An Alternative Scenario for Non-Abelian Quantum Hair

Topologically charged black holes in a theory with a 2-form coupled to a non-abelian gauge field are investigated. It is found that the classification of the ground states is similar to that in the theory of non-abelian discrete quantum hair.Comment: 11p

Torsion Galois representations over CM fields and Hecke algebras in the derived category

We construct algebras of endomorphisms in the derived category of the cohomology of arithmetic manifolds, which are generated by Hecke operators. We construct Galois representations with coefficients in these Hecke algebras and apply this technique to sharpen recent results of P. Scholze

Probes on D3-D7 Quark-Gluon Plasmas

We study the holographic dual model of quenched flavors immersed in a quark-gluon plasma with massless dynamical quarks in the Veneziano limit. This is modeled by embedding a probe D7 brane in a background where the backreaction of massless D7 branes has been taken into account. The background, and hence the effects, are perturbative in the Veneziano parameter N_f/N_c, therefore giving small shifts of all magnitudes like the constituent mass, the quark condensate, and several transport coefficients. We provide qualitative results for the effect of flavor degrees of freedom on the probes. For example, the meson melting temperature is enhanced, while the screening length is diminished. The drag force is also enhanced.Comment: 31 pages, 17 figure

Weakly commensurable groups, with applications to differential geometry

The article contains a survey of our results on weakly commensurable arithmetic and general Zariski-dense subgroups, length-commensurable and isospectral locally symmetric spaces and of related problems in the theory of semi-simple agebraic groups. We have included a discussion of very recent results and conjectures on absolutely almost simple algebraic groups having the same maximal tori and finite-dimensional division algebras having the same maximal subfields.Comment: Improved exposition, updated bibliography. arXiv admin note: substantial text overlap with arXiv:1212.121