Computational Experiments with Cross and Crooked Cross Cuts

In this paper, we study whether cuts obtained from two simplex tableau rows at a time can strengthen the bounds obtained by Gomory mixed-integer (GMI) cuts based on single tableau rows. We also study whether cross and crooked cross cuts, which generalize split cuts, can be separated in an effective manner for practical mixed-integer programs (MIPs) and can yield a nontrivial improvement over the bounds obtained by split cuts. We give positive answers to both these questions for MIPLIB 3.0 problems. Cross cuts are a special case of the t-branch split cuts studied by Li and Richard [Li Y, Richard J-PP (2008) Cook, Kannan and Schrijvers's example revisited. Discrete Optim. 5:724–734]. Split cuts are 1-branch split cuts, and cross cuts are 2-branch split cuts. Crooked cross cuts were introduced by Dash, Günlük, and Lodi [Dash S, Günlük O, Lodi A (2010) MIR closures of polyhedral sets. Math Programming 121:33–60] and were shown to dominate cross cuts by Dash, Günlük, and Molinaro [Dash S, Günlük O, Molinaro M (2012b) On the relative strength of different generalizations of split cuts. IBM Technical Report RC25326, IBM, Yorktown Heights, NY].United States. Office of Naval Research (Grant N000141110724

Matrix Models, Topological Strings, and Supersymmetric Gauge Theories

We show that B-model topological strings on local Calabi-Yau threefolds are large N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover (p,q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.Comment: 22 pages, minor correction

Spatial Clustering of Dark Matter Halos: Secondary Bias, Neighbor Bias, and the Influence of Massive Neighbors on Halo Properties

We explore the phenomenon commonly known as halo assembly bias, whereby dark matter halos of the same mass are found to be more or less clustered when a second halo property is considered, for halos in the mass range $3.7 \times 10^{11} \; h^{-1} \mathrm{M_{\odot}} - 5.0 \times 10^{13} \; h^{-1} \mathrm{M_{\odot}}$. Using the Large Suite of Dark Matter Simulations (LasDamas) we consider nine commonly used halo properties and find that a clustering bias exists if halos are binned by mass or by any other halo property. This secondary bias implies that no single halo property encompasses all the spatial clustering information of the halo population. The mean values of some halo properties depend on their halo's distance to a more massive neighbor. Halo samples selected by having high values of one of these properties therefore inherit a neighbor bias such that they are much more likely to be close to a much more massive neighbor. This neighbor bias largely accounts for the secondary bias seen in halos binned by mass and split by concentration or age. However, halos binned by other mass-like properties still show a secondary bias even when the neighbor bias is removed. The secondary bias of halos selected by their spin behaves differently than that for other halo properties, suggesting that the origin of the spin bias is different than of other secondary biases.Comment: 14 pages, LaTeX; minor revisions, and added references; results unchange

On Geometry and Matrix Models

We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.Comment: 24 page

Revisiting Theories with Enhanced Higgs Couplings to Weak Gauge Bosons

Based on recent LHC Higgs analyses and in anticipation of future results we revisit theories where Higgs bosons can couple to weak gauge bosons with enhanced strength relative to the Standard Model value. Specifically, we look at the Georgi-Machacek model and its generalizations where higher "spin" representations of SU(2)_L break electroweak symmetry while maintaining custodial SU(2). In these theories, there is not only a Higgs-like boson but partner Higgs scalars transforming under representations of custodial SU(2), leading to a rich phenomenology. These theories serve as a consistent theoretical and experimental framework to explain enhanced couplings to gauge bosons, including fermiophobic Higgses. We focus on the phenomenology of a neutral scalar partner to the Higgs, which is determined once the Higgs couplings are specified. Depending on the parameter space, this partner could have i) enhanced fermion and gauge boson couplings and should be searched for at high mass (> 600 GeV), ii) have suppressed couplings and could be searched for at lower masses, where the Standard Model Higgs has already been ruled out, and iii) have fermiophilic couplings, where it can be searched for in heavy Higgs and top resonance searches. In the first two regions, the partner also has substantial decay rates into a pair of Higgs bosons. We touch briefly on the more model-dependent effects of the nontrivial SU(2)_C multiplets, which have exotic signals, such as a doubly-charged Higgs. We also discuss how the loop induced effects of these scalars tend to reduce the Higgs decay rate to photons, adding an additional uncertainty when extracting the couplings for the Higgs boson.Comment: 9 pages, 9 figures, revtex4; v2, references adde

Generalized gravitational entropy without replica symmetry

We explore several extensions of the generalized entropy construction of Lewkowycz and Maldacena, including a formulation that does not rely on preserving replica symmetry in the bulk. We show that an appropriately general ansatz for the analytically continued replica metric gives us the flexibility needed to solve the gravitational field equations beyond general relativity. As an application of this observation we study Einstein-Gauss-Bonnet gravity with a small Gauss-Bonnet coupling and derive the condition that the holographic entanglement entropy must be evaluated on a surface which extremizes the Jacobson-Myers entropy. We find that in both general relativity and Einstein-Gauss-Bonnet gravity replica symmetry breaking terms are permitted by the field equations, suggesting that they do not generically vanish.Comment: 24 pages, 3 figures. v3: fixed some more typos, v2: fixed minor typo