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ContextX-linked hypophosphatemia (XLH) is a genetic disease, causing life-long hypophosphatemia due to overproduction of fibroblast growth factor 23 (FGF23). XLH is associated with Chiari malformations, cranial synostosis, and syringomyelia. FGF23 signals through FGFR1c and requires a coreceptor, α-Klotho, which is expressed in the renal distal convoluted tubules and the choroid plexus (ChP). In the ChP, α-Klotho participates in regulating cerebrospinal fluid (CSF) production by shuttling the sodium/potassium adenosine triphosphatase (Na+/K+-ATPase) to the luminal membrane. The sodium/potassium/chloride cotransporter 1 (NKCC1) also makes a substantial contribution to CSF production.ObjectiveSince CSF production has not been studied in XLH, we sought to determine if there are changes in the expression of these molecules in the ChP of Hyp mice, the murine model of XLH, as a first step toward testing the hypothesis that altered CSF production contributes to the cranial and spinal malformations seen this disease.MethodsSemi-quantitative real-time PCR was used to analyze the level of expression of transcripts for Fgfr1c, and thee key regulators of CSF production, Klotho, Atp1a1 and Slc12a2. In situ hybridization was used to provide anatomical localization for the encoded proteins.ResultsReal-time polymerase chain reaction (RT-PCR) demonstrated significant upregulation of Klotho transcripts in the fourth ventricle of Hyp mice compared to controls. Transcript levels for Fgfr1c were unchanged in Hyp mice. Atp1a1 transcripts encoding the alpha-1 subunit of Na+/K+-ATPase were significantly downregulated in the third and lateral ventricles (LV). Expression levels of the Slc12a2 transcript (which encodes NKCC1) were unchanged in Hyp mice compared to controls. In situ hybridization (ISH) confirmed the presence of all 4 transcripts in the LV ChP both of WT and Hyp mice.ConclusionThis is the first study to document a significant change in the level of expression of the molecular machinery required for CSF production in Hyp mice. Whether similar changes occur in patients with XLH, potentially contributing to the cranial and spinal cord abnormalities frequently seen in XLH, remains to be determined.

Anterior abdominal wall hernias are a common and well described surgical pathology occurring in an estimated 5–10% of the population. Here, we describe a patient found to have acute incarceration of omentum through a patent processus vaginalis secondary to a high energy deceleration injury following airborne operations. Many studies and meta-analysis have been performed to examine the association between occupational risk factors, patient factors, and precipitating events leading to acute hernia and found insufficient evidence to support a causal link between single strenuous events and acute hernia formation. This case highlights and documents the occurrence of an isolated acute inguinal hernia with omental incarceration in the setting of patent processus vaginalis secondary to a single deceleration injury, contradicting the widely held notions described above.

Confining gauge theories contain glueballs and mesons with arbitrary spin, and these particles become metastable at large $N$. However, metastable higher spin particles, when coupled to gravity, are in conflict with causality. This tension can be avoided only if the gravitational interaction is accompanied by interactions involving other higher spin states well below the Planck scale $M_{\rm pl}$. These higher spin states can come from either the QCD sector or the gravity sector, but both these resolutions have some surprising implications. For example, QCD states can resolve the problem since there is a non-trivial mixing between the QCD sector and the gravity sector, requiring all particles to interact with glueballs at tree-level. If gravity sector states restore causality, any weakly coupled UV completion of the gravity-sector must have many stringy features, with an upper bound on the string scale. Under the assumption that gravity is weakly coupled, both scenarios imply that the theory has a stringy description above $N\gtrsim \frac{M_{\rm pl}}{\Lambda_{\rm QCD}}$, where $\Lambda_{\rm QCD}$ is the confinement scale., Comment: 7 pages; Some comments are added

Manufacturing processes have become increasingly sophisticated leading to greater usage of robotics. Sustaining successful manufacturing robotic operations requires a strategic maintenance program. Without careful planning, maintenance can be very costly. To reduce maintenance costs, manufacturers are exploring how they can assess the health of their robot workcell operations to enhance their maintenance strategies. Effective health assessment relies upon capturing appropriate data and generating intelligence from the workcell. Multiple data streams relevant to a robot workcell may be available including robot controller data, a supervisory programmable logic controller data, maintenance logs, process and part quality data, and equipment and process fault and failure data. These data streams can be extremely informative, yet the massive volume and complexity of this data can be overwhelming, confusing, and sometimes paralyzing. Researchers at the National Institute of Standards and Technology have developed a test method and companion sensor to assess the health of robot workcells which will yield an additional and unique data stream. The intent is that this data stream can either serve as a surrogate for larger data volumes to reduce the data collection and analysis burden on the manufacturer, or add more intelligence to assessing robot workcell health. This article presents the most recent effort focused on verifying the companion sensor. Results of the verification test process are discussed along with preliminary results of the sensor’s performance during verification testing. Lessons learned indicate that the test process can be an effective means of quantifying the sensor’s measurement capability particularly after test process anomalies are addressed in future efforts.

Manufacturing processes have become increasingly sophisticated leading to greater usage of robotics. Sustaining successful manufacturing robotic operations requires a strategic maintenance program. Maintenance can be very costly, especially when some manufacturers unnecessarily spend resources (i.e., time, money) to maintain their equipment. To reduce maintenance costs, manufacturers are exploring how they can assess the health of their robot workcell operations to enhance their maintenance strategies. Effective health assessment relies upon capturing appropriate data and generating intelligence from the workcell. Multiple data streams relevant to a robot workcell may be available including robot controller data, a supervisory programmable logic controller data, maintenance logs, process/part quality data, and equipment/process fault and/or failure data. This data can be extremely informative, yet the extreme volume and complexity of this data can be both overwhelming, confusing, and paralyzing. Researchers at the National Institute of Standards and Technology have developed a test method and companion sensor to assess the health of robot workcells, which will yield an additional and unique data stream. The intent is that this data stream can either serve as a surrogate for larger data volumes to reduce the data collection and analysis burden on the manufacturer or add more intelligence to assessing robot workcell health. This article will present the immediate effort focused on verifying the companion sensor. Results of the verification test process are discussed along with preliminary results of the sensor’s performance during verification testing.

We present a prescription for an effective lightcone (LC) Hamiltonian that includes the effects of zero modes, focusing on the case of Conformal Field Theories (CFTs) deformed by relevant operators. We show how the prescription resolves a number of issues with LC quantization, including i) the apparent non-renormalization of the vacuum, ii) discrepancies in critical values of bare parameters in equal-time vs LC quantization, and iii) an inconsistency at large N in CFTs with simple AdS duals. We describe how LC quantization can drastically simplify Hamiltonian truncation methods applied to some large N CFTs, and discuss how the prescription identifies theories where these simplifications occur. We demonstrate and check our prescription in a number of examples., 63 pages, 17 figures. V2: minor modifications

We chart the breakdown of semiclassical gravity by analyzing the Virasoro conformal blocks to high numerical precision, focusing on the heavy-light limit corresponding to a light probe propagating in a BTZ black hole background. In the Lorentzian regime, we find empirically that the initial exponential time-dependence of the blocks transitions to a universal $t^{-\frac{3}{2}}$ power-law decay. For the vacuum block the transition occurs at $t \approx \frac{\pi c}{6 h_L}$, confirming analytic predictions. In the Euclidean regime, due to Stokes phenomena the naive semiclassical approximation fails completely in a finite region enclosing the `forbidden singularities'. We emphasize that limitations on the reconstruction of a local bulk should ultimately stem from distinctions between semiclassical and exact correlators., Comment: 45 pages, 23 figures

The gauge redundancy of quantum gravity makes the definition of local operators ambiguous, as they depend on the choice of gauge or on a `gravitational dressing' analogous to a choice of Wilson line attachments. Recent work identified exact AdS$_3$ proto-fields by fixing to a Fefferman-Graham gauge. Here we extend that work and define proto-fields with general gravitational dressing. We first study bulk fields charged under a $U(1)$ Chern-Simons gauge theory as an illustrative warm-up, and then generalize the results to gravity. As an application, we compute a gravitational loop correction to the bulk-boundary correlator in the background of a black hole microstate, and then verify this calculation using a newly adapted recursion relation. Branch points at the Euclidean horizon are present in the $1/c$ corrections to semiclassical correlators., Comment: 42+20 pages, 5 figures

Causality constrains the gravitational interactions of massive higher spin particles in both AdS and flat spacetime. We explore the extent to which these constraints apply to composite particles, explaining why they do not rule out macroscopic objects or hydrogen atoms. However, we find that they do apply to glueballs and mesons in confining large $N$ gauge theories. Assuming such theories contain massive bound states of general spin, we find parametric bounds in $(3+1)$ spacetime dimensions of the form $N\lesssim \frac{M_{Pl}}{\Lambda_{\text{QCD}}}$ relating $N$, the QCD scale, and the Planck scale. We also argue that a stronger bound replacing $\Lambda_{\text{QCD}}$ with the UV cut-off scale may be derived from eikonal scattering in flat spacetime., Comment: 44 pages + appendices, multiple figures

The receptor for Colony Stimulating Factor 1 (CSF1), c-fms, is highly expressed on mature osteoclasts suggesting a role for this cytokine in regulating the function of these cells. Consistent with this idea, in vitro studies have documented a variety of effects of CSF1 in mature osteoclasts. To better define the role of CSF1 in these cells, we conditionally deleted c-fms in osteoclasts (c-fms-OC-/-) by crossing c-fmsflox/flox mice with mice expressing Cre under the control of the cathepsin K promoter. The c-fms-OC-/- mice were of normal weight and had normal tooth eruption. However, when quantified by DXA, bone mass was significantly higher in the spine and femur of female knock out mice and in the femurs of male knock out mice. MicroCT analyses of femurs showed that female c-fms-OC-/- mice had significantly increased trabecular bone mass with a similar trend in males and both sexes demonstrated significantly increased trabecular number and reduced trabecular spacing. Histomorphometric analysis of the femoral trabecular bone compartment demonstrated a trend towards increased numbers of osteoclasts, +26% in Noc/BPm and +22% in OcS/BS in the k/o animals but this change was not significant. However, when the cellular volume of osteoclasts was quantified, the c-fms-OC-/- cells were found to be significantly smaller than controls. Mature osteoclasts show a marked spreading response when exposed to CSF1 in a non-gradient fashion. However, osteoclasts freshly isolated from c-fms-OC-/- mice had a near complete abrogation of this response. C-fms-OC-/- mice treated with (1–34)hPTH 80 ng/kg/d in single daily subcutaneous doses for 29 days showed an attenuated anabolic response in trabecular bone compared to wild-type animals. Taken together, these data indicate an important non-redundant role for c-fms in regulating mature osteoclast function in vivo.

X-linked Hypophosphatemia (XLH) is caused by loss of function mutations in the PHEX gene. Given the recent availability of a new therapy for XLH, a retrospective analysis of the most recent 261 Chinese patients with XLH evaluated at Peking Union Medical College Hospital was conducted. Clinical, biochemical, radiographic studies, as well as genetic analyses, including Sanger sequencing for point mutations and Multiplex Ligation-dependent Probe Amplification (MLPA) to detect large deletions/duplications were employed. Based on the structure of Neprilysin (NEP), a member of M13 family that includes PHEX, a three-dimensional (3D) model of PHEX was constructed, missense and nonsense mutations were positioned on the predicted structure to visualize relative positions of these two types of variants. Sex differences and genotype-phenotype correlations were also undertaken. Genetic analyses identified 166 PHEX mutations in 261 XLH patients. One hundred and eleven of the 166 mutations were unreported. Four mutational ‘hot-spots’ were identified in this cohort (P534L, G579R, R747X, c.1645+1 G>A). Missense mutations, but not nonsense mutations, clustered in the two putative lobes of the PHEX protein, suggesting these are functionally important regions of the molecule. Circulating levels of intact FGF23 were significantly elevated (median level 101.9 pg/mL; reference range 16.1–42.2 pg/mL). No significant sex differences, as well as no phenotypic differences were identified between patients with putative truncating and non-truncating PHEX mutations. However, patients with N-terminal PHEX mutations had an earlier age of onset of disease (P = 0.015) and higher iFGF23 levels (P = 0.045) as compared to those with C-terminal mutations. These data provide a comprehensive characterization of the largest cohort of patients with XLH reported to date from China, which will help in evaluating the applicability of emerging therapies for this disease in this ethnic group.

Entotherapy[Link] an image‐guided drug‐eluting microcylinder platform, has the potential to bypass the limitations of systemic chemotherapy use in the treatment of canine brain tumours. Gliomas, which are common in dogs and also represent the majority of fatal brain tumours in humans, can be amenable to chemotherapy with temozolomide. Biopolymer microcylinders conjugated with temozolomide and gadolinium were implanted into partially resected tumours of four client‐owned dogs with gliomas. All four dogs presented with generalized seizures and had mild to no neurologic deficits at the time of craniotomy. All dogs underwent craniotomy for implantation of the microcylinders into partially resected gliomas (glioblastoma multiforme {n = 1} or oligodendroglioma {n = 3}). All dogs recovered well from the craniotomy and implantation procedure. This novel procedure appears to be feasible and tolerated in tumour‐bearing dogs. A future controlled clinical study can now aim to evaluate the microcylinder implantation for long‐term efficacy.

First-quantized propagation in quantum gravitational AdS$_3$ backgrounds can be exactly reconstructed using CFT$_2$ data and Virasoro symmetry. We develop methods to compute the bulk-to-boundary propagator in a black hole microstate, $\langle \phi_L \mathcal{O}_L \mathcal{O}_H \mathcal{O}_H\rangle$, at finite central charge. As a first application, we show that the semiclassical theory on the Euclidean BTZ solution sharply disagrees with the exact description, as expected based on the resolution of forbidden thermal singularities, though this effect may appear exponentially small for physical observers., Comment: 34+27 pages, 7 figures; v2: typos corrected

We use conformal symmetry to define an AdS$_3$ proto-field $\phi$ as an exact linear combination of Virasoro descendants of a CFT$_2$ primary operator $\mathcal{O}$. We find that both symmetry considerations and a gravitational Wilson line formalism lead to the same results. The operator $\phi$ has many desirable properties; in particular it has correlators that agree with gravitational perturbation theory when expanded at large $c$, and that automatically take the correct form in all vacuum AdS$_3$ geometries, including BTZ black hole backgrounds. In the future it should be possible to use $\phi$ to probe bulk locality and black hole horizons at a non-perturbative level., Comment: 24+33 pages, 2 figures; V2: refs added, terminology updated

One can obtain exact information about Virasoro conformal blocks by analytically continuing the correlators of degenerate operators. We argued in recent work that this technique can be used to explicitly resolve information loss problems in AdS$_3$/CFT$_2$. In this paper we use the technique to perform calculations in the small $1/c \propto G_N$ expansion: (1) we prove the all-orders resummation of logarithmic factors $\propto \frac{1}{c} \log z$ in the Lorentzian regime, demonstrating that $1/c$ corrections directly shift Lyapunov exponents associated with chaos, as claimed in prior work, (2) we perform another all-orders resummation in the limit of large $c$ with fixed $cz$, interpolating between the early onset of chaos and late time behavior, (3) we explicitly compute the Virasoro vacuum block to order $1/c^2$ and $1/c^3$, corresponding to $2$ and $3$ loop calculations in AdS$_3$, and (4) we derive the heavy-light vacuum blocks in theories with $\mathcal{N}=1,2$ superconformal symmetry., 34+20 pages, 2 figures

We discuss information loss from black hole physics in AdS$_3$, focusing on two sharp signatures infecting CFT$_2$ correlators at large central charge $c$: 'forbidden singularities' arising from Euclidean-time periodicity due to the effective Hawking temperature, and late-time exponential decay in the Lorentzian region. We study an infinite class of examples where forbidden singularities can be resolved by non-perturbative effects at finite $c$, and we show that the resolution has certain universal features that also apply in the general case. Analytically continuing to the Lorentzian regime, we find that the non-perturbative effects that resolve forbidden singularities qualitatively change the behavior of correlators at times $t \sim S_{BH}$, the black hole entropy. This may resolve the exponential decay of correlators at late times in black hole backgrounds. By Borel resumming the $1/c$ expansion of exact examples, we explicitly identify 'information-restoring' effects from heavy states that should correspond to classical solutions in AdS$_3$. Our results suggest a line of inquiry towards a more precise formulation of the gravitational path integral in AdS$_3$., 41+18 pages, 13 figures; v2 typos & refs; v3 intro expanded

Aspects of black hole thermodynamics and information loss can be derived as a consequence of Virasoro symmetry. To bolster the connection between Virasoro conformal blocks and AdS$_3$ quantum gravity, we study sl$(2)$ Chern-Simons Wilson line networks and revisit the idea that they compute a variety of CFT$_2$ observables, including Virasoro OPE blocks, exactly. We verify this in the semiclassical large central charge limit and to low orders in a perturbative $1/c$ expansion. Wilson lines connecting the boundary to points in the bulk play a natural role in bulk reconstruction. Because quantum gravity in AdS$_3$ is rigidly fixed by Virasoro symmetry, we argue that sl$(2)$ Wilson lines provide building blocks for background independent bulk reconstruction. In particular, we show explicitly that they automatically compute the uniformizing coordinates appropriate to any background state., Comment: V3- Added some references V2- Significantly Expanded Appendix on Regulation; 32+21 pages

Black hole microstates and their approximate thermodynamic properties can be studied using heavy-light correlation functions in AdS/CFT. Universal features of these correlators can be extracted from the Virasoro conformal blocks in CFT2, which encapsulate quantum gravitational effects in AdS3. At infinite central charge c, the Virasoro vacuum block provides an avatar of the black hole information paradox in the form of periodic Euclidean-time singularities that must be resolved at finite c. We compute Virasoro blocks in the heavy-light, large c limit, extending our previous results by determining perturbative 1/c corrections. We obtain explicit closed-form expressions for both the `semi-classical' $h_L^2 / c^2$ and `quantum' $h_L / c^2$ corrections to the vacuum block, and we provide integral formulas for general Virasoro blocks. We comment on the interpretation of our results for thermodynamics, discussing how monodromies in Euclidean time can arise from AdS calculations using `geodesic Witten diagrams'. We expect that only non-perturbative corrections in 1/c can resolve the singularities associated with the information paradox., 24+7 pages, 5 figures; v2 fixed typo in eq 2.22, added refs; v3 fixed typos

The Sloan Digital Sky Survey-II (SDSS-II) has embarked on a multi-year project to identify and measure light curves for intermediate-redshift (0.05 < z < 0.35) Type Ia supernovae (SNe Ia) using repeated five-band (ugriz) imaging over an area of 300 sq. deg. The survey region is a stripe 2.5 degrees wide centered on the celestial equator in the Southern Galactic Cap that has been imaged numerous times in earlier years, enabling construction of a deep reference image for discovery of new objects. Supernova imaging observations are being acquired between 1 September and 30 November of 2005-7. During the first two seasons, each region was imaged on average every five nights. Spectroscopic follow-up observations to determine supernova type and redshift are carried out on a large number of telescopes. In its first two three-month seasons, the survey has discovered and measured light curves for 327 spectroscopically confirmed SNe Ia, 30 probable SNe Ia, 14 confirmed SNe Ib/c, 32 confirmed SNe II, plus a large number of photometrically identified SNe Ia, 94 of which have host-galaxy spectra taken so far. This paper provides an overview of the project and briefly describes the observations completed during the first two seasons of operation., Submitted to The Astronomical Journal (24 pages, 10 figures)

Classical field configurations such as the Coulomb potential and Schwarzschild solution are built from the t-channel exchange of many light degrees of freedom. We study the CFT analog of this phenomenon, which we term the `eikonalization' of conformal blocks. We show that when an operator $T$ appears in the OPE $\mathcal{O}(x) \mathcal{O}(0)$, then the large spin $\ell$ Fock space states $[TT \cdots T]_{\ell}$ also appear in this OPE with a computable coefficient. The sum over the exchange of these Fock space states in an $\langle \mathcal{O} \mathcal{O} \mathcal{O} \mathcal{O} \rangle$ correlator build the classical `$T$ field' in the dual AdS description. In some limits the sum of all Fock space exchanges can be represented as the exponential of a single $T$ exchange in the 4-pt correlator of $\mathcal{O}$. Our results should be useful for systematizing $1/\ell$ perturbation theory in general CFTs and simplifying the computation of large spin OPE coefficients. As examples we obtain the leading $\log \ell$ dependence of Fock space conformal block coefficients, and we directly compute the OPE coefficients of the simplest `triple-trace' operators., Comment: 32+17 pages, 6 figures; references added, discussion of eikonal limit clarified

We show that in 2d CFTs at large central charge, the coupling of the stress tensor to heavy operators can be re-absorbed by placing the CFT in a non-trivial background metric. This leads to a more precise computation of the Virasoro conformal blocks between heavy and light operators, which are shown to be equivalent to global conformal blocks evaluated in the new background. We also generalize to the case where the operators carry U(1) charges. The refined Virasoro blocks can be used as the seed for a new Virasoro block recursion relation expanded in the heavy-light limit. We comment on the implications of our results for the universality of black hole thermality in $AdS_3$, or equivalently, the eigenstate thermalization hypothesis for $CFT_2$ at large central charge., Comment: 27+7 pages, 3 figures; typos corrected, citations added

Definitive treatments for primary brain tumours are still sought. Slow-release local chemotherapy may provide a good effect and poly (lactide-co-glycolide) (PLGA) microcylinders could allow this. We evaluated the neurological and histopathological consequences, and MRI visibility, of PLGA microcylinders conjugated with temozolomide and gadolinium implanted in normal canine brains. Eight purpose-bred beagles had cerebral implantation of microcylinders combined with temozolomide and gadolinium. MRI was performed following implantation and 28d later prior to necropsy and brain histopathology. All adverse events were associated with implantation and resolved. Dogs with six microcylinders at 0 and 6.25% gadolinium had mild inflammation and all other dogs had greater brain inflammation, which increased with higher gadolinium concentrations and microcylinder number. Microcylinders with gadolinium were identifiable on MRI. Brain implantation of PLGA microcylinders conjugated with gadolinium and temozolomide is tolerated in healthy beagles. The lowest gadolinium percentage and microcylinder number should be used if this therapy is pursued.

We develop techniques for computing superconformal blocks in 4d superconformal field theories. First we study the super-Casimir differential equation, deriving simple new expressions for superconformal blocks for 4-point functions containing chiral operators in theories with N-extended supersymmetry. We also reproduce these results by extending the "shadow formalism" of Ferrara, Gatto, Grillo, and Parisi to supersymmetric theories, where superconformal blocks can be represented as superspace integrals of three-point functions multiplied by shadow three-point functions., 32 pages

The problem of continuous quantum phase transitions in metals involves critical bosons coupled to a Fermi surface. We solve the theory in the limit of a large number, N_B, of bosonic flavors, where the bosons transform in the adjoint representation, while the fermions are in the fundamental representation of a global SU(N_B) flavor symmetry group. The leading large N_B solution corresponds to a non-Fermi liquid coupled to Wilson-Fisher bosons. In a certain energy range, the fermion velocity vanishes - resulting in the destruction of the Fermi surface. Subleading 1/N_B corrections correspond to a qualitatively different form of Landau damping of the bosonic critical fluctuations. We discuss the model in d=3-epsilon but because of the additional control afforded by large N_B, our results are valid down to d=2. In the limit epsilon << 1, the large N_B solution is consistent with the RG analysis of Ref. 1., 16+5 pages, 5 figures

We study the dynamics of a quantum critical boson coupled to a Fermi surface in intermediate energy regimes where the Landau damping of the boson can be parametrically controlled, either via large Fermi velocity or by large N techniques. We focus on developing a systematic approach to studying the BCS instability, including careful treatment of the enhanced log^2 and log^3 singularities which appear already at 1-loop. We also treat possible instabilities to charge density wave (CDW) formation, and compare the scales Lambda_{BCS} and Lambda_{CDW} of the onset of the instabilities in different parametric regimes. We address the question of whether the dressing of the fermions into a non-Fermi liquid via interactions with the order parameter field can happen at energies > Lambda_{BCS}, Lambda_{CDW}., 34 pages, 4 figures, submitted to PRB

We derive conformal blocks in an inverse spacetime dimension expansion. In this large D limit, the blocks are naturally written in terms of a new combination of conformal cross-ratios. We comment on the implications for the conformal bootstrap at large D., Comment: 14 pages, 2 figures

We study the problem of disorder-free metals near a continuous quantum critical point. We depart from the standard paradigm of Hertz and Millis, and treat both fermions and bosons i.e. order parameter fields) on equal footing. We construct a Wilsonian effective field theory that integrates out only high energy boson and fermion modes. Below the upper critical dimension of the theory (d=3 spatial dimensions), we find new fixed points in which the bosons are described by the Wilson-Fisher fixed point and are coupled to a non-Fermi liquid metal. We describe subtleties with the renormalization group flow of four-Fermi interactions, which can be surmounted in a controlled large N limit. In this limit, we find that the theory has no superconducting instability., Comment: 14 pages, 5 figures; v2: refs added; v3: PRB published version

We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| << |v| < 1. We prove that every CFT with a scalar operator ��must contain infinite sequences of operators O_{��,l} with twist approaching ��-> 2��_��+ 2n for each integer n as l -> infinity. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the ��x ��OPE, and we discuss SCFTs and the 3d Ising Model as examples. Additionally, we show that the OPE coefficients of other large spin operators appearing in the OPE are bounded as l -> infinity. We interpret these results as a statement about superhorizon locality in AdS for general CFTs., 33 pages, no figures; V2 citations added

We show that suitably regulated multi-trace primary states in large N CFTs behave like 'in' and 'out' scattering states in the flat-space limit of AdS. Their transition matrix elements approach the exact scattering amplitudes for the bulk theory, providing a natural CFT definition of the flat space S-Matrix. We study corrections resulting from the AdS curvature and particle propagation far from the center of AdS, and show that AdS simply provides an IR regulator that disappears in the flat space limit.

We provide necessary and sufficient conditions for a Conformal Field Theory to have a description in terms of a perturbative Effective Field Theory in AdS. The first two conditions are well-known: the existence of a perturbative `1/N' expansion and an approximate Fock space of states generated by a finite number of low-dimension operators. We add a third condition, that the Mellin amplitudes of the CFT correlators must be well-approximated by functions that are bounded by a polynomial at infinity in Mellin space, or in other words, that the Mellin amplitudes have an effective theory-type expansion. We explain the relationship between our conditions and unitarity, and provide an analogy with scattering amplitudes that becomes exact in the flat space limit of AdS. The analysis also yields a simple connection between conformal blocks and AdS diagrams, providing a new calculational tool very much in the spirit of the S-Matrix program. We also begin to explore the potential pathologies associated with higher spin fields in AdS by generalizing Weinberg's soft theorems to AdS/CFT. The AdS analog of Weinberg's argument constrains the interactions of conserved currents in CFTs, but there are potential loopholes that are unavailable to theories of massless higher spin particles in flat spacetime., Comment: 31+7 pages, 5 figures

We provide dramatic evidence that `Mellin space' is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into `left' and `right' sub-correlators, in direct analogy with the factorization channels of scattering amplitudes. In the regime where these correlators can be computed by tree level Witten diagrams in AdS, we derive an explicit formula for the residues of Mellin amplitudes at the corresponding factorization poles, and we use the conformal Casimir to show that these amplitudes obey algebraic finite difference equations. By analyzing the recursive structure of our factorization formula we obtain simple diagrammatic rules for the construction of Mellin amplitudes corresponding to tree-level Witten diagrams in any bulk scalar theory. We prove the diagrammatic rules using our finite difference equations. Finally, we show that our factorization formula and our diagrammatic rules morph into the flat space S-Matrix of the bulk theory, reproducing the usual Feynman rules, when we take the flat space limit of AdS/CFT. Throughout we emphasize a deep analogy with the properties of flat space scattering amplitudes in momentum space, which suggests that the Mellin amplitude may provide a holographic definition of the flat space S-Matrix., Comment: 48+15 pages, 11 figures; (v2) section 2.1 corrected