From 3d duality to 2d duality

In this paper we discuss $3d$ ${\cal N}=2$ supersymmetric gauge theories and their IR dualities when they are compactified on a circle of radius $r$, and when we take the $2d$ limit in which $r\to 0$. The $2d$ limit depends on how the mass parameters are scaled as $r\to 0$, and often vacua become infinitely distant in the $2d$ limit, leading to a direct sum of different $2d$ theories. For generic mass parameters, when we take the same limit on both sides of a duality, we obtain $2d$ dualities (between gauge theories and/or Landau-Ginzburg theories) that pass all the usual tests. However, when there are non-compact branches the discussion is subtle because the metric on the moduli space, which is not controlled by supersymmetry, plays an important role in the low-energy dynamics after compactification. Generally speaking, for IR dualities of gauge theories, we conjecture that dualities involving non-compact Higgs branches survive. On the other hand when there is a non-compact Coulomb branch on at least one side of the duality, the duality fails already when the $3d$ theories are compactified on a circle. Using the valid reductions we reproduce many known $2d$ IR dualities, giving further evidence for their validity, and we also find new $2d$ dualities

3d dualities from 4d dualities

Many examples of low-energy dualities have been found in supersymmetric gauge theories with four supercharges, both in four and in three space-time dimensions. In these dualities, two theories that are different at high energies have the same low-energy limit. In this paper we clarify the relation between the dualities in four and in three dimensions. We show that every four dimensional duality gives rise to a three dimensional duality between theories that are similar, but not identical, to the dimensional reductions of the four dimensional dual gauge theories to three dimensions. From these specific three dimensional dualities one can flow to many other low-energy dualities, including known three dimensional dualities and many new ones. We discuss in detail the case of three dimensional SU(N_c) supersymmetric QCD theories, showing how to derive new duals for these theories from the four dimensional duality.Comment: 84 pages, 3 figures, harvmac. v2: added an appendix on the reduction of the 4d index to the 3d partition function, added references, minor corrections and change

Lack of static lattice distortion in Tb2Ti2O7Tb_2 Ti_2 O_7

We investigated the possibility of temperature dependent lattice distortions in the pyrochlore compound Tb$_{2}$Ti$_{2}$O$_{7}$ by measuring the internal magnetic field distribution, using muon spin resonance, and comparing it to the susceptibility. The measurements are done at temperatures as low as 70 mK and external fields up to 6 kG. We find that the evolution of the width of the field distribution can be explained by spin susceptibility only, thus ruling out a temperature dependent hyperfine coupling. We conclude that lattice deformations are absent in Tb$_{2}$Ti$_{2}$O$_{7}$.Comment: 8 pages, 5 figures, accepted for publication in J. Phys. Condens. Matter. (Proceedings of Highly Frustrated Magnetism 2006); Corrections of various typo

On the Composition of Gauge Structures

A formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is based on a pair of related connections that take their values in the product space of the corresponding Lie algebras. The curvature, the covariant exterior derivatives and the associated structural identities, all get contributions from both gauge groups. The various induced structures are classified into those whose composition is given just by trivial means, and those which possess an irreducible nature. The pure irreducible piece, in particular, generates a complete super-space of ghosts with an attendant set of super-BRST variation laws, both of which are purely of a geometrical origin.Comment: Few elaborations are added to section 4 and section 5. To be published in Journal of Physics A: Mathematical and General. 21 page

3d dualities from 4d dualities for orthogonal groups

We extend recent work on the relation of 4d and 3d IR dualities of supersymmetric gauge theories with four supercharges to the case of orthogonal gauge groups. The distinction between different SO(N) gauge theories in 4d plays an important role in this relation. We show that the 4d duality leads to a 3d duality between an SO(N_c) gauge theory with N_f flavors and an SO(N_f-N_c+2) theory with N_f flavors and extra singlets, and we derive its generalization in the presence of Chern-Simons terms. There are two different O(N) theories in 3d, which we denote by O(N)_\pm, and we also show that the O(N_c)_- gauge theory is dual to a Spin(N_f-N_c+2) theory, and derive from 4d the known duality between O(N_c)_+ and O(N_f-N_c+2)_+. We verify the consistency of these 3d dualities by various methods, including index computations.Comment: 49 pages, harvmac. v2: a minor chang

The 2dF gravitational lens survey

The 2 degree Field (2dF) galaxy redshift survey will involve obtaining approximately 2.5 x 10^5 spectra of objects previously identified as galaxy candidates on morphological grounds. Included in these spectra should be about ten gravitationally-lensed quasars, all with low-redshift galaxies as deflectors (as the more common lenses with high-redshift deflectors will be rejected from the survey as multiple point-sources). The lenses will appear as superpositions of galaxy and quasar spectra, and both cross-correlation techniques and principal components analysis should be able to identify candidates systematically. With the 2dF survey approximately half-completed it is now viable to begin a systematic search for these spectroscopic lenses, and the first steps of this project are described here.Comment: PASA (OzLens edition), in press; 4 pages, 0 figure

WISeREP - An Interactive Supernova Data Repository

We have entered an era of massive data sets in astronomy. In particular, the number of supernova (SN) discoveries and classifications has substantially increased over the years from few tens to thousands per year. It is no longer the case that observations of a few prototypical events encapsulate most spectroscopic information about SNe, motivating the development of modern tools to collect, archive, organize and distribute spectra in general, and SN spectra in particular. For this reason we have developed the Weizmann Interactive Supernova data REPository - WISeREP - an SQL-based database (DB) with an interactive web-based graphical interface. The system serves as an archive of high quality SN spectra, including both historical (legacy) data as well as data that is accumulated by ongoing modern programs. The archive provides information about objects, their spectra, and related meta-data. Utilizing interactive plots, we provide a graphical interface to visualize data, perform line identification of the major relevant species, determine object redshifts, classify SNe and measure expansion velocities. Guest users may view and download spectra or other data that have been placed in the public domain. Registered users may also view and download data that are proprietary to specific programs with which they are associated. The DB currently holds >8000 spectra, of which >5000 are public; the latter include published spectra from the Palomar Transient Factory, all of the SUSPECT archive, the Caltech-Core-Collapse Program, the CfA SN spectra archive and published spectra from the UC Berkeley SNDB repository. It offers an efficient and convenient way to archive data and share it with colleagues, and we expect that data stored in this way will be easy to access, increasing its visibility, usefulness and scientific impact.Comment: To be published in PASP. WISeREP: http://www.weizmann.ac.il/astrophysics/wiserep

Nutation versus angular dependent NQR spectroscopy and the impact of underdoping on charge inhomogeneities in YBa2_2Cu3_3Oy_y

We describe two different nuclear quadrupole resonance (NQR) based techniques, designed to measure the local asymmetry of the internal electric field gradient, and the tilt angle of the main NQR principal axis z from the crystallographic axis c. These techniques use the dependence of the NQR signal on the duration of the radio frequency (rf) pulse and on the direction of the rf field H1 with respect to the crystal axis. The techniques are applied to oriented powder of YBa$_{2}$Cu$$O$_{y}$ fully enriched with 63Cu. Measurements were performed at different frequencies, corresponding to different in-plane copper sites with respect to the dopant. Combining the results from both techniques, we conclude that oxygen deficiency in the chain layer lead to a rotation of the NQR main principal axis at the nearby Cu on the CuO2 planes by 20+-degrees. This occurs with no change to the asymmetry. The axis rotation associated with oxygen deficiency means that there must be electric field inhomogeneities in the CuO2 planes only in the vicinity of the missing oxygen.Comment: 9 pages, 10 figure