Unparticle effects in rare (t -> c g g) decay

Rare (t -> c g g) decay can only appear at loop level in the Standard Model (SM), and naturally they are strongly suppressed. These flavor changing decays induced by the mediation of spin-0 and spin-2 unparticles, can appear at tree level in unparticle physics. In this work the virtual effects of unparticle physics in the flavor-changing (t -> c g g) decay is studied. Using the SM result for the branching ratio of the (t -> c g g) decay, the parameter space of d_U and Lambda_U, where the branching ratio of this decay exceeds the one predicted by the SM, is obtained. Measurement of the branching ratio larger than 10^(-9) can give valuable information for establishing unparticle physics.Comment: 15 pages, 7 figures, LaTeX formatte

c=1 String Theory as a Topological G/G Model

The physical states on the free field Fock space of the {SL(2,R)\over SL(2,R) model at any level are computed. Using a similarity transformation on $Q_{BRST}$, the cohomology of the latter is mapped into a direct sum of simpler cohomologies. We show a one to one correspondence between the states of the $k=-1$ model and those of the $c=1$ string model. A full equivalence between the {SL(2,R)\over SL(2,R) and {SL(2,R)\over U(1) models at the level of their Fock space cohomologies is found.Comment: 19

Birational classification of fields of invariants for groups of order 128128

Let $G$ be a finite group acting on the rational function field $\mathbb{C}(x_g : g\in G)$ by $\mathbb{C}$-automorphisms $h(x_g)=x_{hg}$ for any $g,h\in G$. Noether's problem asks whether the invariant field $\mathbb{C}(G)=k(x_g : g\in G)^G$ is rational (i.e. purely transcendental) over $\mathbb{C}$. Saltman and Bogomolov, respectively, showed that for any prime $p$ there exist groups $G$ of order $p^9$ and of order $p^6$ such that $\mathbb{C}(G)$ is not rational over $\mathbb{C}$ by showing the non-vanishing of the unramified Brauer group: $Br_{nr}(\mathbb{C}(G))\neq 0$. For $p=2$, Chu, Hu, Kang and Prokhorov proved that if $G$ is a 2-group of order $\leq 32$, then $\mathbb{C}(G)$ is rational over $\mathbb{C}$. Chu, Hu, Kang and Kunyavskii showed that if $G$ is of order 64, then $\mathbb{C}(G)$ is rational over $\mathbb{C}$ except for the groups $G$ belonging to the two isoclinism families $\Phi_{13}$ and $\Phi_{16}$. Bogomolov and B\"ohning's theorem claims that if $G_1$ and $G_2$ belong to the same isoclinism family, then $\mathbb{C}(G_1)$ and $\mathbb{C}(G_2)$ are stably $\mathbb{C}$-isomorphic. We investigate the birational classification of $\mathbb{C}(G)$ for groups $G$ of order 128 with $Br_{nr}(\mathbb{C}(G))\neq 0$. Moravec showed that there exist exactly 220 groups $G$ of order 128 with $Br_{nr}(\mathbb{C}(G))\neq 0$ forming 11 isoclinism families $\Phi_j$. We show that if $G_1$ and $G_2$ belong to $\Phi_{16}, \Phi_{31}, \Phi_{37}, \Phi_{39}, \Phi_{43}, \Phi_{58}, \Phi_{60}$ or $\Phi_{80}$ (resp. $\Phi_{106}$ or $\Phi_{114}$), then $\mathbb{C}(G_1)$ and $\mathbb{C}(G_2)$ are stably $\mathbb{C}$-isomorphic with $Br_{nr}(\mathbb{C}(G_i))\simeq C_2$. Explicit structures of non-rational fields $\mathbb{C}(G)$ are given for each cases including also the case $\Phi_{30}$ with $Br_{nr}(\mathbb{C}(G))\simeq C_2\times C_2$.Comment: 31 page