Solitons in finite droplets of noncommutative Maxwell-Chern-Simons theory

We find soliton solutions of the noncommutative Maxwell-Chern-Simons theory confined to a finite quantum Hall droplet. The solitons are exactly as hypothesized in \cite{Manu}. We also find new variations on these solitons. We compute their flux and their energies. The model we consider is directly related to the model proposed by Polychronakos\cite{Poly} and studied by Hellerman and Van Raamsdonk\cite{HvR} where it was shown that it is equivalent to the quantum Hall effect.Comment: 18 pages, 7 figures, minor corrections, version accepted for publication, this time really

New Lncs to mesendoderm specification.

Mammalian genomes are pervasively transcribed generating thousands of long noncoding RNAs (lncRNAs) with emergent regulatory roles. Many of these lncRNAs exhibit highly specialised expression patterns during development and typically flank and regulate key developmental factors. In this review, we discuss and summarise the latest advances in our understanding of the roles of lncRNAs during mesendoderm (ME) specification, a key step during gastrulation and the formation of the primitive streak (PS)

Path integration and perturbation theory with complex Euclidean actions

The Euclidean path integral quite often involves an action that is not completely real {\it i.e.} a complex action. This occurs when the Minkowski action contains $t$-odd CP-violating terms. Analytic continuation to Euclidean time yields an imaginary term in the Euclidean action. In the presence of imaginary terms in the Euclidean action, the usual method of perturbative quantization can fail. Here the action is expanded about its critical points, the quadratic part serving to define the Gaussian free theory and the higher order terms defining the perturbative interactions. For a complex action, the critical points are generically obtained at complex field configurations. Hence the contour of path integration does not pass through the critical points and the perturbative paradigm cannot be directly implemented. The contour of path integration has to be deformed to pass through the complex critical point using a generalized method of steepest descent, in order to do so. Typically, what is done is that only the real part of the Euclidean action is considered, and its critical points are used to define the perturbation theory. In this article we present a simple 0+1-dimensional example, of $N$ scalar fields interacting with a U(1) gauge field, in the presence of a Chern-Simons term, where alternatively, the path integral can be done exactly, the procedure of deformation of the contour of path integration can be done explicitly and the standard method of only taking into account the real part of the action can be followed. We show explicitly that the standard method does not give a correct perturbative expansion.Comment: 11 pages, no figures, version to be published in PR

Quasi-hole solutions in finite noncommutative Maxwell-Chern-Simons theory

We study Maxwell-Chern-Simons theory in 2 noncommutative spatial dimensions and 1 temporal dimension. We consider a finite matrix model obtained by adding a linear boundary field which takes into account boundary fluctuations. The pure Chern-Simons has been previously shown to be equivalent to the Laughlin description of the quantum Hall effect. With the addition of the Maxwell term, we find that there exists a rich spectrum of excitations including solitons with nontrivial "magnetic flux" and quasi-holes with nontrivial "charges", which we describe in this article. The magnetic flux corresponds to vorticity in the fluid fluctuations while the charges correspond to sources of fluid fluctuations. We find that the quasi-hole solutions exhibit a gap in the spectrum of allowed charge.Comment: 19+1 pages, 12 figures, colour graphics required, version publishe

Quantum Spacetimes in the Year 1

We review certain emergent notions on the nature of spacetime from noncommutative geometry and their radical implications. These ideas of spacetime are suggested from developments in fuzzy physics, string theory, and deformation quantisation. The review focuses on the ideas coming from fuzzy physics. We find models of quantum spacetime like fuzzy $S^4$ on which states cannot be localised, but which fluctuate into other manifolds like $CP^3$ . New uncertainty principles concerning such lack of localisability on quantum spacetimes are formulated.Such investigations show the possibility of formulating and answering questions like the probabilty of finding a point of a quantum manifold in a state localised on another one. Additional striking possibilities indicated by these developments is the (generic) failure of $CPT$ theorem and the conventional spin-statistics connection. They even suggest that Planck's `` constant '' may not be a constant, but an operator which does not commute with all observables. All these novel possibilities arise within the rules of conventional quantum physics,and with no serious input from gravity physics.Comment: 11 pages, LaTeX; talks given at Utica and Kolkata .Minor corrections made and references adde

Renormalization of the Hamiltonian and a geometric interpretation of asymptotic freedom

Using a novel approach to renormalization in the Hamiltonian formalism, we study the connection between asymptotic freedom and the renormalization group flow of the configuration space metric. It is argued that in asymptotically free theories the effective distance between configuration decreases as high momentum modes are integrated out.Comment: 22 pages, LaTeX, no figures; final version accepted in Phys.Rev.D; added reference and appendix with comment on solution of eq. (9) in the tex

On plane wave and vortex-like solutions of noncommutative Maxwell-Chern-Simons theory

We investigate the spectrum of the gauge theory with Chern-Simons term on the noncommutative plane, a modification of the description of the Quantum Hall fluid recently proposed by Susskind. We find a series of the noncommutative massive ``plane wave'' solutions with polarization dependent on the magnitude of the wave-vector. The mass of each branch is fixed by the quantization condition imposed on the coefficient of the noncommutative Chern-Simons term. For the radially symmetric ansatz a vortex-like solution is found and investigated. We derive a nonlinear difference equation describing these solutions and we find their asymptotic form. These excitations should be relevant in describing the Quantum Hall transitions between plateaus and the end transition to the Hall Insulator.Comment: 17 pages, LaTeX (JHEP), 1 figure, added references, version accepted to JHE

The Fuzzy Disc

We introduce a finite dimensional matrix model approximation to the algebra of functions on a disc based on noncommutative geometry. The algebra is a subalgebra of the one characterizing the noncommutative plane with a * product and depends on two parameters N and theta. It is composed of functions which decay exponentially outside a disc. In the limit in which the size of the matrices goes to infinity and the noncommutativity parameter goes to zero the disc becomes sharper. We introduce a Laplacian defined on the whole algebra and calculate its eigenvalues. We also calculate the two--points correlation function for a free massless theory (Green's function). In both cases the agreement with the exact result on the disc is very good already for relatively small matrices. This opens up the possibility for the study of field theories on the disc with nonperturbative methods. The model contains edge states, a fact studied in a similar matrix model independently introduced by Balachandran, Gupta and Kurkcuoglu.Comment: 17 pages, 8 figures, references added and correcte

Scalar Field Theory on Fuzzy S^4

Scalar fields are studied on fuzzy $S^4$ and a solution is found for the elimination of the unwanted degrees of freedom that occur in the model. The resulting theory can be interpreted as a Kaluza-Klein reduction of CP^3 to S^4 in the fuzzy context.Comment: 16 pages, LaTe

The magnetic mass of transverse gluon, the B-meson weak decay vertex and the triality symmetry of octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse self-dual gluon from three loop diagram, in which a heavy quark pair is created and two self-dual gluons are interchanged. The magnetic mass of the transverse gluon depends on the mass of the pair created quarks, and in the case of charmed quark pair creation, the magnetic mass $m_{mag}$ becomes approximately equal to $T_c$ at $T=T_c\sim 1.14\Lambda_{\bar{MS}}\sim 260$MeV. A possible time-like magnetic gluon mass from two self-dual gluon exchange is derived, and corrections in the B-meson weak decay vertices from the two self-dual gluon exchange are also evaluated.Comment: 22 pages, 9 figure