Let p be prime, K a field of characteristic 0. Let (x1, . . . , xn) ∈ Kn such that xi 6= 0 for all i and xi/xj is not a root of unity for all i 6= j. We prove that there exist integers 0 < e1 < e2 < · · · < en such that det (x ei j ) 6= 0. The proof uses p-adic arguments. As corollaries, we derive the linear independence of certain Witt vectors and study the result of applying the Witt functor ...

We demonstrate that black holes and stars in general relativity can be destabilized by perturbations of non-minimally coupled vector fields. Focusing on static spherically symmetric backgrounds, our analysis shows with sufficiently small mass high densities are subject to ghost or gradient-type instabilities. This holds for a large class vector-tensor theories whenever non-minimal couplings con...

Abstract In this note, we present a synopsis of geometric symmetries for (spin 0) perturbations around (4D) black holes and de Sitter space. For holes, focus on static perturbations, which the (exact) have group structure SO(1,3). The generators consist three spatial rotations, conformal Killing vectors obeying special melodic condition. perturbation solutions form unitary (principal series) re...

For any complex reductive connected Lie group G, many of the structure constants of the ordinary cohomology ring H(G/B;Z) vanish in the Schubert basis, and the rest are strictly positive. We present a combinatorial game, the “root game”, which provides some criteria for determining which of the Schubert intersection numbers vanish. The definition of the root game is manifestly invariant under a...

Non-uniform black strings coupled to a gauge field are constructed by a perturbative method in a wide range of spacetime dimensions. At the linear order of perturbations, we see that the Gregory-Laflamme instability vanishes at the point where the background solution becomes ther-modynamically stable. The emergence/vanishing of the static mode resembles phase transitions, and in fact we find th...

In this paper, we derive a simplified formula of electric dipole moments (EDMs) fermion. the Standard Model, it is well-known that non-trivial cancellations between some rainbow-type diagrams induced by $W$ boson exchanges occur in calculation neutron EDM at two-loop level due to gauge symmetry. The fermion self-energy and vertex correction are related through Ward-Takahashi identity, relation ...