Correlation functions and representation bases in free N=4 Super Yang-Mills

We study exact correlation functions of N=4 SYM at zero coupling. It has been known that it is convenient to label local gauge invariant operators by irreducible representations of symmetric groups/Brauer algebras. We first review the construction of representation bases from the viewpoint of the enhanced symmetry structure of the free theory. We present a basis of multi-matrix models using elements of Brauer algebras, generalising our previous construction for two matrices. We will compute multi-point functions of the basis with the exact N-dependence. In particular we study three-point functions of a class of BPS operators, and we find that they are given by a branching rule of the Brauer algebra. The three-point functions take a factorised form if representations on the operators satisfy a relation.Comment: 28 pages, typos correcte

Antidepressants stimulate population growth in the harpacticoid copepod Nitocra spinipes

Like many pharmaceuticals, antidepressants are designed in such a way that they do not degrade easily. Due to their limited breakdown capabilities, they often enter sewage systems in their active form and may even end up in the environment. Significant concentrations of the commonly prescribed antidepressant citalopram have been measured in freshwater systems in the past. Moreover, recent experiments in our laboratory revealed effects on the life history of the harpacticoid copepod Nitocra spinipes caused by exposure to citalopram at concentrations of 100 ng/L and upward. It is, however, unclear how these effects on individuals propagate to the population level. In this study, freshly initialized populations of N. spinipes were exposed to citalopram hydrobromide at concentrations of 0 (control), 100, 1000 μg/L (18 populations per treatment). After 1, 3, 5, 6, 7, and 8 weeks, 3 replicate populations per treatment were permanently removed from the setup and preserved in 70% ethanol. All samples were first counted manually under a light microscope (excluding the larval stages which were too small) and subsequently photo-documented using a FlowCam. Manual counts showed no effects on the population abundance at 100 μg/L. At 1000 μg/L, population abundances were slightly reduced, at first, but strongly exceeded the control at weeks 7 and 8. This supposed stimulation effect may be attributed to an increased reproduction rate which had been observed earlier in individual females exposed to citalopram. At the time of abstract submission, the FlowCam pictures are still being processed. They are, however, expected to allow for a more thorough evaluation of the population dynamics, including high-resolution size-distributions of each sample, over time. The results of this study indicate no immediate threat of citalopram to N. spinipes at concentrations found in the environment (< 1 μg/L). However, they provide valuable insights into the form and timing of stressor-induced population-level effects on N. spinipes

From Gauss Graphs to Giants

We identify the operators in ${\cal N}=4$ super Yang-Mills theory that correspond to ${1\over 8}$-BPS giant gravitons in AdS$_5\times$S$^5$. Our evidence for the identification comes from (1) counting these operators and showing agreement with independent counts of the number of giant graviton states, and (2) by demonstrating a correspondence between correlation functions of the super Yang-Mills operators and overlaps of the giant graviton wave functions.Comment: 16 pages; v2: matches published versio

Nonplanar integrability at two loops

In this article we compute the action of the two loop dilatation operator on restricted Schur polynomials that belong to the su(2) sector, in the displaced corners approximation. In this non-planar large N limit, operators that diagonalize the one loop dilatation operator are not corrected at two loops. The resulting spectrum of anomalous dimensions is related to a set of decoupled harmonic oscillators, indicating integrability in this sector of the theory at two loops. The anomalous dimensions are a non-trivial function of the 't Hooft coupling, with a spectrum that is continuous and starting at zero at large N, but discrete at finite N.Comment: version to appear in JHE