16251354
A New algorithm of Langevin simulation and its application to the SU(2) and SU(3) lattice gauge
Abstract The 2nd order Runge-Kutta scheme Langevin simulation of unquenched QCD in pseudofermion method derived from our general theory shows a behaviour as a function of the Langevin step t better than the Fukugita, Oyanagi, Ukawa's scheme.
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
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.
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
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
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.
118847627
Interaction between M2-branes and bulk form fields
We construct the interaction terms between the world-volume fields of multiple M2-branes and the 3-and 6-form fields in the context of ABJM theory with U(N)×U(N) gauge symmetry. A consistency check is made in the simplest case of a single M2-brane i.e., our construction matches the known effective action of M2-brane coupled to antisymmetric 3-form field. We show that when dimensionally reduced, our couplings coincide with the effective action of D2-branes coupled to R-R 3-and 5-form fields in type IIA string theory. We also comment on the relation between a coupling with a specific 6-form field configuration and the supersymmetry preserving mass deformation in ABJM theory.
59060118
Donaldson = Seiberg-Witten from Mochizuki's formula and instanton counting
We propose an explicit formula connecting Donaldson invariants and Seiberg-Witten invariants of a 4-manifold of simple type via Nekrasov's deformed partition function for the N=2 SUSY gauge theory with a single fundamental matter. This formula is derived from Mochizuki's formula, which makes sense and was proved when the 4-manifold is complex projective. Assuming our formula is true for a 4-manifold of simple type, we prove Witten's conjecture and sum rules for Seiberg-Witten invariants (superconformal simple type condition), conjectured by Mari\~no, Moore and Peradze.
10853977
Lectures on instanton counting
These notes have two parts. The first is a study of Nekrasov's deformed partition functions $Z(\ve_1,\ve_2,\vec{a};\q,\vec{\tau})$ of N=2 SUSY Yang-Mills theories, which are generating functions of the integration in the equivariant cohomology over the moduli spaces of instantons on $\mathbb R^4$. The second is review of geometry of the Seiberg-Witten curves and the geometric engineering of the gauge theory, which are physical backgrounds of Nekrasov's partition functions. 
The first part is continuation of math.AG/0306198, where we identified the Seiberg-Witten prepotential with $Z(0,0,\vec{a};\q,0)$. 
We put higher Casimir operators to the partition function and clarify their relation to the Seiberg-Witten $u$-plane. We also determine the coefficients of $\ve_1\ve_2$ and $(\ve_1^2+\ve_2^2)/3$ (the genus 1 part) of the partition function, which coincide with two measure factors $A$, $B$ appeared in the $u$-plane integral. 
The proof is based on the blowup equation which we derived in the previous paper.
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.