Gauge theories on a simplicial lattice

We provide an action for gauge theories discretized on simplicial meshes, inspired by finite element methods. The action is discretely gauge invariant and we give a proof of consistency. A discrete Noether's theorem that can be applied to our setting, is also proved.Comment: 24 pages. v2: New version includes a longer introduction and a discrete Noether's theorem. v3: Section 4 on Noether's theorem has been expanded with Proposition 8, section 2 has been expanded with a paragraph on standard LGT. v4: Thorough revision with new introduction and more background materia

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“…We first make some remarks on Lie algebra valued Whitney forms and their associated cochains. The de Rham isomorhisms (15) give isomorphisms:…”

Section: Definitionmentioning

confidence: 99%

A simplicial gauge theory

Christiansen

Halvorsen

2012

Journal of Mathematical Physics

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“…(19) are not orthogonal. This issue was encountered in non-supersymmetric lattice studies during the early 1980s [22][23][24], and is discussed for N = 4 SYM in Ref. [8].…”

Section: A From Topological Twisting To the Lattice Actionmentioning

confidence: 99%

N=4supersymmetry on a space-time lattice

Catterall¹,

Schaich²,

Damgaard³

et al. 2014

Phys. Rev. D

138

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Maximally supersymmetric Yang-Mills theory in four dimensions can be formulated on a spacetime lattice while exactly preserving a single supersymmetry. Here we explore in detail this lattice theory, paying particular attention to its strongly coupled regime. Targeting a theory with gauge group SU(N ), the lattice formulation is naturally described in terms of gauge group U(N ). Although the U(1) degrees of freedom decouple in the continuum limit we show that these degrees of freedom lead to unwanted lattice artifacts at strong coupling. We demonstrate that these lattice artifacts can be removed, leaving behind a lattice formulation based on the SU(N ) gauge group with the expected apparently conformal behavior at both weak and strong coupling.

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“…We find Λ grav = 0.0090(1) √ σ phys which is very similar to the flat case. Assuming that the pure-gauge β-function is a reasonable approximation for the full renormalization relation, our data show that the scaling window opens already at the β values considered, similar to the pure SU(2) case [13]. As a consequence, the continuum limit could be performed along β → ∞, eventually stopping at a finite value corresponding to a lattice spacing equal to the Planck length.…”

Section: String Tensionmentioning

confidence: 80%

“…For pure gauge theory β-functions are derived in the literature also for a simplicial lattice [13]. We fit our string-tension data to the function…”

Section: String Tensionmentioning

confidence: 99%

Phase diagram of Regge quantum gravity coupled to SU(2) gauge theory

et al. 1996

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We analyze Regge quantum gravity coupled to SU(2) gauge theory on 4 3 × 2, 6 3 × 4 and 8 3 × 4 simplicial lattices. It turns out that the window of the well-defined phase of the gravity sector where geometrical expectation values are stable extends to negative gravitational couplings as well as to gauge couplings across the deconfinement phase transition. We study the string tension from Polyakov loops, compare with the β-function of pure gauge theory and conclude that a physical limit through scaling is possible.

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Gauge theories on a simplicial lattice

Cited by 32 publications

References 13 publications

A simplicial gauge theory

A simplicial gauge theory

N=4supersymmetry on a space-time lattice

Phase diagram of Regge quantum gravity coupled to SU(2) gauge theory

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