Bond asymmetry and high-Tc superconductivity

Journal ArticleWe propose a simple mechanism, anchored in weak-coupling BCS theory, which ties together the following facts: high Tc; quasi two dimensionality; orthorhombic distortion and/or disordered lines of oxygen; proximity to a metal-insulator transition; and anomalously small isotope effects

Summing the Instanton Series in N=2 Superconformal Large-N QCD

We consider the multi-instanton collective coordinate integration measure in N=2 supersymmetric SU(N) gauge theory with N_F fundamental hypermultiplets. In the large-N limit, at the superconformal point where N_F=2N and all VEVs are turned off, the k-instanton moduli space collapses to a single copy of AdS_5*S^1. The resulting k-instanton effective measure is proportional to N^{1/2} g^4 Z_k^(6), where Z_k^(6) is the partition function of N=(1,0) SYM theory in six dimensions reduced to zero dimensions. The multi-instanton can in fact be summed in closed form. As a hint of an AdS/CFT duality, with the usual relation between the gauge theory and string theory parameters, this precisely matches the normalization of the charge-k D-instanton measure in type IIB string theory compactified to six dimensions on K3 with a vanishing two-cycle.Comment: 12 pages, amslate

Ringwaldmania reconsidered

The exciting possibility that anomalous baryon and lepton number violation might be observable at the next generation of supercolliders is suggested by an instanton calculation due to Ringwald and Espinoa. Here, the current controversial status of these claims is discussed, and progress on several fronts is described

Valley Bifurcation in an O(3)O(3) σ\sigma Model: Implications for High-Energy Baryon Number Violation

The valley method for computing the total high-energy anomalous cross section $S_{anom}$ is the extension of the optical theorem to the case of instanton-antiinstanton backgrounds. As a toy model for baryon number violation in Electroweak theory, we consider a version of the $O(3)$ $\sigma$ model in which the conformal invariance is broken perturbatively. We show that at a critical energy the saddle-point values of the instanton size and instanton-antiinstanton separation bifurcate into complex conjugate pairs. This nonanalytic behavior signals the breakdown of the valley method at an energy where $S_{anom}$ is still exponentially suppressed. (Figures replaced 5/3/93).Comment: (14 pages, Los Alamos Preprint LA-UR-93-811). 3 uuencoded figures include

Solvability, Consistency and the Renormalization Group in Large-NcN_c Models of Hadrons

We establish the following fundamentals about Lagrangian models of meson-baryon interactions in the large-$N_{c}$ limit: 1. Calculating the leading-order contribution to $1$-meson/$2$-baryon Green's functions in the $1/N_c$ expansion involves summing an infinite class of divergent Feynman diagrams. So long as the bare Lagrangian properly obeys all large-$N_c$ selection rules, this all-loops resummation is accomplished exactly by solving coupled classical field equations with a short-distance cutoff. 2. The only effect of the resummation is to renormalize the bare Yukawa couplings, baryon masses and hyperfine baryon mass splittings of the model. 3. In the process, the large-$N_{c}$ renormalization group flow of these bare parameters is completely determined. We conjecture that variants of the Skyrme model emerge as UV fixed points of such flows.Comment: (LaTeX file with accompanying figures

Scattering amplitudes to all orders in meson exchange

As the number of colors in QCD, N{sub C}, becomes large, it is possible to sum up all meson-exchange contributions, however arbitrarily complicated, to meson-baryon and baryon-baryon scattering. A semi-classical structure for the two-flavor theory emerges, in close correspondence to vector-meson-augmented Skyrme models. In this limit, baryons act as extended static sources for the classical meson fields. This leads to non-linear differential equations for the classical meson fields which can be solved numerically for static radial (hedgehog-like) solutions. The non-linear terms in the equations of motion for the quantized meson fields can then be simplified, to leading order in 1/N{sub C}, by replacing all factors of the meson field but one by the previously-found classical field. This results in linear, Schroedinger-like equations, which are easily solved. For the meson-baryon case the solution can be subsequently analyzed to obtain the phase shifts for the scattering and, from these, the baryon resonance spectrum of the model. As the warm-up, we have carried out this calculation for the simple case of {sigma} mesons only, finding sensible results. 8 refs., 3 figs

From Effective Lagrangians, to Chiral Bags, to Skyrmions with the Large-N_c Renormalization Group

We explicitly relate effective meson-baryon Lagrangian models, chiral bags, and Skyrmions in the following way. First, effective Lagrangians are constructed in a manner consistent with an underlying large-N_c QCD. An infinite set of graphs dress the bare Yukawa couplings at *leading* order in 1/N_c, and are summed using semiclassical techniques. What emerges is a picture of the large-N_c baryon reminiscent of the chiral bag: hedgehog pions for r > 1/\Lambda patched onto bare nucleon degrees of freedom for r < 1/\Lambda, where the ``bag radius'' 1/\Lambda is the UV cutoff on the graphs. Next, a novel renormalization group (RG) is derived, in which the bare Yukawa couplings, baryon masses and hyperfine baryon mass splittings run with \Lambda. Finally, this RG flow is shown to act as a *filter* on the renormalized Lagrangian parameters: when they are fine-tuned to obey Skyrme-model relations the continuum limit \Lambda --> \infty exists and is, in fact, a Skyrme model; otherwise there is no continuum limit.Comment: Figures included (separate file). This ``replaced'' version corrects the discussion of backwards-in-time baryon

Pion-Nucleon Scattering in a Large-N Sigma Model

We review the large-N_c approach to meson-baryon scattering, including recent interesting developments. We then study pion-nucleon scattering in a particular variant of the linear sigma-model, in which the couplings of the sigma and pi mesons to the nucleon are echoed by couplings to the entire tower of I=J baryons (including the Delta) as dictated by large-N_c group theory. We sum the complete set of multi-loop meson-exchange \pi N --> \pi N and \pi N --> \sigma N Feynman diagrams, to leading order in 1/N_c. The key idea, reviewed in detail, is that large-N_c allows the approximation of LOOP graphs by TREE graphs, so long as the loops contain at least one baryon leg; trees, in turn, can be summed by solving classical equations of motion. We exhibit the resulting partial-wave S-matrix and the rich nucleon and Delta resonance spectrum of this simple model, comparing not only to experiment but also to pion-nucleon scattering in the Skyrme model. The moral is that much of the detailed structure of the meson-baryon S-matrix which hitherto has been uncovered only with skyrmion methods, can also be described by models with explicit baryon fields, thanks to the 1/N_c expansion.Comment: This LaTeX file inputs the ReVTeX macropackage; figures accompany i

Soliton quantization and internal symmetry

We apply the method of collective coordinate quantization to a model of solitons in two spacetime dimensions with a global $U(1)$ symmetry. In particular we consider the dynamics of the charged states associated with rotational excitations of the soliton in the internal space and their interactions with the quanta of the background field (mesons). By solving a system of coupled saddle-point equations we effectively sum all tree-graphs contributing to the one-point Green's function of the meson field in the background of a rotating soliton. We find that the resulting one-point function evaluated between soliton states of definite $U(1)$ charge exhibits a pole on the meson mass shell and we extract the corresponding S-matrix element for the decay of an excited state via the emission of a single meson using the standard LSZ reduction formula. This S-matrix element has a natural interpretation in terms of an effective Lagrangian for the charged soliton states with an explicit Yukawa coupling to the meson field. We calculate the leading-order semi-classical decay width of the excited soliton states discuss the consequences of these results for the hadronic decay of the $\Delta$ resonance in the Skyrme model.Comment: 23 pages, LA-UR-93-299

Skyrmion Quantization and the Decay of the Delta

We present the complete solution to the so-called ``Yukawa problem'' of the Skyrme model. This refers to the perceived difficulty of reproducing---purely from soliton physics---the usual pseudovector pion-nucleon coupling, echoed by pion coupling to the higher spin/isospin baryons $(I=J=3/2 , 5/2 , \cdots , N_c/2 )$ in a manner fixed by large-$N_c$ group theory. The solution involves surprisingly elegant interplay between the classical and quantum properties of a new configuration, the ``new improved skyrmion''. This is the near-hedgehog obtained by minimizing the usual skyrmion mass functional augmented by an all-important isorotational kinetic term. The numerics are pleasing: a $\Delta$ decay width within a few MeV of its measured value, and furthermore, the higher-spin baryons $(I=J \ge 5/2 )$ with widths so large ($\Gamma > 800 MeV$) that these undesirable large-$N_c$ artifacts effectively drop out of the spectrum, and pose no phenomenological problem. Beyond these specific results, we ground the Skyrme model in the Feynman Path Integral, and set up a transparent collective coordinate formalism that makes maximal use of the $1/N_c$ expansion. This approach elucidates the connection between skyrmions on the one hand, and Feynman diagrams in an effective field theory on the other.Comment: This TeX file inputs the macropackage harvmac.tex . Choose the ``b'' (big) option or equations will overrun