Current Algebra of Classical Non-Linear Sigma Models

The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current $j_\mu$ associated with the global symmetry of the theory, a composite scalar field $j$, the algebra closes under Poisson brackets.Comment: 6 page

Effect of breed on meat quality and global acceptance of native lambs and their crosses

International projections point to the growth in global production of sheep meat, mainly from developing countries. However, the exigencies of consumers on characterization of production systems, nutritional information, and sensorial analysis to target the preferences must be answered. The aim of this study was to characterize the meat quality and the global acceptance of Brazilian native ovine breeds and their crosses, and discuss these aspects on the current basis of human health and wellbeing. Three native breeds (Morada Nova, Rabo Largo, and Santa Inês) that were managed in semi-intensive systems and raised in semi-arid Brazilian regions were used. Chemical composition and fatty acid analysis, sensory evaluation and health indices were accessed. The combined effects of breed, sex and breed by sex interaction produced differentiation in meat fatty acid (FA) profiles. The cholesterol contents ranged between 51 and 59.1 mg/100 g. The Morada Nova lambs showed the lowest lipid content (1.93%). The Morada Nova x Rabo Largo crossbreed breed has the potential to increase the content of conjugated linoleic acid. The high content of α-linolenic acid, which is considered hypocholesterolemic, was responsible for better health indices. The moderate acceptability obtained in sensory traits is compatible with the requirements of the consumer market. The combination of nutritional and sensory traits associated with human health and wellbeing that is presented by these native ovine breeds qualifies them as a good choice of red meat to be included in a larger proportion in human food. Keywords: fatty acids, healthier meat, semi-arid region, shee

Matching Higher Conserved Charges for Strings and Spins

We demonstrate that the recently found agreement between one-loop scaling dimensions of large dimension operators in N=4 gauge theory and energies of spinning strings on AdS_5 x S^5 extends to the eigenvalues of an infinite number of hidden higher commuting charges. This dynamical agreement is of a mathematically highly intricate and non-trivial nature. In particular, on the gauge side the generating function for the commuting charges is obtained by integrable quantum spin chain techniques from the thermodynamic density distribution function of Bethe roots. On the string side the generating function, containing information to arbitrary loop order, is constructed by solving exactly the Backlund equations of the integrable classical string sigma model. Our finding should be an important step towards matching the integrable structures on the string and gauge side of the AdS/CFT correspondence.Comment: Latex, 33 pages, v2: new section added (completing the analytic proof that the entire infinite towers of commuting gauge and string charges match); references adde

Strings in Homogeneous Background Spacetimes

The string equations of motion for some homogeneous (Kantowski-Sachs, Bianchi I and Bianchi IX) background spacetimes are given, and solved explicitly in some simple cases. This is motivated by the recent developments in string cosmology, where it has been shown that, under certain circumstances, such spacetimes appear as string-vacua. Both tensile and null strings are considered. Generally, it is much simpler to solve for the null strings since then we deal with the null geodesic equations of General Relativity plus some additional constraints. We consider in detail an ansatz corresponding to circular strings, and we discuss the possibility of using an elliptic-shape string ansatz in the case of homogeneous (but anisotropic) backgrounds.Comment: 25 pages, REVTE

The Bethe-Ansatz for N=4 Super Yang-Mills

We derive the one loop mixing matrix for anomalous dimensions in N=4 Super Yang-Mills. We show that this matrix can be identified with the Hamiltonian of an integrable SO(6) spin chain with vector sites. We then use the Bethe ansatz to find a recipe for computing anomalous dimensions for a wide range of operators. We give exact results for BMN operators with two impurities and results up to and including first order 1/J corrections for BMN operators with many impurities. We then use a result of Reshetikhin's to find the exact one-loop anomalous dimension for an SO(6) singlet in the limit of large bare dimension. We also show that this last anomalous dimension is proportional to the square root of the string level in the weak coupling limit.Comment: 35 pages, 3 figures, LaTeX; v2 references added, typos corrected, \Lambda fixed; v3 expanded discussion of higher loops in conclusion, matches published versio

Colored Spin Systems, BKP Evolution and finite N_c effects

Even within the framework of the leading logarithmic approximation the eigenvalues of the BKP kernel for states of more than three reggeized gluons are unknown in general, contrary to the planar limit case where the problem becomes integrable. We consider a 4-gluon kernel for a finite number of colors and define some simple toy models for the configuration space dynamics, which are directly solvable with group theoretical methods. Then we study the dependence of the spectrum of these models with respect to the number of colors and make comparisons with the large limit case.Comment: 17 pages, 4 figures, references update, to appear on EPJ

Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation

We investigate the Baxter equation for the Heisenberg spin model corresponding to a generalized BFKL equation describing composite states of n Reggeized gluons in the multi-color limit of QCD. The Sklyanin approach is used to find an unitary transformation from the impact parameter representation to the representation in which the wave function factorizes as a product of Baxter functions and a pseudo-vacuum state. We show that the solution of the Baxter equation is a meromorphic function with poles (lambda - i r)^{-(n-1)} (r= 0, 1,...) and that the intercept for the composite Reggeon states is expressed through the behavior of the Baxter function around the pole at lambda = i . The absence of pole singularities in the two complex dimensional lambda-plane for the bilinear combination of holomorphic and anti-holomorphic Baxter functions leads to the quantization of the integrals of motion because the holomorphic energy should be the same for all independent Baxter functions.Comment: LaTex, 48 pages, 1 .ps figure, to appear in Phys. Rev.

Exact resolution of the Baxter equation for reggeized gluon interactions

The interaction of reggeized gluons in multi-colour QCD is considered in the Baxter-Sklyanin representation, where the wave function is expressed as a product of Baxter functions Q(lambda) and a pseudo-vacuum state. We find n solutions of the Baxter equation for a composite state of n gluons with poles of rank r in the upper lambda semi-plane and of rank n-1-r in the lower lambda semi-plane (0 leq r leq n-1). These solutions are related by n-2 linear equations with coefficients depending on coth (pi lambda). The poles cancel in the wave function, bilinear combination of holomorphic and anti-holomorphic Baxter functions, guaranteeing its normalizability. The quantization of the intercepts of the corresponding Regge singularities appears as a result of the physical requirements that the holomorphic energies for all solutions of the Baxter equation are the same and the total energies, calculated around two singularities lambda, lambda^* --> + i or -i, coincide. It results in simple properties of the zeroes of the Baxter functions. For illustration we calculate the parameters of the reggeon states constructed from three and four gluons. For the Odderon the ground state has conformal spin |m -m | = 1 and its intercept equals unity. The ground state of four reggeized gluons possesses conformal spin 2 and its intercept turns out to be higher than that for the BFKL Pomeron. We calculate the anomalous dimensions of the corresponding operators for arbitrary alpha_s/omega.Comment: LaTex, 42 pages, 8 .ps figures. Expanded and improved versio

Effective String Theory of Vortices and Regge Trajectories

Starting from a field theory containing classical vortex solutions, we obtain an effective string theory of these vortices as a path integral over the two transverse degrees of freedom of the string. We carry out a semiclassical expansion of this effective theory, and use it to obtain corrections to Regge trajectories due to string fluctuations.Comment: 27 pages, revtex, 3 figures, corrected an error with the cutoff in appendix E (was previously D), added more discussion of Fig. 3, moved some material in section 9 to a new appendi

Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain

We construct the Baxter Q-operator and the representation of the Separated Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the diagrammatical approach, we calculate Sklyanin's integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the Q-operator. We show that the transition kernel to the SoV representation is factorized into the product of certain operators each depending on a single separated variable. As a consequence, it has a universal pyramid-like form that has been already observed for various quantum integrable models such as periodic Toda chain, closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl