A two weight local Tb theorem for the Hilbert transform

We obtain a two weight local Tb theorem for any elliptic and gradient elliptic fractional singular integral operator T on the real line, and any pair of locally finite positive Borel measures on the line. This includes the Hilbert transform and in a sense improves on the T1 theorem by the authors and M. Lacey.Comment: 121 pages, 3 figures, 50 pages of appendices. We correct three gaps in the treatment of the stopping form in v12: the proof of Lemma 9.3 there requires a larger size functional, a collection of pairs is missing from the decomposition at the bottom of page 149, and an error was made in the definition of restricted norm of a stopping form. Main results unchange

A-D-E Quivers and Baryonic Operators

We study baryonic operators of the gauge theory on multiple D3-branes at the tip of the conifold orbifolded by a discrete subgroup Gamma of SU(2). The string theory analysis predicts that the number and the order of the fixed points of Gamma acting on S^2 are directly reflected in the spectrum of baryonic operators on the corresponding quiver gauge theory constructed from two Dynkin diagrams of the corresponding type. We confirm the prediction by developing techniques to enumerate baryonic operators of the quiver gauge theory which includes the gauge groups with different ranks. We also find that the Seiberg dualities act on the baryonic operators in a non-Abelian fashion.Comment: 46 pages, 17 figures; v2: minor corrections, note added in section 1, references adde

Generalized Hörmander conditions and weighted endpoint estimates

We consider two-weight estimates for singular integral operators and their commutators with bounded mean oscillation functions. Hörmander type conditions in the scale of Orlicz spaces are assumed on the kernels. We prove weighted weak-type estimates for pairs of weights (u, Su) where u is an arbitrary nonnegative function and S is a maximal operator depending on the smoothness of the kernel. We also obtain sufficient conditions on a pair of weights (u, v) for the operators to be bounded from Lp(v) to Lp,∞(u). One-sided singular integrals, as the differential transform operator, are under study. We also provide applications to Fourier multipliers and homogeneous singular integrals.Ministerio de Ciencia y TecnologíaJunta de AndalucíaMinisterio de Educación y CienciaUniversidad Autónoma de Madrid / Comunidad de MadridConsejo Nacional de Investigaciones Científicas y Técnicas (Argentina)Secretaría de Ciencia y Tecnología (Universidad Nacional de Córdoba

Unquenched QCD dirac operator spectra at nonzero baryon chemical potential

The microscopic spectral density of the QCD Dirac operator at nonzero baryon chemical potential for an arbitrary number of quark flavors was derived recently from a random matrix model with the global symmetries of QCD. In this paper we show that these results and extensions thereof can be obtained from the replica limit of a Toda lattice equation. This naturally leads to a factorized form into bosonic and fermionic QCD-like partition functions. In the microscopic limit these partition functions are given by the static limit of a chiral Lagrangian that follows from the symmetry breaking pattern. In particular, we elucidate the role of the singularity of the bosonic partition function in the orthogonal polynomials approach. A detailed discussion of the spectral density for one and two flavors is given

Parafermion Hall states from coset projections of abelian conformal theories

The Z_k-parafermion Hall state is an incompressible fluid of k-electron clusters generalizing the Pfaffian state of paired electrons. Extending our earlier analysis of the Pfaffian, we introduce two ``parent'' abelian Hall states which reduce to the parafermion state by projecting out some neutral degrees of freedom. The first abelian state is a generalized (331) state which describes clustering of k distinguishable electrons and reproduces the parafermion state upon symmetrization over the electron coordinates. This description yields simple expressions for the quasi-particle wave functions of the parafermion state. The second abelian state is realized by a conformal theory with a (2k-1)-dimensional chiral charge lattice and it reduces to the Z_k-parafermion state via the coset construction su(k)_1+su(k)_1/su(k)_2. The detailed study of this construction provides us a complete account of the excitations of the parafermion Hall state, including the field identifications, the Z_k symmetry and the partition function.Comment: Latex, 36 pages, 3 tables, 2 figure

RECENT PROGRESSES ON GENUS ONE EXTENSIONS OF MIXED TATE MOTIVES OVER Z (Various aspects of multiple zeta values)

In this survey article, we give an overview of recent progress of construction of genus one extension of the category of mixed Tate motives over ℤ by Brown [6] and Hain-Matsumoto [18]