Non-commutative standard model: model building

A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by _U* (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just . We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherent CP violation and new neutrino interactions. Received: 23 January 2003, Published online: 18 June 2003     

Multi-Trace Superpotentials vs. Matrix Models

We consider ᵊ9=1 supersymmetric U(N) field theories in four dimensions with adjoint chiral matter and a multi-trace tree-level superpotential. We show that the computation of the effective action as a function of the glueball superfield localizes to computing matrix integrals. Unlike the single-trace case, holomorphy and symmetries do not forbid non-planar contributions. Nevertheless, only a special subset of the planar diagrams contributes to the exact result. In addition, the computation of the superpotential localizes to doing matrix integrals. In view of the results of Dijkgraaf and Vafa for single-trace theories, one might have naively expected that these matrix integrals are related to the free energy of a multi-trace matrix model. We explain why this naive identification does not work. Rather, an auxiliary single-trace matrix model with additional singlet fields can be used to exactly compute the field theory superpotential. Along the way we also describe a general technique for computing the large-N limits of multi-trace Matrix models and raise the challenge of finding the field theories whose effective actions they may compute. Since our models can be treated as ᵊ9=1 deformations of pure ᵊ9=2 gauge theory, we show that the effective superpotential that we compute also follows from the ᵊ9=2 Seiberg-Witten solution. Finally, we observe an interesting connection between multi-trace local theories and non-local field theory.     

Phases of supersymmetric gauge theories with flavors

We explore the phases of supersymmetric U(N) gauge theories with fundamental matter that arise as deformations of SQCD by the addition of a superpotential for the adjoint chiral multiplet. As the parameters in the superpotential are varied, the vacua of this theory sweep out various branches, which in some cases have multiple semiclassical limits. In such limits, we recover the vacua of various product gauge group theories, with flavors charged under some group factors. We describe in detail the structure of the vacua in both classical and quantum regimes, and develop general techniques such as an addition and a multiplication map which relate vacua of different gauge theories. We also consider possible indices characterizing different branches and potential relationships with matrix models.     

Confinement and mass gap in abelian gauge

First, we present a simple confining abelian pure gauge theory. Classically, its kinetic term is not positive definite, and it contains a simple UV regularized F⁴ interaction. This provokes the formation of a condensate such that, at the saddle point of the effective potential, the wave function normalization constant of the abelian gauge fields vanishes exactly. Then we study SU(2) pure Yang-Mills theory in an abelian gauge and introduce an auxiliary field for a BRST invariant condensate of dimension 2, which renders the charged sector massive. Under simple assumptions its effective low energy theory reduces to the confining abelian model discussed before, and the VEV of is seen to scale correctly with the renormalization point. Under these assumptions, the confinement condition Z _eff = 0 also holds for the massive charged sector, which suppresses the couplings of the charged fields to the abelian gauge bosons in the infrared regime. Received: 27 November 2002 / Published online: 14 April 2003 RID="a" ID="a" e-mail: Ulrich.Ellwanger@th.u-psud.fr RID="b" ID="b" e-mail: Nicolas.Wschebor@th.u-psud.fr ^* Unité Mixte de Recherche - CNRS - UMR 8627     

Type IIB 2-form fields and gauge coupling constant of 4D ${\cal N}=2$ super QCD

We study the relation between the Type IIB (NSNS and RR) 2-form fields and the (complex) gauge coupling constant of the 4D SU(N _c ) super Yang-Mills theory with N _f fundamental matter particles. We start from the analysis of the D2-brane world-volume theory with heavy N _c quarks on the N _f D6 supergravity background. After a sequence of T- and S-dualities, we obtain the (generalized) 2-forms in the configuration with N _c D5-branes wrapping on a vanishing two-cycle under the influence of the background. These 2-forms show the same behavior as the gauge coupling constant of the 4D super QCD. The background reduces to the orbifold in the twelve-dimensional space-time formally realized by introducing the two parameters as additional space coordinates. The 10D gravity dual is suggested as the 2D flip in this twelve-dimensional space-time. In the case of N _f = 2N _c , this gravity dual becomes AdS₅ x S⁵/Z₂ with a D3-charge which depends on the constant generalized NSNS 2-form. This is the result expected from the M-theory QCD configuration. Based on the known exact result, we also discuss this configuration after including non-perturbative effects.Received: 2 May 2003, Revised: 21 July 2003, Published online: 19 September 2003     

Gauge fluctuations in superconducting films

In this paper we consider a type-I superconducting film modeled by the Ginzburg-Landau model, confined between two parallel planes a distance L apart from one another. Our approach is based on the Gaussian effective potential in the transverse unitarity gauge, which allows to treat gauge contributions in a compact form. Using techniques from dimensional and -function regularizations, modified by the confinement conditions, we investigate the critical temperature as a function of the film thickness L. The contributions from the scalar self-interaction and from the gauge fluctuations are clearly identified. The model suggests the existence of a minimal critical thickness below which superconductivity is suppressed. A comparison with present experimental observations is done.Received: 19 December 2003, Published online: 9 April 2004PACS: 74.20.-z Theories and models of superconducting state - 11.15.Ex Spontaneous breaking of gauge symmetries - 05.10.Cc Renormalization group methods     

Perturbation theory for the two-dimensional abelian Higgs modelin the unitary gauge

In the unitary gauge the unphysical degrees of freedom of spontaneously broken gauge theories are eliminated. The Feynman rules are simpler than in other gauges, but it is non-renormalizable by the rules of power counting. On the other hand, it is formally equal to the limit of the renormalizable R -gauge. We consider perturbation theory to one-loop order in the R -gauge and in the unitary gauge for the case of the two-dimensional abelian Higgs model. An apparent conflict between the unitary gauge and the limit of the R -gauge is resolved, and it is demonstrated that results for physical quantities can be obtained in the unitary gauge.Received: 17 July 2003, Revised: 8 August 2003, Published online: 20 November 2003E.E. Scholz: Present address: DESY, Notkestr. 85, 22603 Hamburg, Germany     

Beta decays with momentum space Majorana spinors

We construct and apply to decays a truly neutral local quantum field that is entirely based upon momentum space Majorana spinors. We make the observation that theory with momentum space Majorana spinors of real C parities is equivalent to Diracs theory. For imaginary C parities, the neutrino mass can drop out from the single decay trace and reappear in , a curious and in principle experimentally testable signature for a non-trivial impact of Majorana framework in polarization experiments.Received: 11 November 2003, Revised: 20 April 2004, Published online: 12 October 2004PACS: 11.30.Er Charge conjugation, parity, time reversal, and other discrete symmetries - 14.60.St Non-standard-model neutrinos, right-handed neutrinos, etc.     

Some applications of renormalized RPA in bosonic field theories

We present some applications of the renormalized RPA in bosonic field theories. We first present some developments for the explicit calculation of the total energy in theory and discuss its phase structure in 1 + 1 dimensions. We also demonstrate that the Goldstone theorem is satisfied in the O(N) model within the renormalized RPA.Received: 29 September 2003, Published online: 2 June 2004PACS: 03.70. + k Theory of quantized fields - 12.39.Fe Chiral Lagrangians - 21.60.Jz Hartree-Fock and random-phase approximations - 24.10.Cn Many-body theory     

Quark mass dependence of masses and decay constants of the pseudo-Goldstone bosons in QCD

The dependence of the pseudo-scalar meson masses and decay constants on sea and valence quark masses is compared to next-to-leading order (NLO) chiral perturbation theory (ChPT). The numerical simulations with two light dynamical quark flavors are performed with the Wilson quark lattice action at gauge coupling and hopping parameters on a 16⁴ lattice. lattice artifacts are taken into account by applying chiral perturbation theory for the Wilson lattice action. The values of the relevant combinations of Gasser-Leutwyler constants L ₄, L ₅, L ₆ and L ₈ are estimated.Received: 7 July 2003, Published online: 2 October 2003     

Chromofields of strings and baryons

We calculate color electric fields of quark/antiquark ( ) and 3-quark (qqq) systems within the Chromodielectric Model (CDM). We explicitly evaluate the string tension of flux tubes in the -system and analyze their profile. To reproduce results of lattice calculations we use a bag pressure from which an effective strong-coupling constant follows. With these parameters we get a Y-shaped configuration for large qqq-systems.Received: 30 September 2002, Published online: 22 October 2003PACS: 11.10.Lm Field theory: Nonlinear or nonlocal theories and models - 11.15.Kc Gauge field theories: Classical and semiclassical techniques - 12.39.Ba Phenomenological quark models: Bag model     

Charged tensor matter fields and Lorentz symmetry violation via spontaneous symmetry breaking

We consider a model with a charged vector field along with a Cremmer-Scherk-Kalb-Ramond (CSKR) matter field coupled to a U(1) gauge potential. We obtain a natural Lorentz symmetry violation due to the local U(1) spontaneous symmetry breaking mechanism triggered by the imaginary part of the vector matter. The choice of the unitary gauge leads to the decoupling of the gauge-KR sector from the Higgs-KR sector. The excitation spectrum is carefully analyzed and the physical modes are identified. We propose an identification of the neutral massive spin-1 Higgs-like field with the massive Z boson of the so-called mirror matter models.Received: 30 October 2003, Revised: 16 March 2004, Published online: 23 June 2004     

Chiral approach to nuclear matter: Role of explicit short-range <Emphasis Type="Italic">NN</Emphasis>-terms

We extend a recent chiral approach to nuclear matter by including the most general (momentum-independent) NN-contact interaction. Iterating this two-parameter contact vertex with itself and with one-pion exchange the emerging energy per particle exhausts all terms possible up to and including fourth order in the small momentum expansion. Two (isospin-dependent) cut-offs are introduced to regularize the (linear) divergences of some three-loop in-medium diagrams. The equation of state of pure neutron matter, , can be reproduced very well up to quite high neutron densities of by adjusting the strength of a repulsive nn-contact interaction. Binding and saturation of isospin-symmetric nuclear matter is a generic feature of our perturbative calculation. Fixing the maximum binding energy per particle to MeV we find that any possible equilibrium density lies below . The additional constraint from the neutron matter equation of state leads however to a somewhat too low saturation density of . We also investigate the effects of the NN-contact interaction on the complex single-particle potential U(p,k _f ) + i W(p,k _f ). We find that the effective nucleon mass at the Fermi surface is bounded from below by . This property keeps the critical temperature of the liquid-gas phase transition at somewhat too high values MeV. The downward bending of the asymmetry energy A(k _f ) above nuclear-matter saturation density is a generic feature of theapproximation to fourth order. We furthermore investigate the effects of the NN-contact interaction on the -term in the nuclear energy density functional . Altogether, there is within this complete fourth-order calculation no magic set of adjustable short-range parameters with which one could reproduce simultaneously and accurately all semi-empirical properties of nuclear matter. In particular, the conditions for a good neutron matter equation of state and for good single-particle properties are mutually exclusive.Received: 28 October 2003, Revised: 9 December 2003, Published online: 23 July 2004PACS: 12.38.Bx Perturbative calculations - 21.65. + f Nuclear matter - 24.10.Cn Many-body theory - 31.15.Ew Density-functional theory     

Vector and axial-vector correlators in a non-local chiral quark model

The behavior of the non-perturbative parts of the isovector-vector and isovector and isosinglet axial-vector correlators at Euclidean momenta is studied in the framework of a covariant chiral quark model with non-local quark-quark interactions. The gauge covariance is ensured with the help of the P-exponents, with the corresponding modification of the quark-current interaction vertices taken into account. The low- and high-momentum behavior of the correlators is compared with the chiral perturbation theory and with the QCD operator product expansion, respectively. The V-A combination of the correlators obtained in the model reproduces quantitatively the ALEPH and OPAL data on hadronic decays, transformed into the Euclidean domain via dispersion relations. The predictions for the electromagnetic mass difference and for the pion electric polarizability are also in agreement with the experimental values. The topological susceptibility of the vacuum is evaluated as a function of the momentum, and its first moment is predicted to be . In addition, the fulfillment of the Crewther theorem is demonstrated.Received: 9 May 2003, Revised: 22 September 2003, Published online: 4 November 2003     

Gauge theories on the $\kappa$-Minkowski spacetime

This study of gauge field theories on -deformed Minkowski spacetime extends previous work on field theories on this example of a non-commutative spacetime. We construct deformed gauge theories for arbitrary compact Lie groups using the concept of enveloping algebra-valued gauge transformations and the Seiberg-Witten formalism. Derivative-valued gauge fields lead to field strength tensors as the sum of curvature- and torsion-like terms. We construct the Lagrangians explicitly to first order in the deformation parameter. This is the first example of a gauge theory that possesses a deformed Lorentz covariance.Received: 17 December 2003, Revised: 6 May 2004, Published online: 23 June 2004     

Symmetry breaking of the symmetric left-right model without a scalar bidoublet

By invoking the existence of a general O(2) symmetry, a minimal left-right symmetric model based on the gauge group is shown to require the existence of only two physical Higgs bosons. The lighter Higgs is predicted to have a small mass which could be evaluated by standard perturbation theory. The fermionic mass matrices are recovered by insertion of ad hoc fermion-Higgs interactions. The model is shown to be undistinguishable from the standard model at the currently reachable energies.Received: 10 August 2003, Revised: 18 October 2003, Published online: 18 December 2003     

$\mbox{Log}(1/x)$ gluon distribution and structure functionsin the loop-loop correlation model

We consider the interaction of the partonic fluctuation of a scalar photon with an external color field to calculate the leading and next-to-leading order gluon distribution of the proton following the work done by Dosch-Hebecker-Metz-Pirner. We relate these gluon distributions to the short and long distance behavior of the cross section of an adjoint dipole scattering off a proton. The leading order result is a constant, while the next-to-leading order result shows a enhancement at small x. To get numerical results for the gluon distributions at the initial scale Q²₀ = 1.8 GeV², we compute the adjoint dipole-proton cross section in the loop-loop correlation model. Quark distributions at the same initial scale are parameterized according to Regge theory. We evolve quark and gluon distributions to higher Q² values using the DGLAP equation and compute charm and proton structure functions in the small-x region for different Q² values.Received: 13 September 2003, Revised: 22 November 2003, Published online: 15 January 2003     

Break of universality for an Ising model with aperiodic Rudin-Shapiro interactions

We analyze the ferromagnetic Ising model on non-Euclidean scale invariant lattices with aperiodic interactions (J_A,J_B,J_C,J_D) defined by Rudin-Shapiro substitution rules with Migdal-Kadanoff renormalization (MKR) and transfer matrix (TM) techniques. The analysis of the invariant sets of the zero-field MKR transformation indicates that the critical behavior, completely distinct from the one of the uniform model, is described by a new off-diagonal fixed point. This contrasts with other aperiodic models where the new critical behavior is described by a period-two cycle. With the new fixed point, values for the thermal critical exponents, and , as well as the period of log-periodic oscillations, are obtained. Exact recursive maps for all thermodynamical functions are derived within the TM approach. The explicit dependence of the thermodynamical functions with respect to temperature is evaluated by the numerical iteration of the set of maps until a previously chosen convergence is achieved. They also indicate that, depending on the actual choice for the aperiodic coupling constants, the magnetic exponents ( and ) assume different values. However the Rushbrook relation is always satisfied.Received: 27 February 2003, Published online: 11 August 2003PACS: 05.50.+q Lattice theory and statistics - 05.10.Cc Renormalization group methods - 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 61.44.Br Quasicrystals     

High scale perturbative gauge coupling in R-parity conserving SUSY <Emphasis Type="Italic">SO</Emphasis>(10) with longer proton lifetime

It is well known that in single step breaking of R-parity conserving SUSY SO(10) that needs the Higgs representations , the GUT gauge coupling violates the perturbative constraint at mass scales a few times larger than the GUT scale. Therefore, if the SO(10) gauge coupling is to remain perturbative up to the Planck scale ( GeV), the scale M_U of the GUT symmetry breaking is to be bounded from below. The bound depends upon specific Higgs representations used for SO(10) symmetry breaking but, as we find, cannot be lower than $1.5 \times 10$¹⁷ GeV. In order to obtain such a high unification scale we propose a two-step SO(10) breaking through SU(2)_L $\times$ SU(2)_R $\times$ U(1)_B-L $\times$SU(3)_C ( ) intermediate gauge symmetry. We estimate the potential threshold and gravitational corrections to the gauge coupling running and show that they can make the picture of perturbative gauge coupling running consistent at least up to the Planck scale. We also show that when by the Higgs representations , gravitational corrections alone with negligible threshold effects may guarantee such perturbative gauge coupling. The lifetime of the proton is found to increase by nearly 6 orders over the present experimental limit for . For the proton decay mediated by a dim = 5 operator a wide range of lifetimes is possible, extending from the current experimental limit up to values 2-3 orders longer. Received: 1 July 2005, Revised: 21 August 2005, Published online: 11 October 2005     

Isospin breaking in $K \rightarrow \pi\pi$ decays

We perform a complete analysis of isospin breaking in amplitudes in chiral perturbation theory, including both strong isospin violation ( ) and electromagnetic corrections to next-to-leading order in the low-energy expansion. The unknown chiral couplings are estimated at leading order in the 1/N_c expansion. We study the impact of isospin breaking on CP conserving amplitudes and rescattering phases. In particular, we extract the effective couplings g₈ and g₂₇ from a fit to branching ratios, finding small deviations from the isospin-limit case. The ratio measuring the enhancement is found to decrease from in the isospin limit to in the presence of isospin breaking. We also analyze the effect of isospin violation on the CP violation parameter , finding a destructive interference between three different sources of isospin violation. Within the uncertainties of large-N_c estimates for the low-energy constants, the isospin violating correction for is below 15%.Received: 21 November 2003, Published online: 4 February 2004Work supported in part by IHP-RTN, Contract No. HPRN-CT2002-00311 (EURIDICE) and by Acciones Integradas, Project No. 19/2003 (Austria), HU2002-0044 (MCYT, Spain)