Homology theory of lattice fermion doubling

Rabin, Jeffrey M.

doi:10.1016/0550-3213(82)90434-5

Cited by 176 publications

(152 citation statements)

References 8 publications

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“…We can see that these operators satisfy the following algebra: 46) which has the same algebraic structure as (2.3). Similarly we can derive the twisted angular momentum and R-symmetry differential operators which satisfy the N = 2 twisted SUSY algebra (2.9):…”

Section: N = 2 Twisted Superspace In Two Dimensionsmentioning

confidence: 98%

“…The Dirac-Kähler fermion mechanism is formulated in any dimensions [42][43][44][45][46][47][48][49]. It is particularly convenient to formulate in even dimensions since the corresponding Clifford algebra is unambiguously defined with a chiral generator.…”

Section: N = 4 Twisted Susy In Four Dimensionsmentioning

confidence: 99%

“…Next we consider how the relation (2.21) has an effect on the transformation law of component fields. We define the Dirac-Kähler field as follows [42][43][44][45][46][47][48][49],…”

Section: N = 4 Twisted Susy In Four Dimensionsmentioning

confidence: 99%

“…and Tsukioka pointed out that the two-dimensional version of topological Yang-Mills action obtained from generalized gauge theory [37][38][39][40] with instanton gauge fixing led to two-dimensional version of N = 2 twisted super Yang-Mills action [41]. It was found in this investigation that the twisting procedure to relate between the ghost-related fermions and matter fermions is essentially DiracKähler fermion mechanism [42][43][44][45][46][47][48][49] and the "flavor" degrees of freedom of the DiracKähler fermion can be interpreted as that of the extended SUSY [41]. It turned out that this Dirac-Kähler twisting mechanism works universally in the quantization of topological field theory and an extended SUSY is generated.…”

Section: Introductionmentioning

confidence: 99%

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N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

2005

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We propose N = 4 twisted superspace formalism in four dimensions by introducing Dirac-Kähler twist. In addition to the BRST charge as a scalar counter part of twisted supercharge we find vector and tensor twisted supercharges. By introducing twisted chiral superfield we explicitly construct off-shell twisted N = 4 SUSY invariant action. We can propose variety of supergauge invariant actions by introducing twisted vector superfield. We may, however, need to find further constraints to identify twisted N = 4 super Yang-Mills action. We propose a superconnection formalism of twisted superspace where constraints play a crucial role. It turns out that N = 4 superalgebra of Dirac-Kähler twist can be decomposed into N = 2 sectors. We can then construct twisted N = 2 super Yang-Mills actions by the superconnection formalism of twisted superspace in two and four dimensions.

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Section: N = 2 Twisted Superspace In Two Dimensionsmentioning

confidence: 98%

Section: N = 4 Twisted Susy In Four Dimensionsmentioning

confidence: 99%

“…Next we consider how the relation (2.21) has an effect on the transformation law of component fields. We define the Dirac-Kähler field as follows [42][43][44][45][46][47][48][49],…”

Section: N = 4 Twisted Susy In Four Dimensionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

2005

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“…[4]. One involves a Dirac-Kähler construction [5,6] which associates the Lorentz spinor supercharges with tensors under a diagonal subgroup of the product of Lorentz and R-symmetry groups of the target theory. (An R-symmetry is a global symmetry which does not commute with supersymmetry).…”

Section: Introductionmentioning

confidence: 99%

Lattice formulation of (2,2) supersymmetric gauge theories with matter fields

Endres¹,

Kaplan

2006

J. High Energy Phys.

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On fractional semidiscrete Dirac operators of Lévy–Leblond type

Faustino

2023

Mathematische Nachrichten

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In this paper, we introduce a wide class of space‐fractional and time‐fractional semidiscrete Dirac operators of Lévy–Leblond type on the semidiscrete space‐time lattice hZn×[0,∞)$h{\mathbb {Z}}^n\times [0,\infty )$ (h>0$h>0$), resembling to fractional semidiscrete counterparts of the so‐called parabolic Dirac operators. The methods adopted here are fairly operational, relying mostly on the algebraic manipulations involving Clifford algebras, discrete Fourier analysis techniques as well as standard properties of the analytic fractional semidiscrete semigroup {}exp(−teiθ(−normalΔh)α)t≥0$\left\lbrace \exp (-te^{i\theta }(-\Delta _h)^{\alpha })\right\rbrace _{t\ge 0}$, carrying the parameter constraints 0<α≤1$0<\alpha \le 1$ and |θ|≤απ2$|\theta |\le \frac{\alpha \pi }{2}$. The results obtained involve the study of Cauchy problems on hZn×[0,∞)$h{\mathbb {Z}}^n\times [0,\infty )$.

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Homology theory of lattice fermion doubling

Cited by 176 publications

References 8 publications

N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

Lattice formulation of (2,2) supersymmetric gauge theories with matter fields

On fractional semidiscrete Dirac operators of Lévy–Leblond type

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