Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions

Fumihiko Sugino; So Matsuura

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Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions

So Matsuura, Fumihiko Sugino

High Energy Physics - Lattice · Submitted 5 Feb 2014

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The authors' main claim We present a lattice formulation for two-dimensional N=(2,2) and (4,4) supersymmetric Yang-Mills theories that resolves vacuum degeneracy for gauge fields without imposing admissibility conditions.

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CitationFumihiko Sugino, So Matsuura. "Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions." arXiv:1402.0952 (2014). https://pith.science/paper/NNOE3LJS

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We present a lattice formulation for two-dimensional N=(2,2) and (4,4) supersymmetric Yang-Mills theories that resolves vacuum degeneracy for gauge fields without imposing admissibility conditions. Cases of U(N) and SU(N) gauge groups are considered, gauge fields are expressed by unitary link variables, and one or two supercharges are preserved on the two-dimensional square lattice. There does not appear fermion doubler, and no fine-tuning is required to obtain the desired continuum theories in a perturbative argument. This formulation is expected to serve as a more convenient basis for numerical simulations. The same approach will also be useful to other two-dimensional supersymmetric lattice gauge theories with unitary link variables constructed so far -- for example, N=(8,8) supersymmetric Yang-Mills theory and N=(2,2) supersymmetric QCD.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a lattice formulation for two-dimensional N=(2,2) and (4,4) supersymmetric Yang-Mills theories that resolves vacuum degeneracy for gauge fields without imposing admissibility conditions.	contribution 1.00	0.95	0.83	asserted 1.00
s1	Cases of U(N) and SU(N) gauge groups are considered, gauge fields are expressed by unitary link variables, and one or two supercharges are preserved on the two-dimensional square lattice.	method 0.91	0.86	0.08	asserted 1.00
s2	There does not appear fermion doubler, and no fine-tuning is required to obtain the desired continuum theories in a perturbative argument.	result 1.00	0.77	0.17	asserted 0.91
s3	This formulation is expected to serve as a more convenient basis for numerical simulations.	interpretation 0.75	0.14	0.11	hedged possibility 0.91
s4	The same approach will also be useful to other two-dimensional supersymmetric lattice gauge theories with unitary link variables constructed so far -- for example, N=(8,8) supersymmetric Yang-Mills theory and N=(2,2) supersymmetric QCD.	future work 0.59	0.15	0.07	hedged possibility 0.93

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Original abstract

We present a lattice formulation for two-dimensional N=(2,2) and (4,4) supersymmetric Yang-Mills theories that resolves vacuum degeneracy for gauge fields without imposing admissibility conditions. Cases of U(N) and SU(N) gauge groups are considered, gauge fields are expressed by unitary link variables, and one or two supercharges are preserved on the two-dimensional square lattice. There does not appear fermion doubler, and no fine-tuning is required to obtain the desired continuum theories in a perturbative argument. This formulation is expected to serve as a more convenient basis for numerical simulations. The same approach will also be useful to other two-dimensional supersymmetric lattice gauge theories with unitary link variables constructed so far -- for example, N=(8,8) supersymmetric Yang-Mills theory and N=(2,2) supersymmetric QCD.

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11 arXiv papers cite this in 19 sentences

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Papers citing it · 13 sentences without a confident label

Uses its method or tool 2 papers

To avoid the problem, we can take an admissibility-type field tensor [ref] or a $tan(θ/2)$-type field tensor [ref] .

Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice · Lattice theory · 0.87
Since the quiver construction will not work in four dimensions we intend to explore an alternative approach using a supersymmetric discretization developed by Sugino [ref] .

Lattice Gauge Theory for Physics Beyond the Standard Model · Extremely Challenging Calculations · 0.93

Compares with it 2 papers

The explicit expression of the action is [equation] with [equation] If we consider the torus discretization corresponding to the square lattice ([ref]) and set $α_s=α_st=α_f=β_f=1$, this action reproduces that of the lattice formulation of two-dimensional $=(2,2)$ supersymmetric Yang-Mills theory given in [ref] .

Topologically Twisted $N=(2,2)$ Supersymmetric Yang-Mills Theory on Arbitrary Discretized Riemann Surface · Definition of the model · 0.95
Reference [ref] discusses another method to avoid the vacuum degeneracy while keeping supersymmetry.

Lattice Formulation of ${\cal N} = 2^*$ Yang-Mills · Lattice Regularized Theory · 0.80

Cites it as background 2 papers

Two possibilities for desired lattice field tensor have been discussed in [ref] and [ref] .

O(a) Improvement of 2D N=(2,2) Lattice SYM Theory · Lattice formulation with an exact supersymmetry · 0.97
We also note that, from a viewpoint of regularization, there have been a large amount of lattice SUSY studies, some of which are for example [ref] , as well as a large amount of non-lattice studies, some of which are for example [ref] .

Non(anti)Commutative Superspace, Baker-Campbell-Hausdorff Closed Forms, and Dirac-K\"ahler Twisted Supersymmetry · Providing a basic framework for Lattice SUSY · 1.00

What it cites · 46 sentences without a confident label

Builds on 2 papers

In this paper, we modify the formulation for two-dimensional $=(2,2)$ and $(4,4)$ SYM theories [ref] so that the vacuum degeneracy is resolved without imposing the admissibility condition.

Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry · Introduction · 0.84
In this paper, we modify the formulation for two-dimensional $=(2,2)$ and $(4,4)$ SYM theories [ref] so that the vacuum degeneracy is resolved without imposing the admissibility condition.

A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry · Introduction · 0.84

Compares with 3 papers

By using the backward difference $Δ_μ^*$ ($Δ_μ^* φ(x)≡φ(x) - φ(x-μ̂)$), the fermion kinetic terms are expressed as [equation] where $Ψ(x)=( ψ_1(x), ψ_2(x), χ(x), 1/2η(x) )^T$, and matrices [equation] satisfy the algebra: [equation] This is the same kinetic action obtained in [ref] , and thus no fermion doubler appears.

A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry · $U(N)$ gauge group · 0.81
Another important point we should notice is that the interactions in ([ref]) are local, similarly to the case of the admissibility condition ([ref]) discussed in [ref] .

Abelian chiral gauge theories on the lattice with exact gauge invariance · $U(N)$ gauge group · 0.88
Another important point we should notice is that the interactions in ([ref]) are local, similarly to the case of the admissibility condition ([ref]) discussed in [ref] .

Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry · $U(N)$ gauge group · 0.88

Cites as background 19 papers

In the next section, we give a short review of the lattice formulation for two-dimensional $=(2,2)$ and $(4,4)$ SYM theories in [ref] .

Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry · Introduction · 0.91
In the next section, we give a short review of the lattice formulation for two-dimensional $=(2,2)$ and $(4,4)$ SYM theories in [ref] .

A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry · Introduction · 0.91
In particular, for theories with extended supersymmetries, some of supercharges are exactly preserved on lattice by applying the so-called orbifolding procedure [ref] or the topological twists [ref] to the discretization.

Ginsparg-Wilson Formulation of 2D N =(2,2) SQCD with Exact Lattice Supersymmetry · Introduction · 0.88

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