Related papers: The Large-N_c Renormalization Group
This thesis focuses on renormalization of quantum field theories. Its first part considers three tensor models in three dimensions, a Fermionic quartic with tensors of rank-3 and two Bosonic sextic, of ranks 3 and 5. We rely upon the…
An effective field theory of quarks, gluons, and pions, with the number $N$ of colors treated as large, is proposed as a basis for calculations of hadronic phenomena at moderate energies. The qualitative consequences of the large $N$ limit…
A generalized Lagrangian for the description of hadronic matter based on the linear $SU(3)_L \times SU(3)_R$ $\sigma$-model is proposed. Besides the baryon octet, the spin-0 and spin-1 nonets, a gluon condensate associated with broken scale…
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…
Massive Yang-Mills theory is known to be renormalizable in 1+1 dimensions. The gluon mass is introduced by coupling the gauge field to an SU(N) principal chiral nonlinear sigma model. The proof of renormalizability relies on the asymptotic…
Fluctuations are included in a chiral nucleon-meson model within the framework of the functional renormalization group. The model, with parameters fitted to reproduce the nuclear liquid-gas phase transition, is used to study the phase…
The ultraviolet completion of a large N QCD model requires introducing new degrees of freedom at certain scale so that the UV behavior may become asymptotically conformal with no Landau poles and no UV divergences of Wilson loops. These UV…
The usual derivation of the Lagrangian of a model for massive vector bosons, by spontaneous symmetry breaking of a gauge theory, implies that the prefactors of the various interaction terms are uniquely determined functions of the coupling…
New renormalisation group flows of three-dimensional Chern--Simons theories with a single gauge group $\textrm{SU}(N)$ and adjoint matter are found holographically. These RG flows have an infrared fixed point given by a CFT with…
A spin-flavor symmetry emerges for baryons in the large-N_c limit. Large-N_c baryons form irreducible representations of the spin-flavor algebra, and their static properties can be computed in a systematic expansion in 1/N_c. Symmetry…
We study unification in the Randall-Sundrum scenario for solving the hierarchy problem, with gauge fields and fermions in the bulk. We calculate the one-loop corrected low-energy effective gauge couplings in a unified theory, broken at the…
In this review we report on advances in topological soliton models of the nucleon. In chapter I we construct an effective lagrangian of QCD with the low mass mesons ($\pi,\rho,A_1$ and the scalar meson $\epsilon$) generalising the Skyrme…
We investigate the chiral sine-Gordon model using the renormalization group method. The chiral sine-Gordon model is a model for $G$-valued fields and describes a new class of phase transitions, where $G$ is a compact Lie group. We show that…
We investigate the reliability of the large $N_f$ expansion of four-dimensional gauge-fermion quantum field theories, focusing on the structure and scheme dependence of the beta function. While the existence of a nontrivial UV fixed point…
These lectures are designed to introduce the methods and results of large N_c QCD in a presentation intended for nuclear and particle physicists alike. Beginning with definitions and motivations of the approach, we demonstrate that all…
We present a renormalization-group (RG) flow argument for s-wave kaon condensation in dense nuclear-star matter predicted in chiral perturbation theory. It is shown that it is the {\it relevant} mass term together with {\it any} attractive…
A scalar theory can have many Gaussian (free) fixed points, corresponding to Lagrangians of the form $\phi\,\Box^k\phi$. We use the non-perturbative RG to study examples of flows between such fixed points. We show that the anomalous…
We use 1+1 dimensional large N Gross-Neveu models as a laboratory to derive microscopically effective Lagrangians for positive energy fermions only. When applied to baryons, the Euler-Lagrange equation for these effective theories assumes…
The stability of nonrelativistic fermionic systems to interactions is studied within the Renormalization Group framework. A brief introduction to $\phi^4$ theory in four dimensions and the path integral formulation for fermions is given.…
The dynamics at the IR fixed point realized in the $SU(N_c)$ gauge theories with massless Dirac fermions is studied by means of the non-perturbative renormalization group. The analysis includes the IR fixed points with non-trivial Yukawa…