Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation

Two families of solutions of a generalized non-Abelian Toda lattice are considered. These solutions are expressed in terms of quasideterminants, constructed by means of Darboux and binary Darboux transformations. As an example of the application of these solutions, we consider the 2-periodic reduction to a matrix sine-Gordon equation. In particular, we investigate the interaction properties of polarized kink solutions.Comment: 14 pages; 4 picture

Threshold photoelectron photoion coincidence spectroscopy of trichloroethene and tetrachloroethene

The threshold photoelectron, the threshold photoelectron photoion coincidence and ion breakdown spectra of trichloroethene and tetrachloroethene have been recorded from 9 – 22 eV. Comparisons with the equivalent data for the three dichloroethene molecules and theoretical calculations highlight the nature of the orbitals involved during photoionisation in this energy range. The ground electronic state of C$_2$HCl$_3^+$ (C$_2$Cl$_4^+$) is bound, with excited valence states dissociating to C$_2$HCl$_2^+$ (C$_2$Cl$_3^+$) and C$_2$HCl$^+$ (C$_2$Cl$_2^+$). Appearance energies suggest that C$_2$HCl$^+$ forms from C$_2$HCl$_3^+$ by loss of two chlorine atoms, whereas C$_2$Cl$_2^+$ forms from C$_2$Cl$_4^+$ by loss of a Cl$_2$ molecule. The translational kinetic energy release into C$_2$HCl$_2^+$ (C$_2$Cl$_3^+$) + Cl is determined as a function of energy. In both cases, the fraction of the available energy released into translational energy of the two products decreases as the photon energy increases

Holography of the N=1 Higher-Spin Theory on AdS4

We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory. We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories. We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.Comment: 19 page

Evaluating the AdS dual of the critical O(N) vector model

We argue that the AdS dual of the three dimensional critical O(N) vector model can be evaluated using the Legendre transform that relates the generating functionals of the free UV and the interacting IR fixed points of the boundary theory. As an example, we use our proposal to evaluate the minimal bulk action of the scalar field that it is dual to the spin-zero ``current'' of the O(N) vector model. We find that the cubic bulk self interaction coupling vanishes. We briefly discuss the implications of our results for higher spin theories and comment on the bulk-boundary duality for subleading N.Comment: 17 pages, 1 figure, v2 references added, JHEP versio

Analysis of Higher Spin Field Equations in Four Dimensions

The minimal bosonic higher spin gauge theory in four dimensions contains massless particles of spin s=0,2,4,.. that arise in the symmetric product of two spin 0 singletons. It is based on an infinite dimensional extension of the AdS_4 algebra a la Vasiliev. We derive an expansion scheme in which the gravitational gauge fields are treated exactly and the gravitational curvatures and the higher spin gauge fields as weak perturbations. We also give the details of an explicit iteration procedure for obtaining the field equations to arbitrary order in curvatures. In particular, we highlight the structure of all the quadratic terms in the field equations.Comment: Latex, 30 pages, several clarifications and few references adde

Lessons from QCD2(N→∞)QCD_2 (N\to\infty): Vacuum structure, Asymptotic Series, Instantons and all that

We discuss two dimensional $QCD (N_c\to\infty)$ with fermions in the fundamental as well as adjoint representation. We find factorial growth $\sim (g^2N_c\pi)^{2k}\frac{(2k)!(-1)^{k-1}}{(2 \pi)^{2k}}$ in the coefficients of the large order perturbative expansion. We argue that this behavior is related to classical solutions of the theory, instantons, thus it has nonperturbative origin. Phenomenologically such a growth is related to highly excited states in the spectrum. We also analyze the heavy-light quark system $Q\bar{q}$ within operator product expansion (which it turns out to be an asymptotic series). Some vacuum condensates \la\bar{q}(x_{\mu}D_{\mu})^{2n}q\ra\sim (x^2)^n\cdot n! which are responsible for this factorial growth are also discussed. We formulate some general puzzles which are not specific for 2D physics, but are inevitable features of any asymptotic expansion. We resolve these apparent puzzles within $QCD_2$ and we speculate that analogous puzzles might occur in real 4-dimensional QCD as well.Comment: latex, 26 pages. A final version to appear in Phys. Rev.

Far-infrared photo-conductivity of electrons in an array of nano-structured antidots

We present far-infrared (FIR) photo-conductivity measurements for a two-dimensional electron gas in an array of nano-structured antidots. We detect, resistively and spectrally resolved, both the magnetoplasmon and the edge-magnetoplasmon modes. Temperature-dependent measurements demonstrates that both modes contribute to the photo resistance by heating the electron gas via resonant absorption of the FIR radiation. Influences of spin effect and phonon bands on the collective excitations in the antidot lattice are observed.Comment: 5 pages, 3 figure

Scalar Field Corrections to AdS_4 Gravity from Higher Spin Gauge Theory

We compute the complete contribution to the stress-energy tensor in the minimal bosonic higher spin theory in D=4 that is quadratic in the scalar field. We find arbitrarily high derivative terms, and that the total sign of the stress-energy tensor depends on the parity of the scalar field.Comment: 15 pages + appendix (30 pages

Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings

The correspondences proposed previously between higher spin gauge theories and free singleton field theories were recently extended into a more complete picture by Klebanov and Polyakov in the case of the minimal bosonic theory in D=4 to include the strongly coupled fixed point of the 3d O(N) vector model. Here we propose an N=1 supersymmetric version of this picture. We also elaborate on the role of parity in constraining the bulk interactions, and in distinguishing two minimal bosonic models obtained as two different consistent truncations of the minimal N=1 model that retain the scalar or the pseudo-scalar field. We refer to these models as the Type A and Type B models, respectively, and conjecture that the latter is holographically dual to the 3d Gross-Neveu model. In the case of the Type A model, we show the vanishing of the three-scalar amplitude with regular boundary conditions. This agrees with the O(N) vector model computation of Petkou, thereby providing a non-trivial test of the Klebanov-Polyakov conjecture.Comment: 30p