Energy and the AdS/CFT correspondence

We consider a scalar field theory on AdS in both minimally and non-minimally coupled cases. We show that there exist constraints which arise in the quantization of the scalar field theory on AdS which cannot be reproduced through the usual AdS/CFT prescription. We argue that the usual energy, defined through the stress-energy tensor, is not the natural one to be considered in the context of the AdS/CFT correspondence. We analyze a new definition of the energy which makes use of the Noether current corresponding to time displacements in global coordinates. We compute the new energy for Dirichlet, Neumann and mixed boundary conditions on the scalar field and for both the minimally and non-minimally coupled cases. Then, we perform the quantization of the scalar field theory on AdS showing that, for 'regular' and 'irregular' modes, the new energy is conserved, positive and finite. We show that the quantization gives rise, in a natural way, to a generalized AdS/CFT prescription which maps to the boundary all the information contained in the bulk. In particular, we show that the divergent local terms of the on-shell action contain information about the Legendre transformed generating functional, and that the new constraints for which the irregular modes propagate in the bulk are the same constraints for which such divergent local terms cancel out. In this situation, the addition of counterterms is not required. We also show that there exist particular cases for which the unitarity bound is reached, and the conformai dimension becomes independent of the effective mass. This phenomenon has no bulk counterpart.

A joint theoretical and kinetic investigation on the fragmentation of (N-halo)-2-amino cycloalkanecarboxylates

A combined theoretical and experimental study to elucidate the molecular mechanism for the Grob fragmentation of different (N-halo)-2-amino cyclocarboxylates with the nitrogen atom in exocyclic position: (N-Cl)-2-amino cyclopropanecarboxylate (1), (N-Cl)-2-amino cyclobutanecarboxylate (2), (N-Cl)-2-amino cyclopentanecarboxylate (3) and (N-Cl)-2-amino cyclohexanecarboxylate (4), and the corresponding acyclic compounds, (N-Cl)-2-amino isobutyric acid (A), (N-Cl)-2-amino butyric acid (B), has been carried out. The kinetics of decomposition for these compounds and related bromine derivatives were experimentally determined by conventional and stopped-flow UV spectrophotometry. The reaction products have been analyzed by GC and spectrophotometry. Theoretical analysis is based in the localization of stationary points (reactants and transition structures) on the potential energy surface. Calculations were carried out at B3LYP/6-31+G* and MP2/6-31+G* computing methods in the gas phase, while solvent effects have been included by means the self-consistent reaction field theory, PCM continuum model, at MP2/6-31+G* and MP4/6-31+G*//MP2/6-31+G* calculation levels. Based on both experimental and theoretical results, the different Grob fragmentation processes show a global synchronicity index close to 0.9, corresponding to a nearly concerted process. At the TSs, the N-Cl bond breaking is more advanced than the C-C cleavage process. An antiperiplanar configuration of these bonds is reached at the TSs, and this geometrical arrangement is the key factor governing the decomposition. In the case of 1 and 2 the ring strain prevents this spatial disposition, leading to a larger value of the activation barrier. Natural population analysis shows that the polarization of the N-Cl and C-C bonds along the bond-breaking process can be considered the driving force for the decomposition and that a negative charge flows from the carboxylate group to the chlorine atom to assist the reaction pathway. A comparison of theoretical and experimental results shows the relevance of calculation level and the inclusion of solvent effects for determining accurate unimolecular rate coefficients for the decomposition process. © 2002 Published by Elsevier Science B.V.

N = 2 sigma models for Ramond-Ramond backgrounds

Using the U(4) hybrid formalism, manifestly N = (2,2) worldsheet supersymmetric sigma models are constructed for the type-IIB superstring in Ramond-Ramond backgrounds. The Kahler potential in these N = 2 sigma models depends on four chiral and antichiral bosonic superfields and two chiral and antichiral fermionic superfields. When the Kahler potential is quadratic, the model is a free conformal field theory which describes a flat ten-dimensional target space with Ramond-Ramond flux and non-constant dilaton. For more general Kahler potentials, the model describes curved target spaces with Ramond-Ramond flux that are not plane-wave backgrounds. Ricci-flatness of the Kahler metric implies the on-shell conditions for the background up to the usual four-loop conformal anomaly. © SISSA/ISAS 2002.

Dynamics of a collapsing and exploding Bose-Einstein condensed vortex state

The dynamics of small repulsive Bose-Einstein condensed vortex states of 85Rb atoms in a cylindrical traps with low angular momentum was studied. The time-dependent mean-field Gross-Pitaevskii equation was used for the study. The condensates collapsed and atoms ejected via explosion and a remnant condensate with a smaller number of atoms emerges that survived for a long time.

On the role of boundary terms in the AdS/CFT correspondence

We consider a scalar field theory on AdS, and show that the usual AdS/CFT prescription is unable to map to the boundary a part of the information arising from the quantization in the bulk. We propose a solution to this problem by defining the energy of the theory in the bulk through the Noether current corresponding to time displacements, and, in addition, by introducing a proper generalized AdS/CFT prescription. We also show how this extended formulation could be used to consistently describe double-trace interactions in the boundary. The formalism is illustrated by focusing on the non-minimally coupled case using Dirichlet boundary conditions. © 2004 Published by Elsevier B.V.

Euclidean 4d exact solitons in a Skyrme type model

We introduce a Skyrme type, four-dimensional Euclidean field theory made of a triplet of scalar fields n→, taking values on the sphere S2, and an additional real scalar field φ, which is dynamical only on a three-dimensional surface embedded in R4. Using a special ansatz we reduce the 4d non-linear equations of motion into linear ordinary differential equations, which lead to the construction of an infinite number of exact soliton solutions with vanishing Euclidean action. The theory possesses a mass scale which fixes the size of the solitons in way which differs from Derrick's scaling arguments. The model may be relevant to the study of the low energy limit of pure SU(2) Yang-Mills theory. © 2004 Elsevier B.V. All rights reserved.

Pure spinor formalism as an N ≤ 2 topological string

Following suggestions of Nekrasov and Siegel, a non-minimal set of fields are added to the pure spinor formalism for the superstring. Twisted ĉ ≤ 3 N ≤ 2 generators are then constructed where the pure spinor BRST operator is the fermionic spin-one generator, and the formalism is interpreted as a critical topological string. Three applications of this topological string theory include the super-Poincaré covariant computation of multiloop superstring amplitudes without picture-changing operators, the construction of a cubic open superstring field theory without contact-term problems, and a new four-dimensional version of the pure spinor formalism which computes F-terms in the spacetime action. © SISSA 2005.

Improved Langevin approach to spinodal decomposition in the chiral transition

We use an improved Langevin description that incorporates both additive and multiplicative noise terms to study the dynamics of phase ordering. We perform real-time lattice simulations to investigate the role played by different contributions to the dissipation and noise. Lattice-size independence is assured by the use of appropriate lattice counterterms. © 2006 American Institute of Physics.

Spinning Hopf solitons on S3 × ℝ

We consider a field theory with target space being the two dimensional sphere S2 and defined on the space-time S3 × . The Lagrangean is the square of the pull-back of the area form on S2. It is invariant under the conformal group SO(4,2) and the infinite dimensional group of area preserving diffeomorphisms of S2. We construct an infinite number of exact soliton solutions with non-trivial Hopf topological charges. The solutions spin with a frequency which is bounded above by a quantity proportional to the inverse of the radius of S3. The construction of the solutions is made possible by an ansatz which explores the conformal symmetry and a U(1) subgroup of the area preserving diffeomorphism group. © SISSA 2006.

Antinucleon spectra in the Dirac equation with scalar and vector Wood-Saxon potentials

We analyze here the spin and pseudospin symmetry for the antinucleon spectra solving the Dirac equation with scalar and vector Wood-Saxon potentials. In relativistic nuclear mean field theories where these potentials have large magnitudes and opposite signs we show that contrary to the nucleon case where pseudospin interaction is never very small and cannot be treated perturbatively, for antinucleon systems this interaction is perturbative and an exact pseudospin symmetry is possible. This result manifests the relativistic nature of the nuclear pseudospin symmetry. © 2009 American Institute of Physics.

Nonpertubative solutions of massless gauged thirring model

We present a nonperturbative quantization of the two-dimensional massless gauged Thirring model by using the path-integral approach. First, we will study the constraint structure of model via the Dirac's formalism and by using the Faddeev-Senjanovic method we calculate the vacuum-vacuum transition amplitude in a Rξ-gauge, then we compute the Green's functions in a nonperturbative framework. © 2010 American Institute of Physics.

Bifundamental fuzzy 2-Sphere and fuzzy killing spinors

We review our construction of a bifundamental version of the fuzzy 2-sphere and its relation to fuzzy Killing spinors, first obtained in the context of the ABJM membrane model. This is shown to be completely equivalent to the usual (adjoint) fuzzy sphere. We discuss the mathematical details of the bifundamental fuzzy sphere and its field theory expansion in a model-independent way. We also examine how this new formulation affects the twisting of the fields, when comparing the field theory on the fuzzy sphere background with the compactification of the 'deconstructed' (higher dimensional) field theory.

Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski- reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a MaxwellCattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles. © 2011 Elsevier B.V. All rights reserved.

Dipolar droplet bound in a trapped Bose-Einstein condensate

We study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by interspecies contact interaction in a trapped nondipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar 164Dy droplet bound in a trapped nondipolar 87Rb BEC with a variable number of 164Dy atoms and interspecies scattering length. A trapped nondipolar BEC of a fixed number of atoms can bind only a dipolar droplet containing fewer atoms than a critical number for the interspecies scattering length between two critical values. The shape and size (statics) as well as the small breathing oscillation (dynamics) of the dipolar BEC droplet are studied using numerical and variational solutions of a mean-field model. We also suggest an experimental procedure for achieving such a 164Dy droplet by relaxing the trap on the 164Dy BEC in a trapped binary 87Rb-164Dy mixture. © 2013 American Physical Society.

Nilpotent orbits and codimension-2 defects of 6d N = (2, 0)theories

We study the local properties of a class of codimension-2 defects of the 6d N = (2, 0) theories of type J = A, D, E labeled by nilpotent orbits of a Lie algebra $g, where g is determined by J and the outer-automorphism twist around the defect. This class is a natural generalization of the defects of the six-dimensional (6d) theory of type SU(N) labeled by a Young diagram with N boxes. For any of these defects, we determine its contribution to the dimension of the Higgs branch, to the Coulomb branch operators and their scaling dimensions, to the four-dimensional (4d) central charges a and c and to the flavor central charge k. © 2013 World Scientific Publishing Company.