Beyond a=ca=c: Gravitational Couplings to Matter and the Stress Tensor OPE

We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs), both generic and holographic. We point out that in large $N$ CFTs with a large gap to single-trace higher spin operators, the stress tensor sector is not only universal, but isolated: that is, $\langle TT{\cal O}\rangle=0$, where ${\cal O}\neq T$ is a single-trace primary. We show that this follows from a suppression of $\langle TT{\cal O}\rangle$ by powers of the higher spin gap, $\Delta_{\rm gap}$, dual to the bulk mass scale of higher spin particles, and explain why $\langle TT{\cal O}\rangle$ is a more sensitive probe of $\Delta_{\rm gap}$ than $a-c$ in 4d CFTs. This result implies that, on the level of cubic couplings, the existence of a consistent truncation to Einstein gravity is a direct consequence of the absence of higher spins. By proving similar behavior for other couplings $\langle T{\cal O}_1{\cal O}_2\rangle$ where ${\cal O}_i$ have spin $s_i\leq 2$, we are led to propose that $1/\Delta_{\rm gap}$ is the CFT "dual" of an AdS derivative in a classical action. These results are derived by imposing unitarity on mixed systems of spinning four-point functions in the Regge limit. Using the same method, but without imposing a large gap, we derive new inequalities on these three-point couplings that are valid in any CFT. These are generalizations of the Hofman-Maldacena conformal collider bounds. By combining the collider bound on $TT$ couplings to spin-2 operators with analyticity properties of CFT data, we argue that all three tensor structures of $\langle TTT\rangle$ in the free-field basis are nonzero in interacting CFTs.Comment: 42+25 pages. v2: added refs, minor change

Unitarity Methods in AdS/CFT

We develop a systematic unitarity method for loop-level AdS scattering amplitudes, dual to non-planar CFT correlators, from both bulk and boundary perspectives. We identify cut operators acting on bulk amplitudes that put virtual lines on shell, and show how the conformal partial wave decomposition of the amplitudes may be efficiently computed by gluing lower-loop amplitudes. A central role is played by the double discontinuity of the amplitude, which has a direct relation to these cuts. We then exhibit a precise, intuitive map between the diagrammatic approach in the bulk using cutting and gluing, and the algebraic, holographic unitarity method of [1] that constructs the non-planar correlator from planar CFT data. Our analysis focuses mostly on four-point, one-loop diagrams — we compute cuts of the scalar bubble, triangle and box, as well as some one-particle reducible diagrams — in addition to the five-point tree and four-point double-ladder. Analogies with S-matrix unitarity methods are drawn throughout

dd-dimensional SYK, AdS Loops, and 6j6j Symbols

We study the $6j$ symbol for the conformal group, and its appearance in three seemingly unrelated contexts: the SYK model, conformal representation theory, and perturbative amplitudes in AdS. The contribution of the planar Feynman diagrams to the three-point function of the bilinear singlets in SYK is shown to be a $6j$ symbol. We generalize the computation of these and other Feynman diagrams to $d$ dimensions. The $6j$ symbol can be viewed as the crossing kernel for conformal partial waves, which may be computed using the Lorentzian inversion formula. We provide closed-form expressions for $6j$ symbols in $d=1,2,4$. In AdS, we show that the $6j$ symbol is the Lorentzian inversion of a crossing-symmetric tree-level exchange amplitude, thus efficiently packaging the double-trace OPE data. Finally, we consider one-loop diagrams in AdS with internal scalars and external spinning operators, and show that the triangle diagram is a $6j$ symbol, while one-loop $n$-gon diagrams are built out of $6j$ symbols.Comment: 62 pages; v2 fixed typos and references, added comments about anomalous dimensions; v3, fixed typos, published versio

The Conformal Bootstrap at Finite Temperature

We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a "thermal inversion formula" whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal one-point functions for all higher-spin currents in the critical $O(N)$ model at leading order in $1/N$. Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.Comment: 59 pages plus appendices, 14 figures. v2: added refs, minor correction

Quantitative assessment of cell fate decision between autophagy and apoptosis

Abstract Autophagy and apoptosis are cellular processes that regulate cell survival and death, the former by eliminating dysfunctional components in the cell, the latter by programmed cell death. Stress signals can induce either process, and it is unclear how cells ‘assess’ cellular damage and make a ‘life’ or ‘death’ decision upon activating autophagy or apoptosis. A computational model of coupled apoptosis and autophagy is built here to analyze the underlying signaling and regulatory network dynamics. The model explains the experimentally observed differential deployment of autophagy and apoptosis in response to various stress signals. Autophagic response dominates at low-to-moderate stress; whereas the response shifts from autophagy (graded activation) to apoptosis (switch-like activation) with increasing stress intensity. The model reveals that cytoplasmic Ca2+ acts as a rheostat that fine-tunes autophagic and apoptotic responses. A G-protein signaling-mediated feedback loop maintains cytoplasmic Ca2+ level, which in turn governs autophagic response through an AMP-activated protein kinase (AMPK)-mediated feedforward loop. Ca2+/calmodulin-dependent kinase kinase β (CaMKKβ) emerges as a determinant of the competing roles of cytoplasmic Ca2+ in autophagy regulation. The study demonstrates that the proposed model can be advantageously used for interrogating cell regulation events and developing pharmacological strategies for modulating cell decisions

Scientific Computing Meets Big Data Technology: An Astronomy Use Case

Scientific analyses commonly compose multiple single-process programs into a dataflow. An end-to-end dataflow of single-process programs is known as a many-task application. Typically, tools from the HPC software stack are used to parallelize these analyses. In this work, we investigate an alternate approach that uses Apache Spark -- a modern big data platform -- to parallelize many-task applications. We present Kira, a flexible and distributed astronomy image processing toolkit using Apache Spark. We then use the Kira toolkit to implement a Source Extractor application for astronomy images, called Kira SE. With Kira SE as the use case, we study the programming flexibility, dataflow richness, scheduling capacity and performance of Apache Spark running on the EC2 cloud. By exploiting data locality, Kira SE achieves a 2.5x speedup over an equivalent C program when analyzing a 1TB dataset using 512 cores on the Amazon EC2 cloud. Furthermore, we show that by leveraging software originally designed for big data infrastructure, Kira SE achieves competitive performance to the C implementation running on the NERSC Edison supercomputer. Our experience with Kira indicates that emerging Big Data platforms such as Apache Spark are a performant alternative for many-task scientific applications

Comparison of [11C]TZ1964B and [18F]MNI659 for PET imaging brain PDE10A in nonhuman primates

Phosphodiesterase 10A (PDE10A) inhibitors show therapeutic effects for diseases with striatal pathology. PET radiotracers have been developed to quantify in vivo PDE10A levels and target engagement for therapeutic interventions. The aim of this study was to compare two potent and selective PDE10A radiotracers, [(11)C]TZ1964B and [(18)F]MNI659 in the nonhuman primate (NHP) brain. Double scans in the same cynomolgus monkey on the same day were performed after injection of [(11)C]TZ1964B and [(18)F]MNI659. Specific uptake was determined in two ways: nondisplaceable binding potential (BP(ND)) was calculated using cerebellum as the reference region and the PDE‐10A enriched striatum as the target region of interest (ROI); the area under the time–activity curve (AUC) for the striatum to cerebellum ratio was also calculated. High‐performance liquid chromatography (HPLC) analysis of solvent‐extracted NHP plasma identified the percentage of intact tracer versus radiolabeled metabolites samples post injection of each radiotracer. Both radiotracers showed high specific accumulation in NHP striatum. [(11)C]TZ1964B has higher striatal retention and lower specific striatal uptake than [(18)F]MNI659. The BP(ND) estimates of [(11)C]TZ1964B were 3.72 by Logan Reference model (LoganREF) and 4.39 by simplified reference tissue model (SRTM); the BP(ND) estimates for [(18)F]MNI659 were 5.08 (LoganREF) and 5.33 (SRTM). AUC ratios were 5.87 for [(11)C]TZ1964B and 7.60 for [(18)F]MNI659. Based on BP(ND) values in NHP striatum, coefficients of variation were ~10% for [(11)C]TZ1964B and ~30% for [(18)F]MNI659. Moreover, the metabolism study showed the percentage of parent compounds were ~70% for [(11)C]TZ1964B and ~50% for [(18)F]MNI659 60 min post injection. These data indicate that either [(11)C]TZ1964B or [(18)F]MNI659 could serve as suitable PDE10A PET radiotracers with distinguishing features for particular clinical application