Embedding of theories with SU(2|4) symmetry into the plane wave matrix model

We study theories with SU(2|4) symmetry, which include the plane wave matrix model, 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k. All these theories possess many vacua. From Lin-Maldacena's method which gives the gravity dual of each vacuum, it is predicted that the theory around each vacuum of 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k is embedded in the plane wave matrix model. We show this directly on the gauge theory side. We clearly reveal relationships among the spherical harmonics on S^3, the monopole harmonics and the harmonics on fuzzy spheres. We extend the compactification (the T-duality) in matrix models a la Taylor to that on spheres.Comment: 56 pages, 6 figures, v2:a footnote and references added, section 5.2 improved, typos corrected, v3:typos corrected, v4: some equations are corrected, eq.(G.2) is added, conclusion is unchange

Euler Top Dynamics of Nambu-Goto P-Branes

We propose a method to obtain new exact solutions of spinning p-branes in flat space-times for any p, which manifest themselves as higher dimensional Euler Tops and minimize their energy functional. We provide concrete examples for the case of spherical topology S^{2}, S^{3} and rotational symmetry \prod_{i}SO(q_{i}). In the case of toroidal topology T^{2}, T^{3} the rotational symmetry is \prod SU(q_{i}) and m target dimensions are compactified on the torus T^{m} . By double dimensional reduction the Light Cone Hamiltonians of T^{2}, T^{3} reduce to those of closed string S^{1} and T^{2} membranes respectively. The solutions are interpreted as non-perturbative spinning soliton states of type IIA-IIB superstrings.Comment: 33 pages, LATEX; more typos corrected; some equation numbering correction

Quantum effective potential for U(1) fields on S^2_L X S^2_L

We compute the one-loop effective potential for noncommutative U(1) gauge fields on S^2_L X S^2_L. We show the existence of a novel phase transition in the model from the 4-dimensional space S^2_L X S^2_L to a matrix phase where the spheres collapse under the effect of quantum fluctuations. It is also shown that the transition to the matrix phase occurs at infinite value of the gauge coupling constant when the mass of the two normal components of the gauge field on S^2_L X S^2_L is sent to infinity.Comment: 13 pages. one figur

On the shape of a D-brane bound state and its topology change

As is well known, coordinates of D-branes are described by NxN matrices. From generic non-commuting matrices, it is difficult to extract physics, for example, the shape of the distribution of positions of D-branes. To overcome this problem, we generalize and elaborate on a simple prescription, first introduced by Hotta, Nishimura and Tsuchiya, which determines the most appropriate gauge to make the separation between diagonal components (D-brane positions) and off-diagonal components. This prescription makes it possible to extract the distribution of D-branes directly from matrices. We verify the power of it by applying it to Monte-Carlo simulations for various lower dimensional Yang-Mills matrix models. In particular, we detect the topology change of the D-brane bound state for a phase transition of a matrix model; the existence of this phase transition is expected from the gauge/gravity duality, and the pattern of the topology change is strikingly similar to the counterpart in the gravity side, the black hole/black string transition. We also propose a criterion, based on the behavior of the off-diagonal components, which determines when our prescription gives a sensible definition of D-brane positions. We provide numerical evidence that our criterion is satisfied for the typical distance between D-branes. For a supersymmetric model, positions of D-branes can be defined even at a shorter distance scale. The behavior of off-diagonal elements found in this analysis gives some support for previous studies of D-brane bound states.Comment: 29 pages, 16 figure

Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.Comment: 34 pages, v2 contains minor corrections to the published versio

Probing the fuzzy sphere regularisation in simulations of the 3d \lambda \phi^4 model

We regularise the 3d \lambda \phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice. In contrast to the 2d version, the radius R plays an independent r\^{o}le. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and \lambda. Thus we identify the phases of disorder, uniform order and non-uniform order. We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere. Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c=1-model in string theory. This observation enables a conjecture about the thermodynamic limit.Comment: 31 pages, 15 figure

The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories

We analyse the fluctuations of the ground-state/funnel solutions proposed to describe M2-M5 systems in the level-k mass-deformed/pure Chern-Simons-matter ABJM theory of multiple membranes. We show that in the large N limit the fluctuations approach the space of functions on the 2-sphere rather than the naively expected 3-sphere. This is a novel realisation of the fuzzy 2-sphere in the context of Matrix Theories, which uses bifundamental instead of adjoint scalars. Starting from the multiple M2-brane action, a U(1) Yang-Mills theory on R^{2,1} x S^2 is recovered at large N, which is consistent with a single D4-brane interpretation in Type IIA string theory. This is as expected at large k, where the semiclassical analysis is valid. Several aspects of the fluctuation analysis, the ground-state/funnel solutions and the mass-deformed/pure ABJM equations can be understood in terms of a discrete noncommutative realisation of the Hopf fibration. We discuss the implications for the possibility of finding an M2-brane worldvolume derivation of the classical S^3 geometry of the M2-M5 system. Using a rewriting of the equations of the SO(4)-covariant fuzzy 3-sphere construction, we also directly compare this fuzzy 3-sphere against the ABJM ground-state/funnel solutions and show them to be different.Comment: 60 pages, Latex; v2: references added; v3: typos corrected and references adde

Seasonal plankton dynamics in Kongsfjorden during two years of contrasting environmental conditions

Seasonal plankton time-series data are presented from Kongsfjorden from two years with contrasting environmental conditions. Kongsfjorden (west coast of Spitsbergen – 79°N) integrates inputs from Atlantic and Arctic waters, and glacier run-off, and is thus a prime location to study impacts on ecosystem dynamics of key environmental drivers that are relevant across the Arctic. Despite extensive research in Kongsfjorden, seasonally-resolved data are scarce. From late April/early May to early September 2019 and 2020, we conducted pelagic sampling at a mid-fjord station at mostly weekly to bi-weekly resolution investigating the environmental drivers of phyto- and zooplankton community composition and phenology. During spring 2019, Atlantic water masses with temperatures > 1 °C were found throughout the upper 250 m of the water column, and little sea ice occurred in the fjord. Spring 2020, in turn, was characterized by the presence of local water masses with sub-zero temperatures and relatively extensive sea-ice cover. The most striking contrast between the two years was the difference in phytoplankton spring bloom composition. In 2019, the spring bloom was dominated by the colonial stage of the haptophyte Phaeocystis pouchetii and diatoms played a minor role, while the spring bloom in 2020 was dominated by diatoms of the genus Thalassiosira succeeded by P. pouchetii. Selective grazing by large copepods and water mass structure seem to have been the decisive factors explaining the marked difference in diatom spring bloom biomass between the years while similar spring abundances of P. pouchetii in both years indicated that this species was less impacted by those factors. Our data suggest that differences in spring bloom composition impacted trophic transfer and carbon export. Recruitment of the dominant copepods Calanus finmarchicus and C. glacialis, Cirripedia and euphausiid larvae as well as the export of carbon to the seabed was more efficient during the diatom-dominated compared to the P. pouchetii–dominated spring bloom. In summer, the plankton composition shifted towards a flagellate-dominated community characterized by mixo- and heterotrophic taxa adapted to a lower nutrient regime and strong top-down control by copepod grazers. However, residual silicic acid after the P. pouchetii–dominated spring bloom fueled a late summer diatom bloom in 2019. Our data provide a first glimpse into the environmental drivers of plankton phenology and underline that high-resolution monitoring over many annual cycles is required to resolve the ephemeral variations of plankton populations against the backdrop of climate change.publishedVersio

LIM kinase function and renal growth: potential role for LIM kinases in fetal programming of kidney development

Aims Maternal dietary restriction during pregnancy impairs nephron development and results in offspring with fewer nephrons. Cell turnover in the early developing kidney is altered by exposure to maternal dietary restriction and may be regulated by the LIM-kinase family of enzymes. We set out to establish whether disturbance of LIM-kinase activity might play a role in the impairment of nephron formation. Main methods E12.5 metanephric kidneys and HK2 cells were grown in culture with the pharmacological LIM-kinase inhibitor BMS5. Organs were injected with DiI, imaged and cell numbers measured over 48 h to assess growth. Cells undergoing mitosis were visualised by pH 3 labelling. Key findings Growth of cultured kidneys reduced to 83% of controls after exposure to BMS5 and final cell number to 25% of control levels after 48 h. Whilst control and BMS5 treated organs showed cells undergoing mitosis (100 ± 11 cells/field vs 113 ± 18 cells/field respectively) the proportion in anaphase was considerably diminished with BMS5 treatment (7.8 ± 0.8% vs 0.8 ± 0.6% respectively; P < 0.01). This was consistent with effects on HK2 cells highlighting a severe impact of BMS5 on formation of the mitotic spindle and centriole positioning. DiI labelled cells migrated in 100% of control cultures vs 0% BMS5 treated organs. The number of nephrogenic precursor cells appeared depleted in whole organs and formation of new nephrons was blocked by exposure to BMS5. Significance Pharmacological blockade of LIM-kinase function in the early developing kidney results in failure of renal development. This is likely due to prevention of dividing cells from completion of mitosis with their resultant loss