization of the idea of cosmological complementarity

A group theoretical approach to quantum gravity in (A)dS

This thesis is devoted to developing a group-theoretical approach towards quantum gravity in (Anti)-de Sitter spacetime. We start with a comprehensive review of the representation theory of de Sitter (dS) isometry group, focusing on the construction of unitary irreducible representations and the computation of characters. The three chapters that follow present the results of novel research conducted as a graduate student. Chapter 4 is based on [1]. We provide a general algebraic construction of higher spin quasinormal modes of de Sitter horizon and identify the boundary operator insertions that source the quasinormal modes from a local QFT point of view. Quasinormal modes of a single higher spin field in dSD furnish two nonunitary lowest-weight representations of the dS isometry group SO(1,D). We also show that quasinormal mode spectrums of higher spin fields are precisely encoded in the Harish-Chandra characters of the corresponding SO(1,D) unitary irreducible representations. Chapter 5 is based on work with D. Anninos, F. Denef and A. Law [2]. With potential application to constraining UV-complete microscopic models of de Sitter quantum gravity, we compute de Sitter entropy as the logarithm of the sphere path integral, for any possible low energy effective field theory containing a massless graviton, in arbitrary dimensions. The path integral is performed exactly at the one-loop level. The one-loop correction to the dS entropy is found to take a universal “bulk−edge” form, with the bulk part being an integral transformation of a Harish-Chandra character encoding quasinormal modes spectrum in a static patch of dS and the edge part being the same integral transformation of an edge character encoding degrees of freedom frozen on the dS horizon. In 3D de Sitter spacetime, the one-loop exact entropy is promoted to an all-loop exact result for truncated higher spin gravity, the latter admitting an SL(n,C) Chern-Simons formulation with n being the spin cut-off. Chapter 6 is based on [3]. Inspired by [2], we revisit the one-loop partition function of any higher spin field in (d + 1)-dimensional Anti-de Sitter spacetime and show that it can be universally expressed as an integral transform of an SO(2, d) bulk character and an SO(2, d − 2) edge character. We apply this character integral formula to various higherspin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters, leading to striking agreement with the predictions of higher spin holography. We also comment on the relation between our character integral formula and Rindler-AdS [4] thermal partition functions

Ladder Symmetries of Black Holes and de Sitter Space: Love Numbers and Quasinormal Modes

In this note, we present a synopsis of geometric symmetries for (spin 0) perturbations around (4D) black holes and de Sitter space. For black holes, we focus on static perturbations, for which the (exact) geometric symmetries have the group structure of SO(1,3). The generators consist of three spatial rotations, and three conformal Killing vectors obeying a special melodic condition. The static perturbation solutions form a unitary (principal series) representation of the group. The recently uncovered ladder symmetries follow from this representation structure; they explain the well-known vanishing of the black hole Love numbers. For dynamical perturbations around de Sitter space, the geometric symmetries are less surprising, following from the SO(1,4) isometry. As is well known, the quasinormal solutions form a non-unitary representation of the isometry group. We provide explicit expressions for the ladder operators associated with this representation. In both cases, the ladder structures help connect the boundary condition at the horizon with that at infinity (black hole) or origin (de Sitter space), and they manifest as contiguous relations of the hypergeometric solutions.Comment: 37 pages, no figures v2: Author ZS added, section 2.1 extende

Hilbert space of Quantum Field Theory in de Sitter spacetime

We study the decomposition of the Hilbert space of quantum field theory in $(d+1)$ dimensional de Sitter spacetime into Unitary Irreducible Representations (UIRs) of its isometry group \SO$(1,d+1)$. Firstly, we consider multi-particle states in free theories starting from the tensor product of single-particle UIRs. Secondly, we study conformal multiplets of a bulk Conformal Field Theory with symmetry group \SO$(2,d+1)$. Our main tools are the Harish-Chandra characters and the numerical diagonalization of the (truncated) quadratic Casimir of \SO$(1,d+1)$. We introduce a continuous density that encodes the spectrum of irreducible representations contained in a reducible one of \SO(1,d+1). Our results are complete for $d=1$ and $d=2$. In higher dimensions, we rederive and extend several results previously known in the literature. Our work provides the foundation for future nonperturbative bootstrap studies of Quantum Field Theory in de Sitter spacetime.Comment: 58 pages + appendices, 44 figures and 4 table

The K\"all\'en-Lehmann representation in de Sitter spacetime

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the K\"all\'en-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we recover the K\"all\'en-Lehmann decomposition in Minkowski space by taking the flat space limit. Using harmonic analysis and the Wick rotation to Euclidean Anti de Sitter, we derive an inversion formula to compute the spectral densities. Using the inversion formula, we relate the analytic structure of the spectral densities to the late-time boundary operator content. We apply our technical tools to study two-point functions of composite operators in free and weakly coupled theories. In the weakly coupled case, we show how the K\"all\'en-Lehmann decomposition is useful to find the anomalous dimensions of the late-time boundary operators. We also derive the K\"all\'en-Lehmann representation of two-point functions of spinning primary operators of a Conformal Field Theory on de Sitter.Comment: 62 pages + appendices, 10 figure

Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions

Motivated by the prospect of constraining microscopic models, we calculate the exact one-loop corrected de Sitter entropy (the logarithm of the sphere partition function) for every effective field theory of quantum gravity, with particles in arbitrary spin representations. In doing so, we universally relate the sphere partition function to the quotient of a quasi-canonical bulk and a Euclidean edge partition function, given by integrals of characters encoding the bulk and edge spectrum of the observable universe. Expanding the bulk character splits the bulk (entanglement) entropy into quasinormal mode (quasiqubit) contributions. For 3D higher-spin gravity formulated as an sl($n$) Chern-Simons theory, we obtain all-loop exact results. Further to this, we show that the theory has an exponentially large landscape of de Sitter vacua with quantum entropy given by the absolute value squared of a topological string partition function. For generic higher-spin gravity, the formalism succinctly relates dS, AdS$^\pm$ and conformal results. Holography is exhibited in quasi-exact bulk-edge cancelation.Comment: 9 + 47 + N page

Hypoglycemic agents and incidence of pancreatic cancer in diabetic patients: a meta-analysis

Background and aims: Hypoglycemic agents are the primary therapeutic approach for the treatment of diabetes and have been postulated to impact pancreatic cancer (PC) incidence in diabetic patients. We conducted a meta-analysis to further evaluate and establish the associations between four common types of hypoglycemic agents [metformin, sulfonylureas, thiazolidinediones (TZDs), and insulin] and PC incidence in individuals with diabetes mellitus (DM).Methods: A comprehensive literature search of PubMed, Web of Science, Embase, and the Cochrane Library identified studies that analyzed the relationship between hypoglycemic agents and PC published between January 2012 and September 2022. Randomized control trials (RCTs), cohorts, and case–control studies were included if there was clear and evaluated defined exposure to the involved hypoglycemic agents and reported PC outcomes in patients with DM. Furthermore, reported relative risks or odds ratios (ORs) or other provided data were required for the calculation of odds ratios. Summary odds ratio estimates with a 95% confidence interval (CI) were estimated using the random-effects model. Additionally, subgroup analysis was performed to figure out the source of heterogeneity. Sensitivity analysis and publication bias detection were also performed.Results: A total of 11 studies were identified that evaluated one or more of the hypoglycemic agents, including three case–control studies and eight cohort studies. Among these, nine focused on metformin, six on sulfonylureas, seven on TZDs, and seven on insulin. Meta-analysis of the 11 observational studies reported no significant association between metformin (OR = 1.04, 95% CI 0.73–1.46) or TZDs (OR = 1.13, 95% CI 0.73–1.75) and PC incidence, while the risk of PC increased by 79% and 185% with sulfonylureas (OR = 1.79, 95% CI 1.29–2.49) and insulin (OR = 2.85, 95% CI 1.75–4.64), respectively. Considerable heterogeneity was observed among the studies and could not be fully accounted for by study design, region, or adjustment for other hypoglycemic agents.Conclusion: Sulfonylureas and insulin may increase the incidence of pancreatic cancer in diabetic patients, with varying effects observed among different ethnicities (Asian and Western). Due to significant heterogeneity across studies, further interpretation of the relationship between hypoglycemic agents and pancreatic cancer incidence in diabetic patients requires well-adjusted data and better-organized clinical trials

Early detection of the risk of developing psychiatric disorders: a study of 461 Chinese university students under chronic stress

Chronic stress, a characteristic of modern time, has a significant impact on general health. In the context of psychiatric disorders, insufficient coping behavior under chronic stress has been linked to higher rates of (1) depressive symptoms among subjects of the general population, (2) relapse among patients under treatment for clinical depression, and (3) negative symptoms among subjects with an elevated vulnerability to psychosis. In this normative study we assessed basic coping behavior among 461 Chinese freshman university students along with their consumption behavior and general health in terms of regular exercises, physical health, psychosomatic disturbances, and mental health. The assessments relied on two instruments that have already demonstrated their capability of (1) reliably detecting insufficient coping behavior under chronic stress and (2) reliably quantifying the interrelation between coping behavior and mental health in the Western world. Thus, we aimed to complement existing data and to develop a generally available, socioculturally independent tool that can be used for the early detection of subjects with an elevated risk of mental health problems. Structural analyses yielded essentially the same scales "activity" and "defeatism" as previous studies on 2,500 students from Switzerland, Italy, Spain, the USA, and Argentina. These scales explained 74.3% of the observed variance in coping behavior among the 461 Chinese students. We found highly significant correlations (p < 0.0001) between the "defeatism" scale on the one hand, and the scales "regular use of medicine," "psychosomatic disturbances," and "impaired mental health" on the other. Particularly intriguing was the finding that a neural net classifier could be constructed to identify students with the highest contributions to the interrelation between "coping behavior" and "mental health," yielding a correlation coefficient as high as r = 0.597 for the respective subgroup. Based on the normative data, an online tool for risk assessments was developed with immediate feedback to users. This study provided another piece of evidence regarding the close link between basic coping behavior and mental health, across cultures and ethnicities. In consequence, our approach to quantifying basic coping behavior, along with other risk factors, can be expected to clear the way for an "early" detection of students with an elevated risk of stress-related mental health problems, nota bene prior to the development of clinically relevant symptoms. The socioeconomic impact of the potential prevention of depressive -disorders, and psychiatric disorders in general, may be enormous