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

Endres, Michael G.; Kaplan, David B.

doi:10.1088/1126-6708/2006/10/076

Cited by 50 publications

(62 citation statements)

References 38 publications

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“…Nevertheless we will see on closer analysis that both approaches are intimately connected and lead to similar lattice actions in the case of Yang-Mills theories. As we will show, the orbifold approach is a very powerful way to generate all the known SYM lattices, and in fact was how they were first derived for spatial lattices [31] and Euclidean spacetime lattices [32,33,34,35].…”

Section: Supersymmetric Lattices From Orbifold Projectionmentioning

confidence: 97%

“…The projection is chosen so as to induce a lattice structure and to preserve one or more supersymmetries of the mother theory. The resulting theory is also gauge invariant and preserves a discrete subgroup of the continuum Lorentz and global symmetries [29,30,31,32,33,34,35,36,37]. The theories obtained in this fashion have a degenerate ground state (called a moduli space), where the distance from the origin of the moduli space has an interpretation as the inverse lattice spacing, as first implemented in "deconstruction" [38,30].…”

Section: Introductionmentioning

confidence: 99%

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Exact lattice supersymmetry☆

Catterall¹,

Kaplan²,

Ünsal³

2008

Journal of End-to-End-testing

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We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.

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Section: Supersymmetric Lattices From Orbifold Projectionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Exact lattice supersymmetry☆

Catterall¹,

Kaplan²,

Ünsal³

2008

Journal of End-to-End-testing

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“…1 Supersymmetric lattices have been constructed for several classes of SYM theories [2][3][4][5][6] including the well known N = 4 SYM theory. 2 There have been a few extensions of these formulations by incorporating matter fields in the adjoint and fundamental representations of the color group [31][32][33][34][35]. Some of them have also been extended to incorporate product gauge groups, resulting in supersymmetric quiver gauge theories on the lattice [34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional N $$ \mathcal{N} $$ = (2, 2) lattice gauge theories with matter in higher representations

Joseph

2014

J. High Energ. Phys.

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We construct two-dimensional N = (2, 2) supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU(N c ) color group. These lattice theories preserve a subset of the supercharges exact at finite lattice spacing. The method of topological twisting is used to construct such theories in the continuum and then the geometric discretization scheme is used to formulate them on the lattice. The lattice theories obtained this way are gaugeinvariant, free from fermion doubling problem and exact supersymmetric at finite lattice spacing. We hope that these lattice constructions further motivate the nonperturbative explorations of models inspired by technicolor, orbifolding and orientifolding in string theories and the Corrigan-Ramond limit.

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“…Lattice formulations for supersymmetric field theories, which preserve a part of their supersymmetry, have been constructed -in [1,2,3,4] for two-dimensional Wess-Zumino models or sigma models without gauge symmetry, in [5,6,7,8,9,10,11,12,13,14,15] for pure super Yang-Mills (SYM) theories, and in [16,17,18] for two-dimensional SYM theories coupled with matter multiplets 1 . For the remaining supercharges, which are broken by the latticization, ref.…”

Section: Introductionmentioning

confidence: 99%

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

Sugino¹,

Kikukawa²

2010

AIP Conference Proceedings

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In this paper, we introduce the overlap Dirac operator, which satisfies the Ginsparg-Wilson relation, to the matter sector of two-dimensional N = (2, 2) lattice supersymmetric QCD (SQCD) with preserving one of the supercharges. It realizes the exact chiral flavor symmetry on the lattice, to make possible to define the lattice action for general number of the flavors of fundamental and anti-fundamental matter multiplets and for general twisted masses. Furthermore, superpotential terms can be introduced with exact holomorphic or anti-holomorphic structure on the lattice. We also consider the lattice formulation of matter multiplets charged only under the central U(1) (the overall U(1)) of the gauge group G = U(N ), and then construct lattice models for gauged linear sigma models with exactly preserving one supercharge and their chiral flavor symmetry.

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

Abstract: We construct lattice actions for a variety of (2, 2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.

Cited by 50 publications

References 38 publications

Exact lattice supersymmetry☆

Exact lattice supersymmetry☆

Two-dimensional N $$ \mathcal{N} $$ = (2, 2) lattice gauge theories with matter in higher representations

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

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