A Faddeev-Niemi Solution that Does Not Satisfy Gauss' Law

Faddeev and Niemi have proposed a reformulation of SU(2) Yang-Mills theory in terms of a U(1) gauge theory with 8 off-shell degrees of freedom. We present a solution to Faddeev and Niemi's formulation which does not solve the SU(2) Yang-Mills Gauss constraints. This demonstrates that the proposed reformulation is inequivalent to Yang-Mills, but instead describes Yang-Mills coupled to a particular choice of external charge.Comment: 10 pages, no figure

Knots and Particles

Using methods of high performance computing, we have found indications that knotlike structures appear as stable finite energy solitons in a realistic 3+1 dimensional model. We have explicitly simulated the unknot and trefoil configurations, and our results suggest that all torus knots appear as solitons. Our observations open new theoretical possibilities in scenarios where stringlike structures appear, including physics of fundamental interactions and early universe cosmology. In nematic liquid crystals and 3He superfluids such knotted solitons might actually be observed.Comment: 9 pages, 4 color eps figures and one b/w because of size limit (color version available from authors

Nonabelian Faddeev-Niemi Decomposition of the SU(3) Yang-Mills Theory

Faddeev and Niemi (FN) have introduced an abelian gauge theory which simulates dynamical abelianization in Yang-Mills theory (YM). It contains both YM instantons and Wu-Yang monopoles and appears to be able to describe the confining phase. Motivated by the meson degeneracy problem in dynamical abelianization models, in this note we present a generalization of the FN theory. We first generalize the Cho connection to dynamical symmetry breaking pattern SU(N+1) -> U(N), and subsequently try to complete the Faddeev-Niemi decomposition by keeping the missing degrees of freedom. While it is not possible to write an on-shell complete FN decomposition, in the case of SU(3) theory of physical interest we find an off-shell complete decomposition for SU(3) -> U(2) which amounts to partial gauge fixing, generalizing naturally the result found by Faddeev and Niemi for the abelian scenario SU(N+1) -> U(1)^N. We discuss general topological aspects of these breakings, demonstrating for example that the FN knot solitons never exist when the unbroken gauge symmetry is nonabelian, and recovering the usual no-go theorems for colored dyons.Comment: Latex 30 page

Exact vortex solutions in a CP^N Skyrme-Faddeev type model

We consider a four dimensional field theory with target space being CP^N which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP^1. We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x^1+i x^2) and (x^3+x^0) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.Comment: 21 pages, plain latex, no figure

SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls

We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d SL(2,R) Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surface times an interval. On the other side we have a partition function of a 3d N=2 superconformal field theory on S^3, which is realized as a duality domain wall in a 4d gauge theory on S^4. We sketch the proof of this conjecture using connections with quantum Liouville theory and quantum Teichmuller theory, and study in detail the example of the once-punctured torus. Motivated by these results we advocate a direct Chern-Simons interpretation of the ingredients of (a generalization of) the Alday-Gaiotto-Tachikawa relation. We also comment on M5-brane realizations as well as on possible generalizations of our proposals.Comment: 53+1 pages, 14 figures; v2: typos corrected, references adde

Effective Field Theory for Few-Nucleon Systems

We review the effective field theories (EFTs) developed for few-nucleon systems. These EFTs are controlled expansions in momenta, where certain (leading-order) interactions are summed to all orders. At low energies, an EFT with only contact interactions allows a detailed analysis of renormalization in a non-perturbative context and uncovers novel asymptotic behavior. Manifestly model-independent calculations can be carried out to high orders, leading to high precision. At higher energies, an EFT that includes pion fields justifies and extends the traditional framework of phenomenological potentials. The correct treatment of QCD symmetries ensures a connection with lattice QCD. Several tests and prospects of these EFTs are discussed.Comment: 55 pages, 18 figures, to appear in Ann. Rev. Nucl. Part. Sci. 52 (2002

Imaging the formation of a p-n junction in a suspended carbon nanotube with scanning photocurrent microscopy

We use scanning photocurrent microscopy (SPCM) to investigate individual suspended semiconducting carbon nanotube devices where the potential profile is engineered by means of local gates. In situ tunable p-n junctions can be generated at any position along the nanotube axis. Combining SPCM with transport measurements allows a detailed microscopic study of the evolution of the band profiles as a function of the gates voltage. Here we study the emergence of a p-n and a n-p junctions out of a n-type transistor channel using two local gates. In both cases the I-V curves recorded for gate configurations corresponding to the formation of the p-n or n-p junction in the SPCM measurements reveal a clear transition from resistive to rectification regimes. The rectification curves can be fitted well to the Shockley diode model with a series resistor and reveal a clear ideal diode behavior.Comment: Accepted for publication in Journal or Applied Physics. 4 pages, 3 figure

Deformed Skyrme Crystals

The Skyrme crystal, a solution of the Skyrme model, is the lowest energy-per-charge configuration of skyrmions seen so far. Our numerical investigations show that, as the period in various space directions is changed, one obtains various other configurations, such as a double square wall, and parallel vortex-like solutions. We also show that there is a sudden "phase transition" between a Skyrme crystal and the charge 4 skyrmion with cubic symmetry as the period is gradually increased in all three space directions.Comment: 13 pages, 6 figures. To be published in JHE

Symmetries of Snyder--de Sitter space and relativistic particle dynamics

We study the deformed conformal-Poincare symmetries consistent with the Snyder--de Sitter space. A relativistic particle model invariant under these deformed symmetries is given. This model is used to provide a gauge independent derivation of the Snyder--de Sitter algebra. Our results are valid in the leading order in the parameters appearing in the model.Comment: 12 pages, LaTeX, version appearing in JHEP, minor changes to match published versio

Scattering of Giant Holes

We study scalar excitations of high spin operators in N=4 super Yang-Mills theory, which are dual to solitons propagating on a long folded string in AdS_3 x S^1. In the spin chain description of the gauge theory, these are associated to holes in the magnon distribution in the sl(2,R) sector. We compute the all-loop hole S-matrix from the asymptotic Bethe ansatz, and expand in leading orders at weak and strong coupling. The worldsheet S-matrix of solitonic excitations on the GKP string is calculated using semiclassical quantization. We find an exact agreement between the gauge theory and string theory results.Comment: 13 pages. v2: minor corrections, references adde