Partition functions of Supersymmetric Gauge Theories in Noncommutative R^{2D} and their Unified Perspective

We investigate cohomological gauge theories in noncommutative R^{2D}. We show that vacuum expectation values of the theories do not depend on noncommutative parameters, and the large noncommutative parameter limit is equivalent to the dimensional reduction. As a result of these facts, we show that a partition function of a cohomological theory defined in noncommutative R^{2D} and a partition function of a cohomological field theory in R^{2D+2} are equivalent if they are connected through dimensional reduction. Therefore, we find several partition functions of supersymmetric gauge theories in various dimensions are equivalent. Using this technique, we determine the partition function of the N=4 U(1) gauge theory in noncommutative R^4, where its action does not include a topological term. The result is common among (8-dim, N=2), (6-dim, N=2), (2-dim, N=8) and the IKKT matrix model given by their dimensional reduction to 0-dim.Comment: 45 pages, no figures, Appendices B and C are added, changes in the text, references are adde

LHCf Measurements of Very Forward Particles at LHC

The LHC forward experiment (LHCf) is specifically designed for measurements of the very forward ($\eta$$>$8.4) production cross sections of neutral pions and neutrons at Large Hadron Collider (LHC) at CERN. LHCf started data taking in December 2009, when the LHC started to provide stable collisions of protons at $\sqrt{s}$=900\,GeV. Since March 2010, LHC increased the collision energy up to $\sqrt{s}$=7\,TeV. By the time of the symposium, LHCf collected 113k events of high energy showers (corresponding to $\sim$7M inelastic collisions) at $\sqrt{s}$=900\,GeV and $\sim$100M showers ($\sim$14 nb$^{-1}$ of integrated luminosity) at $\sqrt{s}$=7\,TeV. Analysis results with the first limited sample of data demonstrate that LHCf will provide crucial data to improve the interaction models to understand very high-energy cosmic-ray air showers.Comment: Invited talk given at XVI International Symposium on Very High Energy Cosmic Ray Interactions (ISVHECRI 2010), Batavia, IL, USA, 28 June 2 July 2010. 6 pages, 10 figure

Hadron Correlations and Fluctuations in 40, 80, and 158 AGeV/c Pb-Au Collisions

Measurements of HBT correlations and event-by-event fluctuations of mean pT and the net charge in Pb-Au collisions at 40, 80, and 158 AGeV/c are presented. From comparisons of HBT radii measured from AGS to RHIC energies, a universal mean free path of pions at the thermal freeze-out of about 1 fm is derived. Non-statistical mean pT fluctuations of about 0.7 % are measured, which are somewhat smaller than fluctuations at RHIC. No indication for the QCD critical point is observed. Fluctuations of the net charge are reproduced by RQMD and URQMD models, but significantly larger than prediction in equilibrated QGP.Comment: 4 pages, 3 figures, talk presented at the XXXVIIIth Rencontres de Moriond, QCD and High Energy Hadronic Interactions, Les Arcs, France, March 22-29, 200

Topological Symmetry Breaking on Einstein Manifolds

It is known that if gauge conditions have Gribov zero modes, then topological symmetry is broken. In this paper we apply it to topological gravity in dimension $n \geq 3$. Our choice of the gauge condition for conformal invariance is $R+{\alpha}=0$ , where $R$ is the Ricci scalar curvature. We find when $\alpha \neq 0$, topological symmetry is not broken, but when $\alpha =0$ and solutions of the Einstein equations exist then topological symmetry is broken. This conditions connect to the Yamabe conjecture. Namely negative constant scalar curvature exist on manifolds of any topology, but existence of nonnegative constant scalar curvature is restricted by topology. This fact is easily seen in this theory. Topological symmetry breaking means that BRS symmetry breaking in cohomological field theory. But it is found that another BRS symmetry can be defined and physical states are redefined. The divergence due to the Gribov zero modes is regularized, and the theory after topological symmetry breaking become semiclassical Einstein gravitational theory under a special definition of observables.Comment: 16 pages, Late

Concrete Classification and Centralizers of Certain Z2⋊SL(2,Z)\mathbb{Z}^2 \rtimes {\rm SL}(2,\mathbb{Z})-actions

We introduce a new class of actions of the group \G on finite von Neumann algebras and call them twisted Bernoulli shift actions. We classify these actions up to conjugacy and give an explicit description of their centralizers. We also distinguish many of those actions on the AFD $\mathrm{II}_1$ factor in view of outer conjugacy.Comment: 24pages, the title was changed, Chap 6 was adde

Property A and the operator norm localization property for discrete metric spaces

We study property A defined by G. Yu and the operator norm localization property defined by X. Chen, R. Tessera, X. Wang, and G. Yu. These are coarse geometric properties for metric spaces which have applications to operator K-theory. It is proved that the two properties are equivalent for discrete metric spaces with bounded geometry.Comment: 10 pages. In this revised version, we make comments on two other coarse geometric properties defined by Brodzki, Niblo, Spakula, Willett, and Wrigh