Let X be a nonsingular algebraic curve of genus g ≥ 3, and let Mξ denote the moduli space of stable vector bundles of rank n ≥ 2 and degree d with fixed determinant ξ over X such that n and d are coprime. We assume that if g = 3 then n ≥ 4 and if g = 4 then n ≥ 3, and suppose further that n0, d0 are integers such that n0 ≥ 1 and nd0 + n0d > nn0(2g − 2). Let E be a semistable vector bundle over ...

We construct unstable classical solutions of Yang-Mills theories and their dual unstable states of type IIB on AdS5. An example is the unstable D0-brane of type IIB located at the center of AdS. This has a field theory dual which is a sphaleron in gauge theories on S3 × R. We argue that the two are dual because both are sphalerons associated to the topology of the instanton/D-instanton. This ag...

We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. If the fibers of G → B are simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result being given by an Atiyah-Singer type formula. We also study traces on the corresponding algebras of pseudodifferentia...

Let D(G) be the minimum quantifier depth of a first order sentence Φ that defines a graph G up to isomorphism in terms of the adjacency and the equality relations. Let D0(G) be a variant of D(G) where we do not allow quantifier alternations in Φ. Using large graphs decomposable in complement-connected components by a short sequence of serial and parallel decompositions, we show examples of G on...

We present main results of the investigation of the rare decay mode D0 → γγ, in which the long distance contributions are expected to be dominant. Using the Heavy Quark Chiral Lagrangian we have considered the anomaly contribution which relates to the annihilation part of the weak Lagrangian and the one loop π, K diagrams. The loop contributions which are proportional to g and contain the a1 Wi...

Theorem. 1.1 Let X be a projective geometrically reduced and irreducible scheme over a field k of (arbitrary) characteristic p and let M , L be line bundles on X with L ample. If p is positive then suppose further that X is smooth in codimension one. For fixed m ≥ 0 there exists d0 = d0(m), depending also on X,L,M, such that for any d ≥ d0 and any generic union Z of (fat) points of multiplicity...

In this paper we reexamine the D-brane spectrum in the Melvin background with non-constant NSNS B-field from the viewpoint of its world-volume and string world-sheet theory. We find that the stable D2-D0 bound state exists even though it does not wrap any nontrivial cycles. We show that this system is stabilized by the presence of the NSNS B-field and the magnetic flux F . Moreover from the non...

We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. In this paper we concentrate on the issues specific to the case when G is trivial, so the action reduces to the action of a Lie group G. For G simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result b...

We construct 1/8, 1/4, and 1/2 BPS solutions spanned by diagonal elements of U(N) constant fluxes in the 6+1 dimensional U(N) super Yang-Mills theory on T 6 with topological stability. These solutions represent BPS bound states of D0, D2, D4, and D6 branes. The consistency with the D-brane charge conservation implies that unstable D0-D2-D6-brane systems in a B field decay to the BPS solutions, ...

Upconversion (UC) luminescence of lanthanide ions (Ln3+) has been extensively investigated for several decades and is a constant research hotspot owing to its fundamental significance and widespread applications. In contrast to the multiple and fixed UC emissions of Ln3+, transition metal (TM) ions, e.g., Mn2+, usually possess a single broadband emission due to its 3d5 electronic configuration....