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Kazuhiro Nagata

Publications and source records attributed to Kazuhiro Nagata.

12 recordsLinked to original sources
arXiv2025

Gauge Covariant Link Formulation of Twisted N=D=4 and N=4 D=5 Super Yang-Mills on a Lattice

We propose a lattice formulation of four dimensional super Yang-Mills model with a twisted N=4 supersymmetry in a manifestly gauge covariant manner. The formulation we employ here is a four dimensional extension of the manifestly gauge covariant method which was developed in our proposals of Dirac-Kahler twisted N=D=2 and N=4 D=3 super Yang-Mills on a lattice. Twisted N=4 supersymmetry algebra is geometrically realized on a four dimensional lattice with link supercharges and the use of link (anti-)commutators. Employing Grassmann parameters with link nature, we explicitly show that the resulting super Yang-Mills action is invariant under all the supercharges on a lattice without chiral fermion problems. As a group and algebraic interpretation of the link approach, we show that promoting bosonic supercovariant derivatives to their exponentials consistently with the lattice Leibniz rule naturally gives rise to the notion of gauge covariant link (anti-)commutators. This can be regarded as a fermionic decomposition of a Lie group element, which may provide a new methodology in super Lie group and super Lie algebra. We also provide a five dimensional lift-up of the formulation with exact N=4 SUSY invariance on a five dimensional lattice.

hep-lat↗
arXiv2025

Non(anti)Commutative Superspace, Baker-Campbell-Hausdorff Closed Forms, and Dirac-Kähler Twisted Supersymmetry

Starting from an elementary calculation of super Lie group elements associating with non(anti)-commutative Grassmann parameters, we derive several closed expressions of Baker-Campbell-Hausdorff (BCH) formula which represent multiplication properties of super Lie group elements in the corresponding superspace. We then show that parametrization of superspace in general may become infinite dimensional due to the presence of non(anti)commutativity. We show that a Dirac-Kähler Twisted SUSY Algebra (also referred to as Marcus B-type Twisted SUSY Algebra or Geometric Langlands Twisted SUSY Algebra) with a certain type of deformation, which we call an exponential deformation, may circumvent this problem. We also provide, in terms of gauge covariantization of the SUSY algebra, a geometric understanding of the exponential deformation, and see that the framework constructed in this paper may serve as a non(anti)commutative superspace framework providing the gauge covariant link formulation of twisted super Yang-Mills on a lattice.

hep-th↗
arXiv2008

Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice

We propose a twisted SUSY invariant formulation of Chern-Simons theory on a Euclidean three dimensional lattice. The SUSY algebra to be realized on the lattice is the N=4 D=3 twisted algebra that was recently proposed by D'Adda et al.. In order to keep the manifest anti-hermiticity of the action, we introduce oppositely oriented supercharges. Accordingly, the naive continuum limit of the action formally corresponds to the Landau gauge fixed version of Chern-Simons theory with complex gauge group which was originally proposed by Witten. We also show that the resulting action consists of parity even and odd parts with different coefficients.

hep-lat↗
arXiv2008

Exact Lattice Supersymmetry at Large N

Employing a novel type of non-commutative product in the Dirac-Kahler twisted superspace on a lattice, we formulate a field theoretically rigid framework of extended supersymmetry on a lattice. As a first example of this treatment, we calculate one-loop (in some cases any loops) quantum corrections for a twisted Wess-Zumino model with N \times N hermitian matrix superfields on a two dimensional lattice. The calculations are entirely given in a lattice superfield framework. We report that the mass and the coupling constant are exactly protected from the radiative corrections at non-zero lattice spacing as far as the planar diagrams are concerned, which implies the realization of exact lattice supersymmetry w.r.t. all the supercharges in the large-N limit.

hep-lat↗
arXiv2008

Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions

We propose a lattice formulation of three dimensional super Yang-Mills model with a twisted N=4 supersymmetry. The extended supersymmetry algebra of all the eight supercharges is fully and exactly realized on the lattice with a modified "Leibniz rule". The formulation we employ here is a three dimensional extension of manifestly gauge covariant method which was developed in our previous proposal of Dirac-Kaehler twisted N=2 super Yang-Mills on two dimensional lattice. The twisted N=4 supersymmetry algebra is geometrically realized on a three dimensional lattice with link supercharges and the use of "shifted" (anti-)commutators. A possible solution to the recent critiques on the link formulation will be discussed.

hep-lat↗
arXiv2007

On the Continuum and Lattice Formulations of N=4 D=3 Twisted Super Yang-Mills

Employing a twisted superspace with eight supercharges, we describe an off-shell formulation of N=4 D=3 twisted super Yang-Mills in the continuum spacetime which underlies the recent proposal of N=4 D=3 twisted super Yang-Mills on a lattice (arXiv:0707.3533[hep-lat]). By a dimensional reduction from the N=2 D=4, we explore the two possible topological twists of N=4 D=3 and then show that the lattice formulation given in arXiv:0707.3533[hep-lat] is essentially categorized as the B-type. We also show that, amongst the two inequivalent twists of N=4 D=3, only the B-type SYM can be realized on the lattice consistently with the Leibniz rule and the gauge covariance on the lattice.

hep-th↗
arXiv2007

Staggered Diquarks for the Singly Heavy Baryons

In the staggered fermion formulation of lattice QCD, we construct diquark operators to be embedded in singly heavy baryons. The group theoretical connections between the continuum and lattice staggered diquark representations are established.

hep-lat↗
arXiv2007

Lattice Formulation of the N=4 D=3 Twisted Super Yang-Mills

A lattice formulation of a three dimensional super Yang-Mills model with a twisted N=4 supersymmetry is proposed. The extended supersymmetry algebra of all eight supercharges is fully and exactly realized on the lattice with a modified "Leibniz rule". The formulation we employ here is a three dimensional extension of the manifestly gauge covariant method which was developed in our previous proposal of Dirac-Kähler twisted N=2 super Yang-Mills on a two dimensional lattice. The twisted N=4 supersymmetry algebra is geometrically realized on a three dimensional lattice with link supercharges and the use of "shifted" (anti-)commutators. A possible solution to the recent critiques on the link formulation will be discussed.

hep-lat↗
arXiv2005

Exact Extended Supersymmetry on a Lattice: Twisted N=2 Super Yang-Mills in Two Dimensions

We propose a lattice action for two dimensional super Yang-Mills theory with a twisted N=2 supersymmetry. The extended supersymmetry is fully and exactly realized on the lattice. The method employed is quite general and its extension to the N=4 supersymmetry in four dimensions is briefly presented. The lattice has a new type of ``fermionic'' links, where odd Grassmann variables, supercharges and fermionic connections sit. The Leibniz rule is preserved on the lattice, although in a modified ``shifted'' form that takes into account the link nature of both derivatives and supercharges. Superfields are semi-local objects and superfield expansion is naturally embedded in the lattice structure. The Dirac-Kähler twist generates the extended twisted supersymmetry, turning the multiplicity of species doublers into the multiplicity due to the extended supersymmetry. In this way the balance between bosonic and fermionic degrees of freedom is preserved.

hep-lat↗
arXiv2004

Twisted N=2 exact SUSY on the lattice for BF and Wess-Zumino

We formulate exact supersymmetric models on a lattice. We introduce noncommutativity to ensure the Leibniz rule. With the help of superspace formalism, we give supertransformations which keep the N=2 twisted SUSY algebra exactly. The action is given as a product of (anti)chiral superfields on the lattice. We present BF and Wess-Zumino models as explicit examples of our formulation. Both models have exact N=2 twisted SUSY in 2 dimensional space at a finite lattice spacing. In component fields, the action has supercharge exact form.

hep-lat↗
arXiv2004

Twisted Superspace on a Lattice

We propose a new formulation which realizes exact twisted supersymmetry for all the supercharges on a lattice by twisted superspace formalism. We show explicit examples of N=2 twisted supersymmetry invariant BF and Wess-Zumino models in two dimensions. We introduce mild lattice noncommutativity to preserve Leibniz rule on the lattice. The formulation is based on the twisted superspace formalism for N=D=2 supersymmetry which was proposed recently. From the consistency condition of the noncommutativity of superspace, we find an unexpected three-dimensional lattice structure which may reduce into two dimensional lattice where the superspace describes semilocally scattered fermions and bosons within a double size square lattice.

hep-lat↗