Coisotropic Branes, Noncommutativity, and the Mirror Correspondence

We study coisotropic A-branes in the sigma model on a four-torus by explicitly constructing examples. We find that morphisms between coisotropic branes can be equated with a fundamental representation of the noncommutatively deformed algebra of functions on the intersection. The noncommutativity parameter is expressed in terms of the bundles on the branes. We conjecture these findings hold in general. To check mirror symmetry, we verify that the dimensions of morphism spaces are equal to the corresponding dimensions of morphisms between mirror objects.Comment: 13 page

Kinematic approach to the mixed state geometric phase in nonunitary evolution

A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the evolution is unitary.Comment: Minor changes; journal reference adde

Coexistence of bulk and surface states probed by Shubnikov-de Haas oscillations in Bi2_2Se3_3 with high charge-carrier density

Topological insulators are ideally represented as having an insulating bulk with topologically protected, spin-textured surface states. However, it is increasingly becoming clear that these surface transport channels can be accompanied by a finite conducting bulk, as well as additional topologically trivial surface states. To investigate these parallel conduction transport channels, we studied Shubnikov-de Haas oscillations in Bi$_2$Se$_3$ thin films, in high magnetic fields up to 30 T so as to access channels with a lower mobility. We identify a clear Zeeman-split bulk contribution to the oscillations from a comparison between the charge-carrier densities extracted from the magnetoresistance and the oscillations. Furthermore, our analyses indicate the presence of a two-dimensional state and signatures of additional states the origin of which cannot be conclusively determined. Our findings underpin the necessity of theoretical studies on the origin of and the interplay between these parallel conduction channels for a careful analysis of the material's performance.Comment: Manuscript including supplemental materia

Gravitationally Collapsing Shells in (2+1) Dimensions

We study gravitationally collapsing models of pressureless dust, fluids with pressure, and the generalized Chaplygin gas (GCG) shell in (2+1)-dimensional spacetimes. Various collapse scenarios are investigated under a variety of the background configurations such as anti-de Sitter(AdS) black hole, de Sitter (dS) space, flat and AdS space with a conical deficit. As with the case of a disk of dust, we find that the collapse of a dust shell coincides with the Oppenheimer-Snyder type collapse to a black hole provided the initial density is sufficiently large. We also find -- for all types of shell -- that collapse to a naked singularity is possible under a broad variety of initial conditions. For shells with pressure this singularity can occur for a finite radius of the shell. We also find that GCG shells exhibit diverse collapse scenarios, which can be easily demonstrated by an effective potential analysis.Comment: 27 pages, Latex, 11 figures, typos corrected, references added, minor amendments in introduction and conclusion introd

Evaluating Matrix Circuits

The circuit evaluation problem (also known as the compressed word problem) for finitely generated linear groups is studied. The best upper bound for this problem is $\mathsf{coRP}$, which is shown by a reduction to polynomial identity testing. Conversely, the compressed word problem for the linear group $\mathsf{SL}_3(\mathbb{Z})$ is equivalent to polynomial identity testing. In the paper, it is shown that the compressed word problem for every finitely generated nilpotent group is in $\mathsf{DET} \subseteq \mathsf{NC}^2$. Within the larger class of polycyclic groups we find examples where the compressed word problem is at least as hard as polynomial identity testing for skew arithmetic circuits

Electroweak phase transition in a nonminimal supersymmetric model

The Higgs potential of the minimal nonminimal supersymmetric standard model (MNMSSM) is investigated within the context of electroweak phase transition. We investigate the allowed parameter space yielding correct electroweak phase transitoin employing a high temperature approximation. We devote to phenomenological consequences for the Higgs sector of the MNMSSM for electron-positron colliders. It is observed that a future $e^+ e^-$ linear collider with $\sqrt{s} = 1000$ GeV will be able to test the model with regard to electroweak baryogenesis.Comment: 28 pages, 5 tables, 12 figure

Electroweak phase transition in the MSSM with four generations

By assuming the existence of the sequential fourth generation to the minimal supersymmetric standard model (MSSM), we study the possibility of a strongly first-order electroweak phase transition. We find that there is a parameter region of the MSSM where the electroweak phase transition is strongly first order. In that parameter region, the mass of the lighter scalar Higgs boson is calculated to be above the experimental lower bound, and the scalar quarks of the third and the fourth generations are heavier than the corresponding quarks.Comment: 12 pages, 2 tables, 2 figure