Renormalization flow of QED

We investigate textbook QED in the framework of the exact renormalization group. In the strong-coupling region, we study the influence of fluctuation-induced photonic and fermionic self-interactions on the nonperturbative running of the gauge coupling. Our findings confirm the triviality hypothesis of complete charge screening if the ultraviolet cutoff is sent to infinity. Though the Landau pole does not belong to the physical coupling domain owing to spontaneous chiral symmetry breaking (chiSB), the theory predicts a scale of maximal UV extension of the same order as the Landau pole scale. In addition, we verify that the chiSB phase of the theory which is characterized by a light fermion and a Goldstone boson also has a trivial Yukawa coupling.Comment: 4 pages, 1 figur

Quantum Monte Carlo study for multiorbital systems with preserved spin and orbital rotational symmetries

We propose to combine the Trotter decomposition and a series expansion of the partition function for Hund's exchange coupling in a quantum Monte Carlo (QMC) algorithm for multiorbital systems that preserves spin and orbital rotational symmetries. This enables us to treat the Hund's (spin-flip and pair-hopping) terms, which is difficult in the conventional QMC method. To demonstrate this, we first apply the algorithm to study ferromagnetism in the two-orbital Hubbard model within the dynamical mean-field theory (DMFT). The result reveals that the preservation of the SU(2) symmetry in Hund's exchange is important, where the Curie temperature is grossly overestimated when the symmetry is degraded, as is often done, to Ising (Z$_2$). We then calculate the $t_{2g}$ spectral functions of Sr$_2$RuO$_4$ by a three-band DMFT calculation with tight-binding parameters taken from the local density approximation with proper rotational symmetry.Comment: 9 pages, 9 figures. Typos corrected, some comments and references adde

Multifractality: generic property of eigenstates of 2D disordered metals.

The distribution function of local amplitudes of eigenstates of a two-dimensional disordered metal is calculated. Although the distribution of comparatively small amplitudes is governed by laws similar to those known from the random matrix theory, its decay at larger amplitudes is non-universal and much slower. This leads to the multifractal behavior of inverse participation numbers at any disorder. From the formal point of view, the multifractality originates from non-trivial saddle-point solutions of supersymmetric $\sigma$-model used in calculations.Comment: 4 two-column pages, no figures, submitted to PRL

Efimov effect from functional renormalization

We apply a field-theoretic functional renormalization group technique to the few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with U(1) symmetry, two-component fermions with U(1)\times SU(2) symmetry and three-component fermions with U(1) \times SU(3) symmetry. We focus on the scale invariant unitarity limit for infinite scattering length. The exact solution for the two-body sector is consistent with the unitary fixed point behavior for all considered systems. Nevertheless, the numerical three-body solution in the s-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3) fermions. The Efimov parameter for the one-component bosons and the three-component fermions is found to be approximately s=1.006, consistent with the result of Efimov.Comment: 21 pages, 6 figures, minor changes, published versio

Non-Perturbative Determination of cSWc_{\rm SW} in Three-flavor Dynamical QCD

We present a fully non-perturbative determination of the $O(a)$ improvement coefficient $c_{\rm SW}$ in three-flavor dynamical QCD for the RG improved as well as the plaquette gauge actions, using the Schr\"odinger functional scheme. Results are compared with one-loop estimates at weak gauge coupling.Comment: 3 pages, 6 figures, Lattice2002(Improvement and Renormalization), Unnecessary files are remove

Calculation of K→ππK\to\pi\pi decay amplitudes from K→πK\to\pi matrix elements in quenched domain-wall QCD

We present a calculation of the $K\to\pi\pi$ decay amplitudes from the $K\to\pi$ matrix elements using leading order relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD with the domain-wall fermion action and the renormalization group improved gluon action. Our results show that the I=2 amplitude is reasonably consistent with experiment whereas the I=0 amplitude is sizably smaller. Consequently the $\Delta I=1/2$ enhancement is only half of the experimental value, and $\epsilon'/\epsilon$ is negative.Comment: Lattice2001(hadronic matrix elements), 3pages, 6 eps figure

Functional renormalization for trion formation in ultracold fermion gases

The energy spectrum for three species of identical fermionic atoms close to a Feshbach resonance is computed by use of a nonperturbative flow equation. Already a simple truncation shows that for large scattering length $|a|$ the lowest energy state is a "trion" (or trimer) bound state of three atoms. At the location of the resonance, for $|a|\to\infty$, we find an infinite set of trimer bound states, with exponentially decreasing binding energy. This feature was pointed out by Efimov. It arises from limit cycle scaling, which also leads to a periodic dependence of the three body scattering coupling on $\ln |a|$. Extending our findings by continuity to nonzero density and temperature we find that a "trion phase" separates a BEC and a BCS phase, with interesting quantum phase transitions for T=0.Comment: 9 pages, 4 figures, minor changes, reference adde

Gauged Nambu-Jona-Lasinio model with extra dimensions

We investigate phase structure of the D (> 4)-dimensional gauged Nambu-Jona-Lasinio (NJL) model with $\delta(=D-4)$ extra dimensions compactified on TeV scale, based on the improved ladder Schwinger-Dyson (SD) equation in the bulk. We assume that the bulk running gauge coupling in the SD equation for the SU(N_c) gauge theory with N_f massless flavors is given by the truncated Kaluza-Klein effective theory and hence has a nontrivial ultraviolet fixed point (UVFP). We find the critical line in the parameter space of two couplings, the gauge coupling and the four-fermion coupling, which is similar to that of the gauged NJL model with fixed (walking) gauge coupling in four dimensions. It is shown that in the presence of such walking gauge interactions the four-fermion interactions become ``nontrivial'' even in higher dimensions, similarly to the four-dimensional gauged NJL model. Such a nontriviality holds only in the restricted region of the critical line (``nontrivial window'') with the gauge coupling larger than a non-vanishing value (``marginal triviality (MT)'' point), in contrast to the four-dimensional case where such a nontriviality holds for all regions of the critical line except for the pure NJL point. In the nontrivial window the renormalized effective potential yields a nontrivial interaction which is conformal invariant. The exisitence of the nontrivial window implies ``cutoff insensitivity'' of the physics prediction in spite of the ultraviolet dominance of the dynamics. In the formal limit D -> 4, the nontrivial window coincides with the known condition of the nontriviality of the four-dimensional gauged NJL model, $9/(2N_c) < N_f - N_c < 9/2 N_c$.Comment: 34 pages, 6 figures, references added, to appear in Phys.Rev.D. The title is changed in PR

Colliders and Brane Vector Phenomenology

Brane world oscillations manifest themselves as massive vector gauge fields. Their coupling to the Standard Model is deduced using the method of nonlinear realizations of the spontaneously broken higher dimensional space-time symmetries. Brane vectors are stable and weakly interacting, and therefore escape particle detectors unnoticed. LEP and Tevatron data on the production of a single photon in conjunction with missing energy are used to delineate experimentally excluded regions of brane vector parameter space. The additional region of parameter space accessible to the LHC as well as a future lepton linear collider is also determined by means of this process.Comment: 12 pages, 13 figure

The Lambda-Lambda Interaction and ^{6}_{Lambda Lambda}He

An OBE potential model for the ^{1}S_0 S = -2 interaction is analyzed with emphasis on the role of coupling between the Lambda Lambda, N Xi, and Sigma Sigma channels. Singlet scalar exchange, an approximation to two-pion exchange, is significant in all channels; surprisingly, the one-pion exchange component is almost negligible. The size of the channel coupling as a function of the overall strength of the OBE model potential is examined. Implications of the analysis for the binding energy of ^{6}_{Lambda Lambda}He are considered; the new experimental datum may suggest a consistency between the extracted Lambda Lambda matrix element and the relation implied by SU(3) among OBE baryon-baryon interactions. \\Comment: 4 pages brief report to Physical Review