The cusp anomalous dimension at three loops and beyond

We derive an analytic formula at three loops for the cusp anomalous dimension Gamma_cusp(phi) in N=4 super Yang-Mills. This is done by exploiting the relation of the latter to the Regge limit of massive amplitudes. We comment on the corresponding three loops quark anti-quark potential. Our result also determines a considerable part of the three-loop cusp anomalous dimension in QCD. Finally, we consider a limit in which only ladder diagrams contribute to physical observables. In that limit, a precise agreement with strong coupling is observed.Comment: 34 pages, 6 figures. v2: references added, typos correcte

Generation of vortices and observation of Quantum Turbulence in an oscillating Bose-Einstein Condensate

We report on the experimental observation of vortex formation and production of tangled vortex distribution in an atomic BEC of Rb-87 atoms submitted to an external oscillatory perturbation. The oscillatory perturbations start by exciting quadrupolar and scissors modes of the condensate. Then regular vortices are observed finally evolving to a vortex tangle configuration. The vortex tangle is a signature of the presence of a turbulent regime in the cloud. We also show that this turbulent cloud has suppression of the aspect ratio inversion typically observed in quantum degenerate bosonic gases during free expansion.Comment: to appear in JLTP - QFS 200

Self-similar expansion of the density profile in a turbulent Bose-Einstein condensate

In a recent study we demonstrated the emergence of turbulence in a trapped Bose-Einstein condensate of Rb-87 atoms. An intriguing observation in such a system is the behavior of the turbulent cloud during free expansion.The aspect ratio of the cloud size does not change in the way one would expect for an ordinary non-rotating (vortex-free) condensate. Here we show that the anomalous expansion can be understood, at least qualitatively, in terms of the presence of vorticity distributed throughout the cloud, effectively counteracting the usual reversal of the aspect ratio seen in free time-of-flight expansion of non-rotating condensates.Comment: 8 pages, 4 figure

The anomaly of the oxygen bond-bending mode at 320 cm−1^{-1} and the additional absorption peak in the c-axis infrared conductivity of underdoped YBa2_{2}Cu3_{3}O7−δ_{7-\delta} single crystals revisited by ellipsometricmeasurements

We have performed ellipsometric measurements of the far-infrared c-axis dielectric response of underdoped YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ single crystals. Here we report a detailed analysis of the temperature-dependent renormalization of the oxygen bending phonon mode at 320 cm$^{-1}$ and the formation of the additional absorption peak around 400-500 cm$^{-1}$. For a strongly underdoped YBa$_{2}$Cu$_{3}$O$_{6.5}$ crystal with T$_{c}$=52 K we find that, in agreement with previous reports based on conventional reflection measurements, the gradual onset of both features occurs well above T$_{c}$ at T*$\sim$150 K. Contrary to some of these reports, however, our data establish that the phonon anomaly and the formation of the additional peak exhibit very pronounced and steep changes right at T$_{c}$. For a less underdoped YBa$_{2}$Cu$_{3}$O$_{6.75}$ crystal with T$_{c}$=80 K, the onset temperature of the phonon anomaly almost coincides with T$_{c}$. Also in contrast to some previous reports, we find for both crystals that a sizeable fraction of the spectral weight of the additional absorption peak cannot be accounted for by the spectral-weight loss of the phonon modes but instead arises from a redistribution of the electronic continuum. Our ellipsometric data are consistent with a model where the bilayer cuprate compounds are treated as a superlattice of intra- and inter-bilayer Josephson-junctions

An exact formula for the radiation of a moving quark in N=4 super Yang Mills

We derive an exact formula for the cusp anomalous dimension at small angles. This is done by relating the latter to the computation of certain 1/8 BPS Wilson loops which was performed by supersymmetric localization. This function of the coupling also determines the power emitted by a moving quark in N=4 super Yang Mills, as well as the coefficient of the two point function of the displacement operator on the Wilson loop. By a similar method we compute the near BPS expansion of the generalized cusp anomalous dimension.Comment: 22 pages, 5 figures. v2: references added, typos correcte

Hidden Simplicity of Gauge Theory Amplitudes

These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the BCFW recursion relations we solve for the tree-level S-matrix in N=4 super Yang-Mills theory, and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree-level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.Comment: 46 pages, 15 figures. v2 ref added, typos fixe

Investigation of A1g phonons in YBa2Cu3O7 by means of LAPW atomic-force calculations

We report first-principles frozen-phonon calculations for the determination of the force-free geometry and the dynamical matrix of the five Raman-active A1g modes in YBa2Cu3O7. To establish the shape of the phonon potentials atomic forces are calculated within the LAPW method. Two different schemes - the local density approximation (LDA) and a generalized gradient approximation (GGA) - are employed for the treatment of electronic exchange and correlation effects. We find that in the case of LDA the resulting phonon frequencies show a deviation from experimental values of approximately -10%. Invoking GGA the frequency values are significantly improved and also the eigenvectors are in very good agreement with experimental findings.Comment: 15 page

Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral \Omega^{(2)}, also plays a key role in a new representation of the remainder function R_6^{(2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) \times (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) \times (parity even) part. The second non-polylogarithmic function, the loop integral \tilde{\Omega}^{(2)}, characterizes this sector. Both \Omega^{(2)} and tilde{\Omega}^{(2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.Comment: 51 pages, 4 figures, one auxiliary file with symbols; v2 minor typo correction

Adenosine triphosphate-sensitive potassium channel Kir subunits implicated in cardioprotection by diazoxide

BACKGROUND: ATP-sensitive potassium (K(ATP)) channel openers provide cardioprotection in multiple models. Ion flux at an unidentified mitochondrial K(ATP) channel has been proposed as the mechanism. The renal outer medullary kidney potassium channel subunit, potassium inward rectifying (Kir)1.1, has been implicated as a mitochondrial channel pore-forming subunit. We hypothesized that subunit Kir1.1 is involved in cardioprotection (maintenance of volume homeostasis and contractility) of the K(ATP) channel opener diazoxide (DZX) during stress (exposure to hyperkalemic cardioplegia [CPG]) at the myocyte and mitochondrial levels. METHODS AND RESULTS: Kir subunit inhibitor Tertiapin Q (TPN-Q) was utilized to evaluate response to stress. Mouse ventricular mitochondrial volume was measured in the following groups: isolation buffer; 200 μmol/L of ATP; 100 μmol/L of DZX+200 μmol/L of ATP; or 100 μmol/L of DZX+200 μmol/L of ATP+TPN-Q (500 or 100 nmol/L). Myocytes were exposed to Tyrode’s solution (5 minutes), test solution (Tyrode’s, cardioplegia [CPG], CPG+DZX, CPG+DZX+TPN-Q, Tyrode’s+TPN-Q, or CPG+TPN-Q), N=12 for all (10 minutes); followed by Tyrode’s (5 minutes). Volumes were compared. TPN-Q, with or without DZX, did not alter mitochondrial or myocyte volume. Stress (CPG) resulted in myocyte swelling and reduced contractility that was prevented by DZX. TPN-Q prevented the cardioprotection afforded by DZX (volume homeostasis and maintenance of contractility). CONCLUSIONS: TPN-Q inhibited myocyte cardioprotection provided by DZX during stress; however, it did not alter mitochondrial volume. Because TPN-Q inhibits Kir1.1, Kir3.1, and Kir3.4, these data support that any of these Kir subunits could be involved in the cardioprotection afforded by diazoxide. However, these data suggest that mitochondrial swelling by diazoxide does not involve Kir1.1, 3.1, or 3.4

Synaptic abnormalities in the infralimbic cortex of a model of congenital depression

Multiple lines of evidence suggest that disturbances in excitatory transmission contribute to depression. Whether these defects involve the number, size, or composition of glutamatergic contacts is unclear. This study used recently introduced procedures for fluorescence deconvolution tomography in a well-studied rat model of congenital depression to characterize excitatory synapses in layer I of infralimbic cortex, a region involved in mood disorders, and of primary somatosensory cortex. Three groups were studied: (1) rats bred for learned helplessness (cLH); (2) rats resistant to learned helplessness (cNLH); and (3) control Sprague Dawley rats. In fields within infralimbic cortex, cLH rats had the same numerical density of synapses, immunolabeled for either the postsynaptic density (PSD) marker PSD95 or the presynaptic protein synaptophysin, as controls. However, PSD95 immunolabeling intensities were substantially lower in cLH rats, as were numerical densities of synapse-sized clusters of the AMPA receptor subunit GluA1. Similar but less pronounced differences (comparable numerical densities but reduced immunolabeling intensity for PSD95) were found in the somatosensory cortex. In contrast, non-helpless rats had 25% more PSDs than either cLH or control rats without any increase in synaptophysin-labeled terminal frequency. Compared with controls, both cLH and cNLH rats had fewer GABAergic contacts. These results indicate that congenital tendencies that increase or decrease depression-like behavior differentially affect excitatory synapses