Chaos Driven Decay of Nuclear Giant Resonances: Route to Quantum Self-Organization

The influence of background states with increasing level of complexity on the strength distribution of the isoscalar and isovector giant quadrupole resonance in $^{40}$Ca is studied. It is found that the background characteristics, typical for chaotic systems, strongly affects the fluctuation properties of the strength distribution. In particular, the small components of the wave function obey a scaling law analogous to self-organized systems at the critical state. This appears to be consistent with the Porter-Thomas distribution of the transition strength.Comment: 14 pages, 4 Figures, Illinois preprint P-93-12-106, Figures available from the author

DLCQ of Fivebranes, Large N Screening, and L^2 Harmonic Forms on Calabi Manifolds

We find one explicit L^2 harmonic form for every Calabi manifold. Calabi manifolds are known to arise in low energy dynamics of solitons in Yang-Mills theories, and the L^2 harmonic form corresponds to the supersymmetric ground state. As the normalizable ground state of a single U(N) instanton, it is related to the bound state of a single D0 to multiple coincident D4's in the non-commutative setting, or equivalently a unit Kaluza-Klein mode in DLCQ of fivebrane worldvolume theory. As the ground state of nonabelian massless monopoles realized around a monopole-``anti''-monopole pair, it shows how the long range force between the pair is screened in a manner reminiscent of large N behavior of quark-anti-quark potential found in AdS/CFT correspondence.Comment: LaTeX, 23 page

Non-Abelian (p,q) Strings in the Warped Deformed Conifold

We calculate the tension of $(p,q)$-strings in the warped deformed conifold using the non-Abelian DBI action. In the large flux limit, we find exact agreement with the recent expression obtained by Firouzjahi, Leblond and Henry-Tye up to and including order $1/M^2$ terms if $q$ is also taken to be large. Furthermore using the finite $q$ prescription for the symmetrised trace operation we anticipate the most general expression for the tension valid for any $(p,q)$. We find that even in this instance, corrections to the tension scale as $1/M^2$ which is not consistent with simple Casimir scaling.Comment: 18 pages, Latex, 1 figure; Added a discussion of the case when the warp factor parameter $b\neq 1$ and typos correcte

BPS Electromagnetic Waves on Giant Gravitons

We find new 1/8-BPS giant graviton solutions in $AdS_5 \times S^5$, carrying three angular momenta along $S^5$, and investigate their properties. Especially, we show that nonzero worldvolume gauge fields are admitted preserving supersymmetry. These gauge field modes can be viewed as electromagnetic waves along the compact D3 brane, whose Poynting vector contributes to the BPS angular momenta. We also analyze the (nearly-)spherical giant gravitons with worldvolume gauge fields in detail. Expressing the $S^3$ in Hopf fibration ($S^1$ fibred over $S^2$), the wave propagates along the $S^1$ fiber.Comment: 25 pages, no figures, v2: references adde

Electrified Fuzzy Spheres and Funnels in Curved Backgrounds

We use the non-Abelian DBI action to study the dynamics of $N$ coincident $Dp$-branes in an arbitrary curved background, with the presence of a homogenous world-volume electric field. The solutions are natural extensions of those without electric fields, and imply that the spheres will collapse toward zero size. We then go on to consider the $D1-D3$ intersection in a curved background and find various dualities and automorphisms of the general equations of motion. It is possible to map the dynamical equation of motion to the static one via Wick rotation, however the additional spatial dependence of the metric prevents this mapping from being invertible. Instead we find that a double Wick rotation leaves the static equation invariant. This is very different from the behaviour in Minkowski space. We go on to construct the most general static fuzzy funnel solutions for an arbitrary metric either by solving the static equations of motion, or by finding configurations which minimise the energy. As a consistency check we construct the Abelian $D3$-brane world-volume theory in the same generic background and find solutions consistent with energy minimisation. In the $NS$5-brane background we find time dependent solutions to the equations of motion, representing a time dependent fuzzy funnel. These solutions match those obtained from the $D$-string picture to leading order suggesting that the action in the large $N$ limit does not need corrections. We conclude by generalising our solutions to higher dimensional fuzzy funnels.Comment: 38 pages, Latex; references adde

Singularities and closed time-like curves in type IIB 1/2 BPS geometries

We study in detail the moduli space of solutions discovered in LLM relaxing the constraint that guarantees the absence of singularities. The solutions fall into three classes, non-singular, null-singular and time machines with a time-like naked singularity. We study the general features of these metrics and prove that there are actually just two generic classes of space-times - those with null singularities are in the same class as the non-singular metrics. AdS/CFT seems to provide a dual description only for the first of these two types of space-time in terms of a unitary CFT indicating the possible existence of a chronology protection mechanism for this class of geometries.Comment: 34 pages, 7 figures, LaTeX. References adde

Vortices, Instantons and Branes

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a U(k) gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities shared by quantum field theories in two and four dimensions.Comment: 32 Pages, 4 Figure

Demagnetization via Nucleation of the Nonequilibrium Metastable Phase in a Model of Disorder

We study both analytically and numerically metastability and nucleation in a two-dimensional nonequilibrium Ising ferromagnet. Canonical equilibrium is dynamically impeded by a weak random perturbation which models homogeneous disorder of undetermined source. We present a simple theoretical description, in perfect agreement with Monte Carlo simulations, assuming that the decay of the nonequilibrium metastable state is due, as in equilibrium, to the competition between the surface and the bulk. This suggests one to accept a nonequilibrium "free-energy" at a mesoscopic/cluster level, and it ensues a nonequilibrium "surface tension" with some peculiar low-T behavior. We illustrate the occurrence of intriguing nonequilibrium phenomena, including: (i) Noise-enhanced stabilization of nonequilibrium metastable states; (ii) reentrance of the limit of metastability under strong nonequilibrium conditions; and (iii) resonant propagation of domain walls. The cooperative behavior of our system may also be understood in terms of a Langevin equation with additive and multiplicative noises. We also studied metastability in the case of open boundaries as it may correspond to a magnetic nanoparticle. We then observe burst-like relaxation at low T, triggered by the additional surface randomness, with scale-free avalanches which closely resemble the type of relaxation reported for many complex systems. We show that this results from the superposition of many demagnetization events, each with a well- defined scale which is determined by the curvature of the domain wall at which it originates. This is an example of (apparent) scale invariance in a nonequilibrium setting which is not to be associated with any familiar kind of criticality.Comment: 26 pages, 22 figure