Contact Terms and Duality Symmetry in The Critical Dissipative Hofstadter Model

The dissipative Hofstadter model describes the quantum mechanics of a charged particle in two dimensions subject to a periodic potential, uniform magnetic field, and dissipative force. Its phase diagram exhibits an SL(2,Z) duality symmetry and has an infinite number of critical circles in the dissipation/magnetic field plane. In addition, multi-critical points on a particular critical circle correspond to non-trivial solutions of open string theory. The duality symmetry is expected to provide relations between correlation functions at different multi-critical points. Many of these correlators are contact terms. However we expect them to have physical significance because under duality they transform into functions that are non-zero for large separations of the operators. Motivated by the search for exact, regulator independent solutions for these contact terms, in this paper we derive many properties and symmetries of the coordinate correlation functions at the special multi-critical points. In particular, we prove that the correlation functions are homogeneous, piecewise-linear functions of the momenta, and we prove a weaker version of the anticipated duality transformation. Consequently, the possible forms of the correlation functions are limited to lie in a finite dimensional linear space. We treat the potential perturbatively and these results are valid to all orders in perturbation theory.Comment: 65 pages, six figures, CTP#217

Canonically quantized soliton in the bound state approach to heavy baryons in the Skyrme model

The bound state extension of Skyrme's topological soliton model for the heavy baryons is quantized canonically in arbitrary reducible representations of the SU(3) flavor group. The canonical quantization leads to an additional negative mass term, which stabilizes the quantized soliton solution. The heavy flavor meson in the field of the soliton is treated with semiclassical quantization. The representation dependence of the calculated spectra for the strange, charm and bottom baryons is explored and compared to the extant empirical spectra.Comment: 13 pages, 8 table

Critical Theories of the Dissipative Hofstadter Model

It has recently been shown that the dissipative Hofstadter model (dissipative quantum mechanics of an electron subject to uniform magnetic field and periodic potential in two dimensions) exhibits critical behavior on a network of lines in the dissipation/magnetic field plane. Apart from their obvious condensed matter interest, the corresponding critical theories represent non-trivial solutions of open string field theory, and a detailed account of their properties would be interesting from several points of view. A subject of particular interest is the dependence of physical quantities on the magnetic field since it, much like $\theta_{\rm QCD}$, serves only to give relative phases to different sectors of the partition sum. In this paper we report the results of an initial investigation of the free energy, $N$-point functions and boundary state of this type of critical theory. Although our primary goal is the study of the magnetic field dependence of these quantities, we will present some new results which bear on the zero magnetic field case as well.Comment: 42 pages (25 reduced

2D Dilaton-Maxwell Gravity as a Fixed Point of the Renormalization Group

A general model of dialton-Maxwell gravity in two dimensions is investigated. The corresponding one-loop effective action and the generalized $\beta$-functions are obtained. A set of models that are fixed points of the renormalization group equations are presented.Comment: 7 pages, LaTeX file, UB-ECM-PF 92/Mar1

Loop Variables and Gauge Invariance in (Open) Bosonic String Theory

We give a simplified and more complete description of the loop variable approach for writing down gauge invariant equations of motion for the fields of the open string. A simple proof of gauge invariance to all orders is given. In terms of loop variables, the interacting equations look exactly like the free equations, but with a loop variable depending on an extra parameter, thus making it a band of finite width. The arguments for gauge invariance work exactly as in the free case. We show that these equations are Wilsonian RG equations with a finite world-sheet cutoff and that in the infrared limit, equivalence with the Callan-Symanzik $\beta$-functions should ensure that they reproduce the on-shell scattering amplitudes in string theory. It is applied to the tachyon-photon system and the general arguments for gauge invariance can be easily checked to the order calculated. One can see that when there is a finite world sheet cutoff in place, even the U(1) invariance of the equations for the photon, involves massive mode contributions. A field redefinition involving the tachyon is required to get the gauge transformations of the photon into standard form.Comment: 20 pages, Late

Heavy quark potential in the instanton liquid model

We study the heavy quark potential in the instanton liquid model by carefully measuring Wilson loops out to a distance of order 3$fm$. A random instanton ensemble with a fixed radius $\rho$ = 1/3$fm$ generates a potential $V(R)$ growing very slowly at large $R$. In contrast, a more realistic size distribution growing as $\rho^6$ at small $\rho$ and decaying as $\rho^{-5}$ at large $\rho$, leads to a potential which grows linearly with $R$. The string tension, however, is only about 1/10 of the phenomenological value.Comment: LATTICE98(confine

Multisensory Integration Sites Identified by Perception of Spatial Wavelet Filtered Visual Speech Gesture Information

Perception of speech is improved when presentation of the audio signal is accompanied by concordant visual speech gesture information. This enhancement is most prevalent when the audio signal is degraded. One potential means by which the brain affords perceptual enhancement is thought to be through the integration of concordant information from multiple sensory channels in a common site of convergence, multisensory integration (MSI) sites. Some studies have identified potential sites in the superior temporal gyrus/sulcus (STG/S) that are responsive to multisensory information from the auditory speech signal and visual speech movement. One limitation of these studies is that they do not control for activity resulting from attentional modulation cued by such things as visual information signaling the onsets and offsets of the acoustic speech signal, as well as activity resulting from MSI of properties of the auditory speech signal with aspects of gross visual motion that are not specific to place of articulation information. This fMRI experiment uses spatial wavelet bandpass filtered Japanese sentences presented with background multispeaker audio noise to discern brain activity reflecting MSI induced by auditory and visual correspondence of place of articulation information that controls for activity resulting from the above-mentioned factors. The experiment consists of a low-frequency (LF) filtered condition containing gross visual motion of the lips, jaw, and head without specific place of articulation information, a midfrequency (MF) filtered condition containing place of articulation information, and an unfiltered (UF) condition. Sites of MSI selectively induced by auditory and visual correspondence of place of articulation information were determined by the presence of activity for both the MF and UF conditions relative to the LF condition. Based on these criteria, sites of MSI were found predominantly in the left middle temporal gyrus (MTG), and the left STG/S (including the auditory cortex). By controlling for additional factors that could also induce greater activity resulting from visual motion information, this study identifies potential MSI sites that we believe are involved with improved speech perception intelligibility

Dirichlet Boundary State in Linear Dilaton Background

Dirichlet-branes have emerged as important objects in studying nonperturbative string theory. It is important to generalize these objects to more general backgrounds other than the usual flat background. The simplest case is the linear dilaton condensate. The usual Dirichlet boundary condition violates conformal invariance in such a background. We show that by switching on a certain boundary interaction, conformal invariance is restored. An immediate application of this result is to two dimensional string theory.Comment: 6 pages, harvmac, some remarks are modified and one reference is added, formulas remain the sam

The More, the Not Marry-Er: In Search of a Policy Behind Eligibility for California Domestic Partnerships

This Comment examines California Assembly Bill 25 which grants certain civic rights to state-registered domestic partners. The author seeks to provide background to the development of the current statutory scheme and examine whether any coherent policy supports the statute\u27s expansion to include greater numbers of opposite-sex couples. The author begins by examining the substantive benefits that California domestic partnerships provide and to whom those benefits are offered. She continues to explore the background of the current domestic partnership scheme in California against the backdrop of the ways that other states have sought to address the needs of nontraditional couples and families. The author then examines the legislative history of Assembly Bill 25 and the possible purposes behind expanding eligibility for domestic partnerships. The author concludes that there is no concrete policy behind such an expansion. She offers suggestions regarding the likely purpose behind this expansion and recommends that other states that wish to follow California\u27s model adopt a clear policy behind eligibility