Lessons from crossing symmetry at large N

20 pages, v2: Assumptions stated more clearly, version published in JHEPWe consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.Peer reviewe

Large spin systematics in CFT

20 pages; v2: version published in JHEPUsing conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity, unitarity, crossing-symmetry and the structure of the conformal partial wave expansion. We obtain results for both, perturbative CFT to all order in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new "reciprocity" principle for structure constants. We argue that these results extend also to non-conformal theories.Peer reviewe

Effective Conformal Theory and the Flat-Space Limit of AdS

We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, O, we consider the anomalous dimensions, gamma(n,l), of the double-trace operators of the form O (del^2)^n (del)^l O. Purely from the CFT we find that perturbative unitarity places a bound on these dimensions of |gamma(n,l)|<4. Non-renormalizable AdS interactions lead to violations of the bound at large values of n. We also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. We show that the presence of the heavy field "unitarizes" the growth in the anomalous dimensions, and leads to a resonance-like behavior in gamma(n,l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, we demonstrate that bulk flat-space S-matrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum of anomalous dimensions in d-dimensional CFTs and flat-space S-matrix elements in d+1 dimensions. We comment on the emergence of flat-space locality from the CFT perspective.Comment: 46 pages, 2 figures. v2: JHEP published versio

Simplifying instanton corrections to N=4 SYM correlators

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How consistent are the transcriptome changes associated with cold acclimation in two species of the Drosophila virilis group?

This work was financially support by a Marie Curie Initial Training Network grant, “Understanding the evolutionary origin of biological diversity” (ITN-2008–213780 SPECIATION), grants from the Academy of Finland to A.H. (project 132619) and M.K. (projects 268214 and 272927), a grant from NERC, UK to M.G.R. (grant NE/J020818/1), and NERC, UK PhD studentship to D.J.P. (NE/I528634/1).For many organisms the ability to cold acclimate with the onset of seasonal cold has major implications for their fitness. In insects, where this ability is widespread, the physiological changes associated with increased cold tolerance have been well studied. Despite this, little work has been done to trace changes in gene expression during cold acclimation that lead to an increase in cold tolerance. We used an RNA-Seq approach to investigate this in two species of the Drosophila virilis group. We found that the majority of genes that are differentially expressed during cold acclimation differ between the two species. Despite this, the biological processes associated with the differentially expressed genes were broadly similar in the two species. These included: metabolism, cell membrane composition, and circadian rhythms, which are largely consistent with previous work on cold acclimation/cold tolerance. In addition, we also found evidence of the involvement of the rhodopsin pathway in cold acclimation, a pathway that has been recently linked to thermotaxis. Interestingly, we found no evidence of differential expression of stress genes implying that long-term cold acclimation and short-term stress response may have a different physiological basis.PostprintPeer reviewe

Large introns in relation to alternative splicing and gene evolution: a case study of Drosophila bruno-3

Background: Alternative splicing (AS) of maturing mRNA can generate structurally and functionally distinct transcripts from the same gene. Recent bioinformatic analyses of available genome databases inferred a positive correlation between intron length and AS. To study the interplay between intron length and AS empirically and in more detail, we analyzed the diversity of alternatively spliced transcripts (ASTs) in the Drosophila RNA-binding Bruno-3 (Bru-3) gene. This gene was known to encode thirteen exons separated by introns of diverse sizes, ranging from 71 to 41,973 nucleotides in D. melanogaster. Although Bru-3's structure is expected to be conducive to AS, only two ASTs of this gene were previously described. Results: Cloning of RT-PCR products of the entire ORF from four species representing three diverged Drosophila lineages provided an evolutionary perspective, high sensitivity, and long-range contiguity of splice choices currently unattainable by high-throughput methods. Consequently, we identified three new exons, a new exon fragment and thirty-three previously unknown ASTs of Bru-3. All exon-skipping events in the gene were mapped to the exons surrounded by introns of at least 800 nucleotides, whereas exons split by introns of less than 250 nucleotides were always spliced contiguously in mRNA. Cases of exon loss and creation during Bru-3 evolution in Drosophila were also localized within large introns. Notably, we identified a true de novo exon gain: exon 8 was created along the lineage of the obscura group from intronic sequence between cryptic splice sites conserved among all Drosophila species surveyed. Exon 8 was included in mature mRNA by the species representing all the major branches of the obscura group. To our knowledge, the origin of exon 8 is the first documented case of exonization of intronic sequence outside vertebrates. Conclusion: We found that large introns can promote AS via exon-skipping and exon turnover during evolution likely due to frequent errors in their removal from maturing mRNA. Large introns could be a reservoir of genetic diversity, because they have a greater number of mutable sites than short introns. Taken together, gene structure can constrain and/or promote gene evolution

Chemoattractant Receptor Homologous to the T Helper 2 Cell (CRTH2) Is Not Expressed in Human Amniocytes and Myocytes

BACKGROUND: 15-deoxy-Δ 12,14- Prostaglandin J2 (15dPGJ2) inhibits Nuclear factor kappa B (NF-κB) in human myocytes and amniocytes and delays inflammation induced preterm labour in the mouse. 15dPGJ2 is a ligand for the Chemoattractant Receptor Homologous to the T helper 2 cell (CRTH2), a G protein-coupled receptor, present on a subset of T helper 2 (Th2) cells, eosinophils and basophils. It is the second receptor for Prostaglandin D2, whose activation leads to chemotaxis and the production of Th2-type interleukins. The cellular distribution of CRTH2 in non-immune cells has not been extensively researched, and its identification at the protein level has been limited by the lack of specific antibodies. In this study we explored the possibility that CRTH2 plays a role in 15dPGJ2-mediated inhibition of NF-κB and would therefore represent a novel small molecule therapeutic target for the prevention of inflammation induced preterm labour. METHODS: The effect of a small molecule CRTH2 agonist on NF-κB activity in human cultured amniocytes and myocytes was assessed by detection of p65 and phospho-p65 by immunoblot. Endogenous CRTH2 expression in amniocytes, myocytes and peripheral blood mononuclear cells (PBMCs) was examined by PCR, western analysis and flow cytometry, with amniocytes and myocytes transfected with CRTH2 acting as a positive control in flow cytometry studies. RESULTS: The CRTH2 agonist had no effect on NF-κB activity in amniocytes and myocytes. Although CRTH2 mRNA was detected in amniocytes and myocytes, CRTH2 was not detectable at the protein level, as demonstrated by western analysis and flow cytometry. 15dPGJ2 inhibited phospho-65 in PBMC'S, however the CRTH2 antagonist was not able to attenuate this effect. In conclusion, CRTH2 is not expressed on human amniocytes or myocytes and plays no role in the mechanism of 15dPGJ2-mediated inhibition of NF-κB

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe

Bounds on OPE coefficients in 4D Conformal Field Theories

We numerically study the crossing symmetry constraints in 4D CFTs, using previously introduced algorithms based on semidefinite programming. We study bounds on OPE coefficients of tensor operators as a function of their scaling dimension and extend previous studies of bounds on OPE coefficients of conserved vector currents to the product groups SO(N) 7SO(M). We also analyze the bounds on the OPE coefficients of the conserved vector currents associated with the groups SO(N), SU(N) and SO(N) 7SO(M) under the assumption that in the singlet channel no scalar operator has dimension less than four, namely that the CFT has no relevant deformations. This is motivated by applications in the context of composite Higgs models, where the strongly coupled sector is assumed to be a spontaneously broken CFT with a global symmetry. \ua9 The Authors