Calogero-Sutherland Approach to Defect Blocks

Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave functions of an integrable multi-particle Calogero-Sutherland problem. This generalizes a recent observation in 1602.01858 and makes extensive mathematical results from the modern theory of multi-variable hypergeometric functions available for studies of conformal defects. Applications range from several new relations with scalar four-point blocks to a Euclidean inversion formula for defect correlators.Comment: v2: changes for clarit

Illusory perceptions of space and time preserve cross-saccadic perceptual continuity

When voluntary saccadic eye movements are made to a silently ticking clock, observers sometimes think that the second hand takes longer than normal to move to its next position. For a short period, the clock appears to have stopped (chronostasis). Here we show that the illusion occurs because the brain extends the percept of the saccadic target backwards in time to just before the onset of the saccade. This occurs every time we move the eyes but it is only perceived when an external time reference alerts us to the phenomenon. The illusion does not seem to depend on the shift of spatial attention that accompanies the saccade. However, if the target is moved unpredictably during the saccade, breaking perception of the target's spatial continuity, then the illusion disappears. We suggest that temporal extension of the target's percept is one of the mechanisms that 'fill in' the perceptual 'gap' during saccadic suppression. The effect is critically linked to perceptual mechanisms that identify a target's spatial stability

Bounds on 4D Conformal and Superconformal Field Theories

We derive general bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. In any CFT containing a scalar primary phi of dimension d we show that crossing symmetry of implies a completely general lower bound on the central charge c >= f_c(d). Similarly, in CFTs containing a complex scalar charged under global symmetries, we bound a combination of symmetry current two-point function coefficients tau^{IJ} and flavor charges. We extend these bounds to N=1 superconformal theories by deriving the superconformal block expansions for four-point functions of a chiral superfield Phi and its conjugate. In this case we derive bounds on the OPE coefficients of scalar operators appearing in the Phi x Phi* OPE, and show that there is an upper bound on the dimension of Phi* Phi when dim(Phi) is close to 1. We also present even more stringent bounds on c and tau^{IJ}. In supersymmetric gauge theories believed to flow to superconformal fixed points one can use anomaly matching to explicitly check whether these bounds are satisfied.Comment: 47 pages, 9 figures; V2: small corrections and clarification

Superconformal symmetry and maximal supergravity in various dimensions

In this paper we explore the relation between conformal superalgebras with 64 supercharges and maximal supergravity theories in three, four and six dimensions using twistorial oscillator techniques. The massless fields of N=8 supergravity in four dimensions were shown to fit into a CPT-self-conjugate doubleton supermultiplet of the conformal superalgebra SU(2,2|8) a long time ago. We show that the fields of maximal supergravity in three dimensions can similarly be fitted into the super singleton multiplet of the conformal superalgebra OSp(16|4,R), which is related to the doubleton supermultiplet of SU(2,2|8) by dimensional reduction. Moreover, we construct the ultra-short supermultiplet of the six-dimensional conformal superalgebra OSp(8*|8) and show that its component fields can be organized in an on-shell superfield. The ultra-short OSp(8*|8) multiplet reduces to the doubleton supermultiplet of SU(2,2|8) upon dimensional reduction. We discuss the possibility of a chiral maximal (4,0) six-dimensional supergravity theory with USp(8) R-symmetry that reduces to maximal supergravity in four dimensions and is different from six-dimensional (2,2) maximal supergravity, whose fields cannot be fitted into a unitary supermultiplet of a simple conformal superalgebra. Such an interacting theory would be the gravitational analog of the (2,0) theory.Comment: 54 pages, PDFLaTeX, Section 5 and several references added. Version accepted for publication in JHE

Simplifying instanton corrections to N=4 SYM correlators

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Algebraic conformal quantum field theory in perspective

Conformal quantum field theory is reviewed in the perspective of Axiomatic, notably Algebraic QFT. This theory is particularly developped in two spacetime dimensions, where many rigorous constructions are possible, as well as some complete classifications. The structural insights, analytical methods and constructive tools are expected to be useful also for four-dimensional QFT.Comment: Review paper, 40 pages. v2: minor changes and references added, so as to match published versio

Deconstructing Conformal Blocks in 4D CFT

We show how conformal partial waves (or conformal blocks) of spinor/tensor correlators can be related to each other by means of differential operators in four dimensional conformal field theories. We explicitly construct such differential operators for all possible conformal partial waves associated to four-point functions of arbitrary traceless symmetric operators. Our method allows any conformal partial wave to be extracted from a few \u201cseed\u201d correlators, simplifying dramatically the computation needed to bootstrap tensor correlators. \ua9 2015, The Author(s)

The Effects Of N, P And Crude Oil On The Decomposition Of Spartina Alterniflora Belowground Biomass

We conducted a laboratory experiment to examine how the decomposition of particulate belowground organic matter from a salt marsh is enhanced, or not, by different mixtures of crude oil, nitrogen (N), or phosphorus (P) acting individually or synergistically. The experiment was conducted in 3.8 L sampling chambers producing varying quantities of gas whose volume was used as a surrogate measure of organic decomposition under anaerobic conditions. Gas production after 28 days, from highest to lowest, was +NP = +N \u3e\u3e\u3e +P, or +oil. The gas production under either +P or +oil conditions was indistinguishable from gas production in the control chamber. Nitrogen, not phosphorus, or +NP, was the dominant factor controlling organic decomposition rates in these experiments. The implication for organic salt marsh soils is that shoreline erosion is enhanced by salt marsh oiling, presumably by its toxicity, but not by its effect on the decomposition rates of plant biomass belowground. Nutrient additions, on the other hand, may compromise the soil strength, creating a stronger disparity in soil strength between upper and lower soil layers leading to marsh loss. Nutrient amendments intended to decrease oil concentration in the marsh may not have the desired effect, and are likely to decrease soil strength, thereby enhancing marsh-to-water conversions in organic salt marsh soils

Seed conformal blocks in 4D CFT

We compute in closed analytical form the minimal set of \u201cseed\u201d conformal blocks associated to the exchange of generic mixed symmetry spinor/tensor operators in an arbitrary representation (\u2113, \u2113) of the Lorentz group in four dimensional conformal field theories. These blocks arise from 4-point functions involving two scalars, one (0, |\u2113 12 \u2113|) and one (|\u2113 12 \u2113|, 0) spinors or tensors. We directly solve the set of Casimir equations, that can elegantly be written in a compact form for any (\u2113, \u2113), by using an educated ansatz and reducing the problem to an algebraic linear system. Various details on the form of the ansatz have been deduced by using the so called shadow formalism. The complexity of the conformal blocks depends on the value of p = |\u2113 12 \u2113| and grows with p, in analogy to what happens to scalar conformal blocks in d even space-time dimensions as d increases. These results open the way to bootstrap 4-point functions involving arbitrary spinor/tensor operators in four dimensional conformal field theories