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
122826026
Hermitian Fermi Coordinates, Dimensions and Path Integrals
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.
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
12944099
Confinement in the lattice Landau Gauge QCD simulation
The running coupling and the Kugo‐Ojima parameter of the confinement criterion are measured for the quenched SU(3) β = 6.4, 6.45, 564 lattice and the unquenched β = 5.2, 203 × 48 lattice of JLQCD, β = 2.1, κ = 0.1357, 0.1382, 243 × 48 lattice of CP‐PACS and βimp = 6.76, amu,d = 0.007, 6.83, amu,d = 0.040, 203 × 64 lattice of MILC collaboration.The quenched SU(3) 564 lattice data suggest presence of infrared fixed point of αs = 2.5(5) and the approach of the ensemble of the 1st copy to the Gribov boundary. The running coupling of q > 2GeV can be fitted by the perturbative QCD(pQCD) + c/q2 correction. We find the Kugo‐Ojima parameter u(0) = −0.83(3).The rotational symmetry of the gluon propagator of the unquenched SU(3) is partially recovered, but its magnitude depends on whether the Wilson fermion or the Kogut‐Susskind(KS) fermion are coupled to the gauge field. The gluon propagator coupled to KS fermion is more suppressed than that coupled to Wilson fermion. The running coupling inherits the same trend. T...
8772231
Instantons in Deformed Super Yang-Mills Theories
We study the instanton effective action in deformed four-dimensional N=2 and N=4 super Yang-Mills (SYM) theories. These deformed gauge theories are defined on the D-brane world-volume in the presence of constant, self-dual Ramond-Ramond (R-R) 3-form field strength background $\mathcal{F}$ which is scaled as $(2 \pi \alpha')^{1/2} \mathcal{F} = fixed$ in the zero-slope limit $\alpha' \to 0$. The instanton effective action is obtained by solving equations of motion of the deformed N=2 SYM action. We show that this effective action correctly reproduces the string theory result derived from D3/D(-1)-branes system in the lowest order of the backgrounds and gauge coupling constant.
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.
119243767
1/N Expansion of the 2D CPN−1 Model on Non(anti)commutative Superspace
We study UV properties of the two-dimensional supersymmetric CP N −1 model on non(anti)commutative superspace. We show that the deformed model has the same UV property as the ordinary model in the leading order of 1/N and that the deformation gives rise to UV divergence which cannot be dealt with in the next-to-leading order.
14508627
PERVERSE COHERENT SHEAVES ON BLOW-UP. II. WALL-CROSSING AND BETTI NUMBERS FORMULA
This is the second of series of papers studyig moduli spaces of a certain class of coherent sheaves, which we call stable perverse coherent sheaves, on the blow-up p: b X → X of a projective surface X at a point 0. The followings are main results of this paper: a) We describe the wall-crossing between moduli spaces caused by twisting of the line bundle O(C) associated with the exceptional divisor C. b) We give the formula for virtual Hodge numbers of moduli spaces of stable perverse coherent sheaves. Moreover we also give proofs of the followings which we observed in a special case in (24): c) The moduli space of stable perverse coherent sheaves is isomorphic to the usual moduli space of stable coherent sheaves on the original surface if the first Chern class is orthogonal to (C). d) The moduli space becomes isomorphic to the usual moduli space of stable coherent sheaves on the blow-up after twisting by O(−mC) for sufficiently largem. Therefore usual moduli spaces of stable sheaves on the blow-up and the original surfaces are connected via wall-crossings.
119481701
Instanton Equations for the Supersymmetric CPN−1 Sigma Model on Non(anti)commutative Superspace
We study the instanton equation of the supersymmetric CP N −1 sigma model on non(anti)commutative superspace in two dimensions. We show that the undeformed instanton equation is consistent with the deformed equations of motion. Then we conclude that the instanton equation is not deformed by superspace non(anti)commutativity. 1. Introduction Studies of strings with non-trivial classical values of its field components have brought about new development in quantum field theories. If one allows some of the field components to possess background values on D-branes, one obtains new classes of quantum field theories in the low energy limits of string theory. They have novel features due to the non(anti)commutativity (NC) properties of spacetime coordinates or superspace coordinates. Superstring theory with its graviphoton field in the R-R sector having a self-dual background value gives rise to supersymmetric Yang-Mills theories with N =1 /2 supersymmetry as an effective field theory, 1) providing a good realization of the NC superspace considered in different contexts some time ago. 2) NC field theories and SUSY field theories on NC superspace (field theories with deformed SUSY) have properties quite different from the usual field theories, and they need to be examined, in comparison with their commutative partners. Perturbative properties of SUSY field theories on NC superspace have been studied extensively in the last few years. Positive results have been obtained concerning the renormalizability of the model. 3)–5) One non-perturbative issue in deformed SUSY field theories is whether and how its instanton equation is modified from that of the usual SUSY field theories. This question has been studied in the case of super Yang-Mills theories in d = 4, and the modified self-dual equation has been derived, 6) and is extended to the NC deformed N = 2 SUSY case. 7) The solutions to this new self-dual equation have also been studied. 8) N = 2 SUSY CP N −1 models in d = 2 share many nice properties of super Yang-Mills theories and it allows exact treatment. From this point of view, we have constructed extension of the SUSY CP N −1 model to NC superspace. 5),9) The usual