Talks

Integrability in gauge/string dualities will be reviewed in a broad perspective with a particular emphasis on the recently proposed equations describing the full planar spectrum of anomalous dimensions in AdS/CFT [N.Gromov, V.Kazakov, PV]. These are a concise version of Thermodynamic Bethe equations, called Y-system, which generalize the asymptotic Bethe equations of Beisert and Staudacher (which yield the full spectrum of N=4 SYM for asymptotically long local operators) and incorporate the 4-loop results for the shortest twist two operators obtained by Bajnok and Janik from the dual string sigma model (thus reproducing perturbative gauge theory computations with thousands of diagrams). On the way, we will explain some of the interesting open problems in the field.

The observed thermal properties of the ICM shows much greater dispersion than expected if the gas was subject only to shock-heating by mergers and during infall. This diversity can be best understood as a byproduct of AGN feedback occurring in galaxies destined to become cluster members, both before and after cluster formation. Theoretical considerations suggest that the level of preheating ought to vary from one proto-cluster region to another. The entropy profiles of roughly 50% of the clusters with long central cooling times require that the gas be "preheated" to high entropy. Gas density profiles in such systems form hot central cores. Clusters with gas that isn't preheated to sufficiently high values forms peaked density profiles. I will show how variable preheating explain the various observed X-ray/X-ray correlations and discuss some of its implications for SZ studies. I will also present optical results that shed new light on the fate of the cold gas in cooling-unstable clusters, and propose observations tests of the "AGN preheating" aspect of the picture.

Scaling relations among galaxy cluster observables, which will become available in large future samples of galaxy clusters, could be used to constrain not only cluster structure,but also cosmology. I will discuss the utility of this approach, employing a physically motivated parametric model to describe cluster structure, and applying it to the expected relation between the Sunyaev-Zel’dovich decrement (S_{\nu}) and the emission–weighted X–ray temperature (Tew). With a suitable choice of fiducial parameter values, the cluster model satisfies several existing observational constraints. A Fisher matrix is employed to estimate the joint errors on cosmological and cluster structure parameters from a measurement of S_{\nu} vs. Tew in a future survey. I will also compare the cosmology constraints from the scaling relation to those expected from the number counts (dN/dz) of the same clusters.

The growing fascination with unconventional pairing is driven in part by continuing discoveries of exotic superconductors. The first of these, superfluid 3He, was found by Osheroff, Richardson, and Lee in 1971. This was followed soon thereafter by superconductivity in the heavy fermion compound, UPt3. And then an explosion of interest accompanied the observation of superconductivity in cuprates, Sr2RuO4, and organic materials. The newest discoveries are sperconducting compounds of FeAs. These systems have been demonstrated (or in some cases it is just suspected) that they have pairing condensates with non-zero angular momentum, L= 1, 2, and even 3. But all of them have the common hallmark of a high degree of sensitivity to impurities. In this talk I will discuss impurity effects in the best known of these unconventionally paired systems, 3He, a paradigm for the other unconventional superconductors. Impurity scattering is deftly controlled in superfluid 3He by imbibing it into high porosity silica aerogel. We can understand the suppression of its superfluid state (the transition temperature), the effect on its order parameter (the pairing energy), the appearance of quasiparticle bound states (gaplessness), and possibly new phases, in the context of current theory. I will discuss experiments from many laboratories and their theoretical interpretation leading to the topical question of the day, “Can anisotropic scattering stabilize new anisotropic states?”

'The discovery in 1996 of superconductivity at 0.2K near a magnetic quantum phase transition in CeIn3 opened a new dynasty of superconducting heavy electron materials, with many peculiar parallels to cuprate superconductors. In 2000, the introduction of additional layers of XIn_2, led to the discovery of the so-called ''115'' superconductors, with a tenfold increase in Tc[1]. By 2002, the replacement of Ce by Pu, drove the Tc up by an additional order of magnitude to 18.5K[2]. The recent discovery of a second material in this family has further deepened the mystery. In this talk I'll discuss the two newest ''high temperature'' heavy fermion superconductors in this series: PuCoGa5 and NpPd_2Al_5. These materials radically challenge the way we think about strongly correlated superconductivity. The way these materials directly transition from Curie paramagnets into anisotropic superconductors suggests a central role of spin as a driver for heavy electron superconductors - not just as the pairing glue - but as the basic fabric of the condensate. Motivated by these new materials, I'll discuss a model for superconductivity in the highest temperature superconductors in which the superconducting condensate involves formation of composite pairs between spins and conduction electrons[3]. Using this idea, we'll discuss how the physics of superconductivity and the Kondo effect can be combined, giving rise to a composite pairing model for the new superconductors. [1]}H. Hegger, C. Petrovic, E. G. Moshopoulou, M. F. Hundley, J. L. Sarrao, Z. Fisk, and J. D. Thompson, ''Pressure-Induced Superconductivity in Quasi-2D $CeRhIn_{5}$'' Phys. Rev. Lett. 84, 4986-4989 (2000). [2]J. L. Sarrao et al. , ``Plutonium-based superconductivity with a transition temperature above 18 K'', Nature (London) {bf 420}, 297-299 (2002). [3] Rebecca Flint, M. Dzero, P. Coleman, ''Heavy electrons and the symplectic symmetry of spin.'', Nature Physics 4, 643 - 648 (2008).Nature Physics, '