120240569
How Dense Are the Coulomb Gauge Fixing Degeneracies? Geometrical Formulation of the Coulomb Gauge
121927270
Spontaneous breaking of chiral symmetry in a vector-gluon model
Solutions of the self-consistent equation for fermion propagator in a vector-gluon model are fully examined. The equation is characterized by a set of parameters, i.e., the coupling constant g, the bare mass of the fermion mo and the cutoff A. It is proved that with a suitable gauge chosen, the equation without ~utoff has solutions ·only in the case mo=O, It is then shown that, if g'/4n Bn, the "normal-state" solution for the equation without cutoff, even if it existed, should necessarily have an unphysical singularity. This fact implies that the "normal-state" solution becomes unstable for a su.fficiently large value of g'. § l. Introduction The. reason for success of low energy theorems obtained by current algebra and PCAC-treatment may be well understood in terms of chiral symmetry in which the pseudoscalar mesons play a special role among hadtons as the Nambu­ Goldstone (NG) bosons1l transforming nonlinearly under chiral transformation. On the other hand, in the composite hadron models based on SU(3) or SU(6), it is clear that there is no vital distinction between pseudoscalar mesons and others such as vector- and tensor-mesons. It is therefore worth expecting that the pseudoscalar NG bosons can also be interpreted as the bound states in con­ formity with the viewpoint of the composite model. . This homogeneity and· heterogeneity ot the pseudoscalar mesons to other mesons should rather be in­ vestigated by comparing their internal structure with composite particles· . . In this respect it would be meaningful to study a model in which spontaneous breaking of chiral symmetry is realized by a composite NG boson: The Nambu­ Jona-Lasinio model2l is known as such an example. However, the use of chain approximation and the momentum cutoff inevitable for the local four-fermion
14092663
Roles of the quark field in the infrared lattice Coulomb gauge and Landau gauge QCD
Fac of Infor Sci; Utsunomiya Univ, Utsunomiya, 320-8585 JapanE-mail:nakajima@is.utsunomiya-u.ac.jpThe effective coupling of QCD is measured by using the gauge conﬁgurations produced by theMILC collaboration in which the Kogut Susskind (KS) fermion is incorporated and by using thatproducedby the QCDOC collaborationin which the domain wall fermion (DWF) is incorporated.We ﬁx the gauge to the Landau gauge and to the Coulomb gauge. Th e infrared effective couplingin the Coulomb gauge agrees with the recent extraction at JLab, but that in the Landau gaugeshows infrared suppression. The suppression is expected to be due to the color anti-symmetricghost propagator which in the unquenched conﬁgurations has stronger infrared singularity thanthe color diagonal ghost propagator. The Coulomb form factor in the infrared depends on the kindof the fermion incorporated in the system and the temperature.The quark has the effect of quenching randomness and the ﬂuct uation of the color anti-symmetricghost propagator is reduced in the unquenched conﬁguration , and the Kugo-Ojima parameterc iscloser to 1 in the unquenched conﬁguration than in the quench ed conﬁguration.The XXV International Symposium on Lattice Field TheoryJuly 30 - August 4 2007Regensburg, Germany
16425609
Numerical studies of confinement in the lattice Landau gauge
Critical conjectures on confinement in the Landau gauge is numerically tested in focus to Gribov copy effects. One of the subjects is of the Kugo-Ojima confinement criterion and the other is of various viewpoints in the Gribov-Zwanziger theory. We use the smearing gauge as a reference gauge free of Gribov copy, and performed three types of simulations, log U, U-linear and log U in the smearing gauge. It is found that Gribov copy effect on the Kugo-Ojima parameter is small. log U and U-linear simulations yield only global scale factor difference in gluon propagator, but nontrivial difference of momentum behaviour in ghost propagator, and about 10% difference in Kugo-Ojima parameter. The horizon function defined by Zwanziger is evaluated in three types of gauge field and compared. All data show the negative horizon function as expected.
122826026
Hermitian Fermi Coordinates, Dimensions and Path Integrals
14432580
Test of the Kugo-Ojima confinement criterion in the lattice landau gauge
We present the first results of numerical test of the Kugo-Ojima confinement criterion in the lattice Landau gauge. The Kugo-Ojima criterion of colour confinement in the BRS formulation of the continuum gauge theory is given by uba(0) = −δba, where 
∫dXeip(x−)〈O|TDμca(X)g(Av×c)b(Y)|O〉=(gμvPμPvp2)Uba(p2). (∗) 
 
 
We measured the lattice version of uba(0) in use of 1/(−∂D (A)) where Dμ(A) is a lattice covariant derivative in the new definition of the gauge field as U = eA. We obtained that uba(0) is consistent with −cδba, c = 0.7 in SU(3) quenched simulation data of β = 5.5, on 84 and 124. We report the β dependence and finite-size effect of c.
119569923
Instanton counting on blowup. II. K-theoretic partition
function
AbstractWe study Nekrasov's deformed partition function $Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ of 5-dimensional supersymmetric
Yang-Mills theory compactified on a circle. Mathematically it is the
generating function of the characters of the coordinate rings of the moduli
spaces of instantons on $\mathbb R^4$. We show that it satisfies a system of
functional equations, called blowup equations, whose solution is unique.
As applications, we prove (a) $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta) = \varepsilon_1\varepsilon_2 \log Z(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$ is regular at $\varepsilon_1 = \varepsilon_2 = 0$ (a part of Nekrasov's conjecture), and (b) the genus $1$ parts, which are first several Taylor coefficients of $F(\varepsilon_1,\varepsilon_2,\vec{a};\mathfrak q,\boldsymbol\beta)$, are written explicitly in terms of $\tau = d^2 F(0,0,\vec{a};\mathfrak q,\boldsymbol\beta)/da^2$ in rank $2$ case.
18268747
Central charges in non(anti)commutative N=2 supersymmetric U(N) gauge theory
Abstract We study the central charge of the deformed N = ( 1 , 0 ) supersymmetry algebra in non(anti)commutative N = 2 supersymmetric U ( N ) gauge theory. In the cases of N = 1 / 2 superspace and N = 2 harmonic superspace with the singlet deformation, we find that the central charge is deformed by the non(anti)commutative parameters but depends on the electric and magnetic charges. For generic deformation of N = 2 harmonic superspace, we compute the O ( C ) correction to the central charges in the case of U ( 1 ) gauge group.
16605019
Testing the seesaw mechanism at collider energies in the Randall-Sundrum model
The Randall-Sundrum model with gauge fields and fermions in the bulk has several attractive features including the gauge coupling unification, a candidate for the dark matter, and an explanation for the hierarchical Yukawa couplings. 
In this paper, we point out that the 1st Kaluza-Klein modes of right-handed neutrinos may be produced at colliders, for both Dirac and Majorana neutrino cases. Furthermore, we can see whether the neutrino masses are Dirac type or Majorana type from the mass spectrum of KK particles.
16529601
Theoretical Framework for R-parity Violation
We propose a theoretical framework for R-parity violation. It is realized by a class of Calabi-Yau compactification of heterotic string theory. Trilinear R-parity violation in superpotential is either absent or negligibly small without an unbroken symmetry, due to a selection rule based on charge counting of a spontaneously broken U(1) symmetry. Although such a selection rule cannot be applied in general to nonrenormalizable operators in the low-energy effective superpotential, it is valid for terms trilinear in low-energy degrees of freedom, and hence can be used as a solution to the dimension-4 proton decay problem in the minimal supersymmetric standard model. Bilinear R-parity violation is generated, but there are good reasons why it is small enough to satisfy its upper bounds from neutrino mass and washout of baryon/lepton asymmetry. All R-parity violating dimension-5 operators can be generated. In this theoretical framework, nucleons can decay through squark-exchange diagrams combining dimension-5 and bilinear R-parity violating operators. B ― L breaking neutron decay is predicted.
14300277
Morita equivalence of noncommutative supertori
In this paper we study the extension of Morita equivalence of noncommutative tori to the supersymmetric case. The structure of the symmetry group yielding Morita equivalence appears to be intact but its parameter field becomes supersymmetrized having both body and soul parts. Our result is mainly in the two dimensional case in which noncommutative supertori have been constructed recently: The group SO(2,2,VZ0), where VZ0 denotes Grassmann even number whose body part belongs to Z, yields Morita equivalent noncommutative supertori in two dimensions.