On the short-distance structure of irrational non-commutative gauge theories

As shown by Hashimoto and Itzhaki in hep-th/9911057, the perturbative degrees of freedom of a non-commutative Yang-Mills theory (NCYM) on a torus are quasi-local only in a finite energy range. Outside that range one may resort to a Morita equivalent (or T-dual) description appropriate for that energy. In this note, we study NCYM on a non-commutative torus with an irrational deformation parameter $\theta$. In that case, an infinite tower of dual descriptions is generically needed in order to describe the UV regime. We construct a hierarchy of dual descriptions in terms of the continued fraction approximations of $\theta$. We encounter different descriptions depending on the level of the irrationality of $\theta$ and the amount of non-locality tolerated. The behavior turns out to be isomorphic to that found for the phase structure of the four-dimensional Villain $Z_N$ lattice gauge theories, which we revisit as a warm-up. At large 't Hooft coupling, using the AdS/CFT correspondance, we find that there are domains of the radial coordinate $U$ where no T-dual description makes the derivative expansion converge. The radial direction obtains multifractal characteristics near the boundary of AdS.Comment: 17 pages, 4 figures, uses JHEP.cl

On canonical quantization of the gauged WZW model with permutation branes

In this paper we perform canonical quantization of the product of the gauged WZW models on a strip with boundary conditions specified by permutation branes. We show that the phase space of the $N$-fold product of the gauged WZW model $G/H$ on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of the double Chern-Simons theory on a sphere with $N$ holes times the time-line with $G$ and $H$ gauge fields both coupled to two Wilson lines. For the special case of the topological coset $G/G$ we arrive at the conclusion that the phase space of the $N$-fold product of the topological coset $G/G$ on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of Chern-Simons theory on a Riemann surface of the genus $N-1$ times the time-line with four Wilson lines.Comment: 18 page

Observational evidence for the shrinking of bright maser spots

The nature of maser emission means that the apparent angular size of an individual maser spot is determined by the amplification process as well as by the instrinsic size of the emitting cloud. Highly sensitive MERLIN radio interferometry images spatially and spectrally resolve water maser clouds around evolved stars. We measured the properties of clouds around the red supergiant S Per and the AGB stars IK Tau, RT Vir, U Her and U Ori, to test maser beaming theory. Spherical clouds are expected to produce an inverse relationship between maser intensity and apparent size, which would not be seen from cylindrical or slab-like regions. We analysed the maser properties, in order to estimate the saturation state, and investigated the variation of observed spot size with intensity and across the spectral line profiles. Circumstellar masers emanate from discrete clouds from about one to 20 AU in diameter depending on the star. Most of the maser features have negative excitation temperatures close to zero and modest optical depths, showing that they are mainly unsaturated. Around S Per and (at most epochs) RT Vir and IK Tau, the maser component size shrinks with increasing intensity. In contrast, the masers around U Ori and U Her tend to increase in size, with a larger scatter. The water masers from S Per, RT Vir and IK Tau are mainly beamed into spots with an observed angular size much smaller than the emitting clouds and smallest of all at the line peaks. This suggests that the masers are amplification-bounded, emanating from approximately spherical clouds. Many of the masers around U Her and U Ori have apparent sizes which are more similar to the emitting clouds and have less or no dependence on intensity, suggesting that these masers are matter-bounded. This is consistent with an origin in flattened clouds and these two stars have shown other behaviour indicating the presence of shocks.Comment: 17 pages, 26 figure files, accepted by A&A 2010 Oct 2

On Induced Gravity in 2-d Topological Theories

We study 2-d $\phi F$ gauge theories with the objective to understand, also at the quantum level, the emergence of induced gravity. The wave functionals - representing the eigenstates of a vanishing flat potential - are obtained in the $\phi$ representation. The composition of the space they describe is then analyzed: the state corresponding to the singlet representation of the gauge group describes a topological universe. For other representations a metric which is invariant under the residual gauge group is induced, apart from possible topological obstructions. Being inherited from the group metric it is rather rigid.Comment: 38, tex, 160/93/e

Nonlocal Effects of Partial Measurements and Quantum Erasure

Partial measurement turns the initial superposition not into a definite outcome but into a greater probability for it. The probability can approach 100%, yet the measurement can undergo complete quantum erasure. In the EPR setting, we prove that i) every partial measurement nonlocally creates the same partial change in the distant particle; and ii) every erasure inflicts the same erasure on the distant particle's state. This enables an EPR experiment where the nonlocal effect does not vanish after a single measurement but keeps "traveling" back and forth between particles. We study an experiment in which two distant particles are subjected to interferometry with a partial "which path" measurement. Such a measurement causes a variable amount of correlation between the particles. A new inequality is formulated for same-angle polarizations, extending Bell's inequality for different angles. The resulting nonlocality proof is highly visualizable, as it rests entirely on the interference effect. Partial measurement also gives rise to a new form of entanglement, where the particles manifest correlations of multiple polarization directions. Another novelty in that the measurement to be erased is fully observable, in contrast to prevailing erasure techniques where it can never be observed. Some profound conceptual implications of our experiment are briefly pointed out.Comment: To be published in Phys. Rev. A 63 (2001). 19 pages, 12 figures, RevTeX 3.

A Circumstellar Disc in a High-Mass Star Forming Region

We present an edge-on Keplerian disc model to explain the main component of the 12.2 and 6.7 GHz methanol maser emission detected toward NGC7538-IRS1 N. The brightness distribution and spectrum of the line of bright masers are successfully modeled with high amplification of background radio continuum emission along velocity coherent paths through a maser disc. The bend seen in the position-velocity diagram is a characteristic signature of differentially rotating discs. For a central mass of 30 solar masses, suggested by other observations, our model fixes the masing disc to have inner and outer radii of about 350 AU and 1000 AU.Comment: 11 pages, accepted for publication in ApJ Letter

Lattice Supersymmetry and Topological Field Theory

It is known that certain theories with extended supersymmetry can be discretized in such a way as to preserve an exact fermionic symmetry. In the simplest model of this kind, we show that this residual supersymmetric invariance is actually a BRST symmetry associated with gauge fixing an underlying local shift symmetry. Furthermore, the starting lattice action is then seen to be entirely a gauge fixing term. The corresponding continuum theory is known to be a topological field theory. We look, in detail, at one example - supersymmetric quantum mechanics which possesses two such BRST symmetries. In this case, we show that the lattice theory can be obtained by blocking out of the continuum in a carefully chosen background metric. Such a procedure will not change the Ward identities corresponding to the BRST symmetries since they correspond to topological observables. Thus, at the quantum level, the continuum BRST symmetry is preserved in the lattice theory. Similar conclusions are reached for the two-dimensional complex Wess-Zumino model and imply that all the supersymmetric Ward identities are satisfied {\it exactly} on the lattice. Numerical results supporting these conclusions are presented.Comment: 18 pages, 2 figure

Exact Lattice Supersymmetry: the Two-Dimensional N=2 Wess-Zumino Model

We study the two-dimensional Wess-Zumino model with extended N=2 supersymmetry on the lattice. The lattice prescription we choose has the merit of preserving {\it exactly} a single supersymmetric invariance at finite lattice spacing $a$. Furthermore, we construct three other transformations of the lattice fields under which the variation of the lattice action vanishes to $O(ga^2)$ where $g$ is a typical interaction coupling. These four transformations correspond to the two Majorana supercharges of the continuum theory. We also derive lattice Ward identities corresponding to these exact and approximate symmetries. We use dynamical fermion simulations to check the equality of the massgaps in the boson and fermion sectors and to check the lattice Ward identities. At least for weak coupling we see no problems associated with a lack of reflection positivity in the lattice action and find good agreement with theory. At strong coupling we provide evidence that problems associated with a lack of reflection positivity are evaded for small enough lattice spacing.Comment: 29 pages, 10 figures. New results at strong coupling added. Minor corrections to text and one reference added. Version to appear in Phys. Rev.

The solution to Wheeler-DeWitt is eight

We describe a new geometrical solution to the Wheeler-DeWitt equation in two dimensional quantum gravity. The solution is the amplitude of a surface whose boundary consists of two tangent loops. We further discuss a new method for estimating singular geometries amplitudes, which uses explicit recursive counting of discrete surfaces.Comment: 10 tex pages + 5 ps figure

Weak Measurement of the Arrival Times of Single Photons and Pairs of Entangled Photons

In this paper we propose a setup for the weak measurement of photon arrival time. It is found that the weak values of this arrival time can lie far away from the expectation value, and in principle also in regions forbidden by special relativity. We discuss in brief the implications of these results as well as their reconciliation with the principle of causality. Furthermore, an analysis of the weak arrival times of a pair of photons in a Bell state shows that these weak arrival times are correlated.Comment: 4 pages, 1 figur