Nilpotent invariants in N=4 SYM

It is shown that there are no nilpotent invariants in N=4 analytic superspace for $n\leq4$ points. It is argued that there is (at least) one such invariant for n=5 points which is not invariant under U(1)_Y. The consequences of these results are that the n=2 and 3 point correlation functions of the N=4 gauge-invariant operators which correspond to KK multiplets in AdS supergravity are given exactly by their tree level expressions, the 4 point correlation functions of such operators are invariant under U(1)_Y and correlation functions with $n\geq 4$ points have non-trivial dependence on the Yang-Mills coupling constant.Comment: 9 page

Massless Higher Spins and Holography

We treat free large N superconformal field theories as holographic duals of higher spin (HS) gauge theories expanded around AdS spacetime with radius R. The HS gauge theories contain massless and light massive AdS fields. The HS current correlators are written in a crossing symmetric form including only exchange of other HS currents. This and other arguments point to the existence of a consistent truncation to massless HS fields. A survey of massless HS theories with 32 supersymmetries in D=4,5,7 (where the 7D results are new) is given and the corresponding composite operators are discussed. In the case of AdS_4, the cubic couplings of a minimal bosonic massless HS gauge theory are described. We examine high energy/small tension limits giving rise to massless HS fields in the Type IIB string on AdS_5 x S^5 and M theory on AdS_{4/7} x S^{7/4}. We discuss breaking of HS symmetries to the symmetries of ordinary supergravity, and a particularly natural Higgs mechanism in AdS_5 x S^5 and AdS_4 x S^7 where the HS symmetry is broken by finite g_{YM}. In AdS_5 x S^5 it is shown that the supermultiplets of the leading Regge trajectory cross over into the massless HS spectrum. We propose that g_{YM}=0 corresponds to a critical string tension of order 1/R^2 and a finite string coupling of order 1/N. In AdS_7 x S^4 we give a rotating membrane solution coupling to the massless HS currents, and describe these as limits of Wilson surfaces in the A_{N-1}(2,0) SCFT, expandable in terms of operators with anomalous dimensions that are asymptotically small for large spin. The minimal energy configurations have semi-classical energy E=s for all s and the geometry of infinitely stretched strings with energy and spin density concentrated at the endpoints.Comment: 77 pages, latex, minor corrections to eqs 4.26-30, a refined discussion of long strings in Sec

Holographic Normal Ordering and Multi-particle States in the AdS/CFT Correspondence

The general correlator of composite operators of N=4 supersymmetric gauge field theory is divergent. We introduce a means for renormalizing these correlators by adding a boundary theory on the AdS space correcting for the divergences. Such renormalizations are not equivalent to the standard normal ordering of current algebras in two dimensions. The correlators contain contact terms that contribute to the OPE; we relate them diagrammatically to correlation functions of compound composite operators dual to multi-particle states.Comment: 18 pages, one equation corr., further comments and refs. adde

The contribution of testing in the fight against COVID-19: Evidence from Italy

Background: In response to the epidemic of coronavirus disease 2019 (COVID-19), a few countries have rolled out widespread testing of the population, while in other countries only people requiring hospital admission are being screened. After an extensive testing strategy during the initial few weeks in the early phase of the epidemic, the Italian Ministry of Health made its testing policy more stringent. In this study we assess the contribution of the testing policy containing the spread of the COVID-19 epidemic in Northern Italy. Methods: The analysis is focused on the evolution of the epidemic and related health intervention in four regions where ∼80% of the national death toll due to COVID-19 has occurred. The assumed under-estimation of asymptomatic cases has led us to make use of the number of deaths due to the epidemic to analyze the effectiveness of testing. The analysis is conducted through an autoregressive time-series approach where we use official data from the Ministry of Health. Results: The results of the analysis confirm a negative relationship between the number of tests carried out and the progression of the epidemic. In particular, results reveal that the tests are particularly effective in breaking the chain of transmission when they are implemented at the early stages of the spread of the virus. Conclusions: A large-scale testing policy is recommended as a critical contribution to effectively contain the epidemic. In addition, it is highly recommended to set up all necessary measures to enable the quick scale-up of testing capacity whenever required

Conjugated measures of computational complexity

It is shown here that using the Kleene’s normal form for partial recursive functions (p.r. functions) it is possible to develop a different normal form which will give a relation between these p.r. functions and certain related step-counting ones. Also this new form suggests an interesting serial expansion in terms of minimal functions of these p.r. functions. The notion of conjugated systems of computational complexity is eventually introduced.</jats:p