Collective Quartics and Dangerous Singlets in Little Higgs

Any extension of the standard model that aims to describe TeV-scale physics without fine-tuning must have a radiatively-stable Higgs potential. In little Higgs theories, radiative stability is achieved through so-called collective symmetry breaking. In this letter, we focus on the necessary conditions for a little Higgs to have a collective Higgs quartic coupling. In one-Higgs doublet models, a collective quartic requires an electroweak triplet scalar. In two-Higgs doublet models, a collective quartic requires a triplet or singlet scalar. As a corollary of this study, we show that some little Higgs theories have dangerous singlets, a pathology where collective symmetry breaking does not suppress quadratically-divergent corrections to the Higgs mass.Comment: 4 pages; v2: clarified the existing literature; v3: version to appear in JHE

Inversion For Permeability From Stoneley Wave Velocity And Attenuation

The in situ permeability of a formation is obtained by the inversion of Stoneley wave phase velocity and attenuation, which are evaluated by applying the Extended Prony's method to the array sonic logging data. The Maximum Likelihood inversion is used together with logarithmic parameterization of the permeabilities. Formation shear wave velocity is also inverted for. This process is tested on both synthetic and field data. Logarithmic parameterization contributes to rapid convergence of the algorithm. Permeabilities estimated from field data are in good agreement with core measurements.Massachusetts Institute of Technology. Full Waveform Acoustic Logging Consortiu

Fourth-Order Finite Difference Acoustic Logs In A Transversely Isotropic Formation

In this paper we present a finite difference scheme for seismic wave propagation in a fluid-filled borehole in a transversely isotropic formation. The first-order hyperbolic differential equations are approximated explicitly on a staggered grid using an algorithm that is fourth-order accurate in space and second-order accurate in time. The grid dispersion and grid anisotropy are analyzed. Grid dispersion and anisotropy are well suppressed by a grid size of 10 points per wavelength. The stability condition is also obtained from the dispersion analysis. This finite difference scheme is implemented on the nCUBE2 parallel computer with a grid decomposition algorithm. The finite difference synthetic waveforms are compared with those generated using the discrete wavenumber method. They are in good agreement. The damping layers effectively absorbed the boundary reflections. Four vertically heterogeneous borehole models: a horizontal layered formation, a borehole with a radius change, a semi-infinite borehole, and a semi-infinite borehole with a layer, are studied using the finite difference method. Snapshots from the finite difference results provide pictures of the radiating wavefields.Massachusetts Institute of Technology. Borehole Acoustics and Logging Consortiu

Acoustic Logging In Randomly Stratified Formations

The propagation of borehole acoustic waves in the presence of various types of heterogeneous formations is investigated by modeling them as stratified media with varying velocity-depth distributions. Two types of formations are modeled, using translational and cyclic random models, respectively. Borehole acoustic wavefields for the heterogeneity formation models are simulated using finite-difference techniques. The wavefield modeling results show that the borehole acoustic waves can be significantly affected by the formation heterogeneities. Specifically, the scattering due to heterogeneity can cause significant amplitude attenuation and travel time delay for the transmitted waves. The borehole guided waves are also sensitive to the formation heterogeneity. The effects of the random formation heterogeneity on the borehole acoustic waves are controlled by two factors: the degree of heterogeneity variation and the heterogeneity scale length relative to the wavelength.Massachusetts Institute of Technology. Borehole Acoustics and Logging Consortiu

Borehole Wave Propagation In Isotropic And Anisotropic Media III: Anisotropic Formation

In this paper we extend the 3-D finite difference method to simulate wave propagations in an anisotropic medium. The scheme is tested in the homogeneous medium. The finite difference results agree excellently with the analytic solutions of a point force source in the transversely isotropic medium. The finite difference synthetics are compared with ultrasonic lab measurements in a scaled borehole drilled along the X axis in an orthorhombic phenolite solid. Both monopole and dipole logs agree well. The 3-D time domain finite difference method is applied to the fluid-filled borehole wave propagation problems in the anisotropic formation. The following results are obtained: 1. In a borehole drilled along the Z axis in a phenolite formation, the monopole log shows the P wave travelling with velocity v[subscript zz]. There are no shear-pseudo-Rayleigh wave arrivals. The dipole log is dominated by the single slow flexural mode. 2. In a borehole drilled along the Y axis in a phenolite formation, the monopole log shows the P wave travelling with velocity v[subscript yy]. There are shear-pseudo-Rayleigh wave arrivals shown on the monopole seismograms between the P and Stoneley waves due to the shear wave anisotropy. The anisotropy also causes the shear wave splitting in the dipole log. The two shear wave arrivals correspond to the fast and the slow flexural modes. 3. The disagreement between the shear wave velocity from the Stoneley wave inversion and the direct shear wave log velocity from field data is beyond the errors in the measurements. It is shown that the formation permeability is not the cause of the discrepancy. From the estimated "shear/pseudo-Rayleigh" phase velocities in the array full waveform log and the 3-D finite difference synthetics in the anisotropic formation, the discrepancy can be explained as shear wave anisotropy.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumERL/nCUBE Geophysical Center for Parallel Processin

Borehole Wave Propagation In Isotropic And Anisotropic Media I: Finite Difference Method

In this paper we developed a 3-D finite difference method to simulate wave propagations in an isotropic medium. The wave equation is formulated into the first-order hyperbolic equations by using velocity and stress and then discretizing it on a staggered grid. The 3-D time domain finite difference scheme is second order accurate in time and fourth order accurate in space. The grid dispersion and anisotropy are analyzed and the stable condition of the scheme is obtained. Higdon's absorbing boundary condition is discussed and generalized to the anisotropic medium. The scheme can provide realistic 3-D wave propagation simulation by the use of a parallel computer. The scheme is tested in the homogeneous medium. The finite difference results agree excellently with the analytic solutions of a point explosion source in the acoustic medium and a point force source in the elastic medium. The finite difference method accurately models not only the far field P and S waves, but also the near field term. It demonstrates that the second-order Higdon's absorbing boundary condition works very well in an acoustic and elastic medium.Massachusetts Institute of Technology. Borehole Acoustics and Logging ConsortiumERL/nCUBE Geophysical Center for Parallel Processin

Mother Moose: Generating Extra Dimensions from Simple Groups at Large N

We show that there exists a correspondence between four dimensional gauge theories with simple groups and higher dimensional gauge theories at large N. As an example, we show that a four dimensional {N}=2 supersymmetric SU(N) gauge theory, on the Higgs branch, has the same correlators as a five dimensional SU(N) gauge theory in the limit of large N provided the couplings are appropriately rescaled. We show that our results can be applied to the AdS/CFT correspondence to derive correlators of five or more dimensional gauge theories from solutions of five dimensional supergravity in the large t'Hooft coupling limit.Comment: 12 pages, references adde

3d Modularity

We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d $\mathcal{N}=2$ theories where such structures a priori are not manifest. These modular structures include: mock modular forms, $SL(2,\mathbb{Z})$ Weil representations, quantum modular forms, non-semisimple modular tensor categories, and chiral algebras of logarithmic CFTs.Comment: 119 pages, 10 figures and 20 table