6939385
The running coupling in lattice Landau gauge with unquenched Wilson fermion and KS fermion
The running coupling of the Wilson fermon(JLQCD/CP-PACS) and that of Kogut-Susskind(KS) fermion(MILC) are measured in the lattice Landau gauge QCD in MOM scheme. The quark propagator of the KS fermion is also measured and we find that it is infrared vanishing, which implies that quarks are confined. The renormalization factor of the running coupling and the tadpole renormalization define the scale of the quark wave function. Effects of the A 2 condensates of a few GeV 2 are observed in the running coupling and also in the quark propagator.
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
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.
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
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
2668770
Coupling between M2-branes and form fields
In the context of low-energy effective theory of multiple M2-branes, we construct the interaction terms between the world-volume fields of M2-branes and the antisymmetric tensor fields of three- and six-forms. By utilizing the compactification procedure, we show coincidence between the dimensionally reduced coupling and the R-R coupling to D-branes in type II string theory. We also discuss that a cubic term proportional to six-form field reproduces the quartic mass-deformation term in the world-volume theory of multiple M2-branes.
118415383
Instanton Effective Action in Deformed Super Yang-Mills Theories
We study the ADHM construction of instantons in N = 2 supersymmetric Yang‐Mills theory deformed in constant Ramond‐Ramond (R‐R) 3‐form field strength background in type IIB superstrings. We compare the deformed instanton effective action with the effective action of fractional D3/D(−1) branes at the orbifold singularity of C2/Z2 in the same R‐R background. We find discrepancy between them at the second order in deformation parameters, which comes from the coupling of the translational zero modes of the D(−1)‐branes to the R‐R background. We improve the deformed action by adding a term with spacetime dependent gauge coupling such that the action reproduces the effective action of the fractional branes.
119132882
Refined Chern-Simons theory and Hilbert schemes of points on the plane
Dedicated to Professor Igor Frenkel on the occasion of his sixtieth birthday Abstract. Aganagic and Shakirov propose a refinement of the SU(N) Chern- Simons theory for links in three manifolds with S 1 -symmetry, such as torus knots in S 3 , based on deformation of the S and T matrices, originally found by Kirillov and Cherednik. We relate the large N limit of the S matrix to the Hilbert schemes of points on the affine plane. As an application, we find an explicit formula for the Euler characteristics of the universal sheaf, applied arbitrary Schur functor.
15745084
Deformation of super Yang-Mills theories in R-R 3-form background
We study deformation of = 2 and = 4 super Yang-Mills theories, which are obtained as the low-energy effective theories on the (fractional) D3-branes in the presence of constant Ramond-Ramond 3-form background. We calculate the Lagrangian at the second order in the deformation parameter from open string disk amplitudes. In = 4 case we find that all supersymmetries are broken for generic deformation parameter but part of supersymmetries are unbroken for special case. We also find that classical vacua admit fuzzy sphere configuration. In = 2 case we determine the deformed supersymmetries. We rewrite the deformed Lagrangians in terms of = 1 superspace, where the deformation is interpreted as that of coupling constants.
115158728
Noncommutative supertori in two dimensions
First we consider the deformations of superspaces with = (1, 1) and = (2, 2) supersymmetries in two dimensions. Among these the construction of noncommutative supertorus with odd spin structure is possible only in the case of = (2, 2) supersymmetry broken down to = (1, 1). However, for the even spin structures the construction of noncommutative supertorus is possible for both = (1, 1) and = (2, 2) cases. The spin structures are realized by implementing the translational properties along the cycles of commutative supertorus in the operator version: Odd spin structure is realized by the translation in the fermionic direction in the same manner as in the construction of noncommutative torus, and even spin structures are realized with appropriate versions of the spin angular momentum operator.