The acyclicity of the complex of homologous curves

We show that the complex of homologous curves of a closed, oriented surface of genus g is (g-3)--acyclic.Comment: Added citations of related work of Looijenga. Added a discussion in the introduction regarding the relationship between the results of Section 5 and work of Looijenga on the complex of separating curve

Complete Derandomization of Identity Testing and Reconstruction of Read-Once Formulas

In this paper we study the identity testing problem of arithmetic read-once formulas (ROF) and some related models. A read-once formula is formula (a circuit whose underlying graph is a tree) in which the operations are {+,x} and such that every input variable labels at most one leaf. We obtain the first polynomial-time deterministic identity testing algorithm that operates in the black-box setting for read-once formulas, as well as some other related models. As an application, we obtain the first polynomial-time deterministic reconstruction algorithm for such formulas. Our results are obtained by improving and extending the analysis of the algorithm of [Shpilka-Volkovich, 2015

Many Low Income Women In Texas Do Not Get the Effective Contraception They Want After Giving Birth

Population Research Cente

All lines on a smooth cubic surface in terms of three skew lines

Jordan showed that the incidence variety of a smooth cubic surface containing 27 lines has solvable Galois group over the incidence variety of a smooth cubic surface containing 3 skew lines. As noted by Harris, it follows that for any smooth cubic surface, there exist formulas for all 27 lines in terms of any 3 skew lines. In response to a question of Farb, we compute these formulas explicitly. We also discuss how these formulas relate to Schl\"afli's count of lines on real smooth cubic surfaces.Comment: 21 pages, 5 figures, 1 table. Final version for journa

A note on the Coulomb branch of susy Yang-Mills

We compute the force between oppositely charged W bosons in the large N limit of Yang-Mills with 16 supercharges broken to SU(N) x U(1) by a finite Higgs vev. We clarify some issues regarding Wilson line computations and show that there is a regime in which the force between W bosons is independent of separation distance.Comment: 11 pages, LaTeX, v2: misprint corrected, v3: references adde

Instability and Degeneracy in the BMN Correspondence

Non-degenerate perturbation theory, which was used to calculate the scale dimension of operators on the gauge theory side of the correspondence, breaks down when effects of triple trace operators are included. We interpret this as an instability of excited single-string states in the dual string theory for decay into the continuum of degenerate 3-string states. We apply time-dependent perturbation theory to calculate the decay widths from gauge theory. These widths are new gauge theory data which can be compared with future calculations in light cone string field theory.Comment: 23 pages, no figure

The general Leigh-Strassler deformation and integrability

The success of the identification of the planar dilatation operator of N=4 SYM with an integrable spin chain Hamiltonian has raised the question if this also is valid for a deformed theory. Several deformations of SYM have recently been under investigation in this context. In this work we consider the general Leigh-Strassler deformation. For the generic case the S-matrix techniques cannot be used to prove integrability. Instead we use R-matrix techniques to study integrability. Some new integrable points in the parameter space are found.Comment: 22 pages, 8 figures, reference adde

Consistent supersymmetric Kaluza--Klein truncations with massive modes

We construct consistent Kaluza--Klein reductions of D=11 supergravity to four dimensions using an arbitrary seven-dimensional Sasaki--Einstein manifold. At the level of bosonic fields, we extend the known reduction, which leads to minimal N=2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the Sasaki--Einstein space, and still consistent with N=2 supersymmetry. In the context of flux compactifications, the Sasaki--Einstein reductions are generalizations of type IIA SU(3)-structure reductions which include both metric and form-field flux and lead to a massive universal tensor multiplet. We carry out a similar analysis for an arbitrary weak G_2 manifold leading to an N=1 supergravity with massive fields. The straightforward extension of our results to the case of the seven-sphere would imply that there is a four-dimensional Lagrangian with N=8 supersymmetry containing both massless and massive spin two fields. We use our results to construct solutions of M-theory with non-relativistic conformal symmetry.Comment: 33 pages. v2: Added section on skew-whiffed solutions and some brief comments on holographic superconductors. v3: typos corrected, version to be published in JHE