Two-dimensional $\mathcal{N}=(2,2)$ Lattice Gauge Theories with Matter in Higher Representations

Abstract

We construct two-dimensional $\mathcal{N}=(2,2)$ 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 gauge-invariant, 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.

arXiv comment16 pages, 1 figure. v2: New section on fine tuning added. Slight modification in abstract. Version matches with the one accepted for publication

References in corpus (39)

• Light Composite Higgs from Higher Representations versus Electroweak Precision Measurements -- Predictions for LHC
• Supersymmetry on a Spatial Lattice
• Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with Four Supercharges
• Exact Results in Non-Supersymmetric Large N Orientifold Field Theories
• A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories with Sixteen Supercharges
• Exact lattice supersymmetry
• A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
• Supersymmetry on a Euclidean Spacetime Lattice II: Theories with Eight Supercharges
• SUSY Relics in One-Flavor QCD from a New 1/N Expansion
• Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry
• Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions
• A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice
• Twisted Supersymmetric Gauge Theories and Orbifold Lattices
• Exact Extended Supersymmetry on a Lattice: Twisted N=2 Super Yang-Mills in Two Dimensions
• From Twisted Supersymmetry to Orbifold Lattices
• Thermal phases of D1-branes on a circle from lattice super Yang-Mills
• Restoration of supersymmetry on the lattice: Two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory
• Lattice formulation of $\mathcal{N}=4$ super Yang-Mills theory
• Geometry of Orbifolded Supersymmetric Lattice Gauge Theories
• Classification of Supersymmetric Lattice Gauge Theories by Orbifolding
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Perturbative renormalization of lattice N=4 super Yang-Mills theory
• Two-dimensional lattice for four-dimensional N=4 supersymmetric Yang-Mills
• N=4 Supersymmetry on a Space-Time Lattice
• A proposal of a fine tuning free formulation of 4d N=4 super Yang-Mills
• Lattice formulation of (2,2) supersymmetric gauge theories with matter fields
• Twisted supersymmetries in lattice $\mathcal{N}=4$ super Yang-Mills theory
• Phase Structure of Lattice N=4 Super Yang-Mills
• Two-dimensional N=(2,2) Supersymmetric Lattice Gauge Theory with Matter Fields in the Fundamental Representation
• On the sign problem in 2D lattice super Yang--Mills
• Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges
• Unity of Supersymmetry Breaking Models
• Supersymmetric Yang--Mills theories with exact supersymmetry on the lattice
• Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions
• Lattice formulation of three-dimensional $\mathcal{N}=4$ gauge theory with fundamental matter fields
• An object oriented code for simulating supersymmetric Yang--Mills theories
• Investigating the sign problem for two-dimensional $\mathcal{N}=(2,2)$ and $\mathcal{N}=(8,8)$ lattice super Yang--Mills theories
• Supersymmetric quiver gauge theories on the lattice
• Eigenvalue spectrum of lattice $\mathcal{N}=4$ super Yang-Mills

Cited by in corpus (7)

• Parallel software for lattice N=4 supersymmetric Yang--Mills theory
• Progress and prospects of lattice supersymmetry
• Lattice studies of supersymmetric gauge theories
• Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice
• Wolf Space Coset Spectrum in the Large $\mathcal{N}=4$ Holography
• Lattice Formulation of $\mathcal{N}=2^{\ast }$ Yang-Mills
• $\mathcal{N}=2^{\ast }$ Yang-Mills on the Lattice