Comments on Noncommutative Sigma Models

We review the derivation of a noncommutative version of the nonlinear sigma model on \CPn and it's soliton solutions for finite $\theta$ emphasizing the similarities it bears to the GMS scalar field theory. It is also shown that unlike the scalar theory, some care needs to be taken in defining the topological charge of BPS solitons of the theory due to nonvanishing surface terms in the energy functional. Finally it is shown that, like its commutative analogue, the noncommutative \CPn-model also exhibits a non-BPS sector. Unlike the commutative case however, there are some surprises in the noncommutative case that merit further study.Comment: 22 pages, 4 figures, LaTeX (JHEP3), Minor changes, Discussion expanded and references adde

Quasi-localized states on noncommutative solitons

We consider noncommutative gauge theories which have zero mass states propagating along both commutative and noncommutative dimensions. Solitons in these theories generically carry U(m) gauge group on their world-volume. From the point of view of string theory, these solitons correspond to ``branes within branes''. We show that once the world-volume U(m) gauge theory is in the Higgs phase, light states become quasi-localized, rather than strictly localized on the soliton, i.e. they mix with light bulk modes and have finite widths to escape into the noncommutative dimensions. At small values of U(m) symmetry breaking parameters, these widths are small compared to the corresponding masses. Explicit examples considered are adjoint scalar field in the background of a noncommutative vortex in U(1)-Higgs theory, and gauge fields in instanton backgrounds in pure gauge noncommutative theories.Comment: 27 pages, references and comments added, final version to appear in JHE

Transmogrifying Fuzzy Vortices

We show that the construction of vortex solitons of the noncommutative Abelian-Higgs model can be extended to a critically coupled gauged linear sigma model with Fayet-Illiopolous D-terms. Like its commutative counterpart, this fuzzy linear sigma model has a rich spectrum of BPS solutions. We offer an explicit construction of the degree$-k$ static semilocal vortex and study in some detail the infinite coupling limit in which it descends to a degree$-k$ \C\Pk^{N} instanton. This relation between the fuzzy vortex and noncommutative lump is used to suggest an interpretation of the noncommutative sigma model soliton as tilted D-strings stretched between an NS5-brane and a stack of D3-branes in type IIB superstring theory.Comment: 21 pages, 4 figures, LaTeX(JHEP3

Bogomolny equations for vortices in the noncommutative torus

We derive Bogomolny-type equations for the Abelian Higgs model defined on the noncommutative torus and discuss its vortex like solutions. To this end, we carefully analyze how periodic boundary conditions have to be handled in noncommutative space and discussed how vortex solutions are constructed. We also consider the extension to an $U(2)\times U(1)$ model, a simplified prototype of the noncommutative standard model.Comment: 23 pages, no figure

Scalar Solitons on the Fuzzy Sphere

We study scalar solitons on the fuzzy sphere at arbitrary radius and noncommutativity. We prove that no solitons exist if the radius is below a certain value. Solitons do exist for radii above a critical value which depends on the noncommutativity parameter. We construct a family of soliton solutions which are stable and which converge to solitons on the Moyal plane in an appropriate limit. These solutions are rotationally symmetric about an axis and have no allowed deformations. Solitons that describe multiple lumps on the fuzzy sphere can also be constructed but they are not stable.Comment: 24 pages, 2 figures, typo corrected and stylistic changes. v3: reference adde

Exact noncommutative solitons in p-adic strings and BSFT

The tachyon field of p-adic string theory is made noncommutative by replacing ordinary products with noncommutative products in its exact effective action. The same is done for the boundary string field theory, treated as the p -> 1 limit of the p-adic string. Solitonic lumps corresponding to D-branes are obtained for all values of the noncommutative parameter theta. This is in contrast to usual scalar field theories in which the noncommutative solitons do not persist below a critical value of theta. As theta varies from zero to infinity, the solution interpolates smoothly between the soliton of the p-adic theory (respectively BSFT) to the noncommutative soliton.Comment: 1+14 pages (harvmac b), 1 eps figure, v2: references added, typos correcte

Two-group randomised, parallel trial of cognitive and exposure therapies for problem gambling: a research protocol

BACKGROUND: Problem gambling is a serious public health concern at an international level where population prevalence rates average 2% or more and occurs more frequently in younger populations. The most empirically established treatments until now are combinations of cognitive and behavioural techniques labelled cognitive behaviour therapy (CBT). However, there is a paucity of high quality evidence for the comparative efficacy of core CBT interventions in treating problem gamblers. This study aims to isolate and compare cognitive and behavioural (exposure-based) techniques to determine their relative efficacy. METHODS: A sample of 130 treatment-seeking problem gamblers will be allocated to either cognitive or exposure therapy in a two-group randomised, parallel design. Repeated measures will be conducted at baseline, mid and end of treatment (12 sessions intervention period), and at 3, 6 and 12 months (maintenance effects). The primary outcome measure is improvement in problem gambling severity symptoms using the Victorian Gambling Screen (VGS) harm to self-subscale. VGS measures gambling severity on an extensive continuum, thereby enhancing sensitivity to change within and between individuals over time. DISCUSSION: This article describes the research methods, treatments and outcome measures used to evaluate gambling behaviours, problems caused by gambling and mechanisms of change. This study will be the first randomised, parallel trial to compare cognitive and exposure therapies in this population. ETHICS AND DISSEMINATION: The study was approved by the Southern Adelaide Health Service/Flinders University Human Research Ethics Committee. Study findings will be disseminated through peer-reviewed publications and conference presentations. TRIAL REGISTRATION: Australian New Zealand Clinical Trials Registry: ACTRN 12610000828022.David P Smith, Malcolm W Battersby, Peter W Harvey, Rene G Pols, Robert Ladouceu

Non BPS noncommutative vortices

We construct exact vortex solutions to the equations of motion of the Abelian Higgs model defined in non commutative space, analyzing in detail the properties of these solutions beyond the BPS point. We show that our solutions behave as smooth deformations of vortices in ordinary space time except for parity symmetry breaking effects induced by the non commutative parameter $\theta$.Comment: 17 pages, 5 figure

D0 Matrix Mechanics: New Fuzzy Solutions at Large N

We wish to consider in this report the large N limit of a particular matrix model introduced by Myers describing D-brane physics in the presence of an RR flux background. At finite N, fuzzy spheres appear naturally as non-trivial solutions to this matrix model and have been extensively studied. In this report, we wish to demonstrate several new classes of solutions which appear in the large N limit, corresponding to the fuzzy cylinder,the fuzzy plane and a warped fuzzy plane. The latter two solutions arise from a possible "central extension" to our model that arises after we account for non-trivial issues involved in the large N limit. As is the case for finite N, these new solutions are to be interpreted as constituent D0-branes forming D2 bound states describing new fuzzy geometries.Comment: revised version: references added, derivation of "central extensions" improved upon. To appear in JHE

Tachyon Condensation of D2/D4-Brane System in Noncommutative Gauge Theory

In this paper we construct the 2+1 effective theory of the light states in D2/D4-brane system in the context of noncommutative Yang-Mills theory. This effective theory is noncommutative and tachyonic, however, it is not taking the form of an Abelian Higgs model as naively expected. We solve the classical solutions of the effective theory which are nicely corresponding to different states during the tachyon condensation process of the dissolution of D2-brane into D4-brane. We also find that if the expected stable self-dual D0/D4 configuration as the unit-winding vortex exists, it would be highly calibrated in the effective theory and be out of the reach of the analytic solutions.Comment: 16 pages, no figure, Latex, uses JHEP.cls; revised version, more classical solutions added, some arguments improved in secion 4, typos corrected; 3rd version, more clarifications on classical solutions in section 4; 4th version, more careful analysis on classical soution