Lattice formulation of $\mathcal{N}=4$ super Yang-Mills theory

Abstract

We construct a lattice action for $\mathcal{N}=4$ super Yang-Mills theory in four dimensions which is local, gauge invariant, free of spectrum doubling and possesses a single exact supersymmetry. Our construction starts from the observation that the fermions of the continuum theory can be mapped into the component fields of a single real anticommuting Kahler-Dirac field. The original supersymmetry algebra then implies the existence of a nilpotent scalar supercharge $Q$ and a corresponding set of bosonic superpartners. Using this field content we write down a $Q$-exact action and show that, with an appropriate change of variables, it reduces to a well-known twist of $\mathcal{N}=4$ super Yang-Mills theory due to Marcus. Using the discretization prescription developed in an earlier paper on the $\mathcal{N}=2$ theory in two dimensions we are able to translate this geometrical action to the lattice.

15 pages. 1 reference corrected

References in corpus (7)

• A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice
• Twisted Superspace on a Lattice
• Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice
• Supersymmetry breaking in two dimensions: the lattice N=1 Wess-Zumino model
• Phase diagram of the lattice Wess-Zumino model from rigorous lower bounds on the energy
• N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one exact supersymmetry
• Lattice Supersymmetry via Twisting

Cited by in corpus (58)

• A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories with Sixteen Supercharges
• Exact lattice supersymmetry
• Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions
• Twisted Supersymmetric Gauge Theories and Orbifold Lattices
• Towards lattice simulation of the gauge theory duals to black holes and hot strings
• From Twisted Supersymmetry to Orbifold Lattices
• More $\mathcal{N}=4$ superconformal bootstrap
• Two-Dimensional Compact N=(2,2) Lattice Super Yang-Mills Theory with Exact Supersymmetry
• Geometry of Orbifolded Supersymmetric Lattice Gauge Theories
• Classification of Supersymmetric Lattice Gauge Theories by Orbifolding
• Simulations of $\mathcal{N}=2$ super Yang-Mills theory in two dimensions
• Two-dimensional N=(2,2) super Yang-Mills theory on the lattice via dimensional reduction
• A proposal of a fine tuning free formulation of 4d N=4 super Yang-Mills
• Relationship between various supersymmetric lattice models
• A Critique of the Link Approach to Exact Lattice Supersymmetry
• Compact Gauge Fields for Supersymmetric Lattices
• Lattice four-dimensional N=4 SYM is practical
• Lattice formulation of (2,2) supersymmetric gauge theories with matter fields
• Twisted supersymmetric sigma model on the lattice
• First results from simulations of supersymmetric lattices
• Perturbative Study of the Supersymmetric Lattice Theory from Matrix Model
• Lattice Supersymmetry: Equivalence between the Link Approach and Orbifolding
• Phases of $\Nc= \infty$ QCD-like gauge theories on $S^3\times S^1$ and nonperturbative orbifold-orientifold equivalences
• Lattice Formulation of Two-Dimensional N=(2,2) SQCD with Exact Supersymmetry
• Relations among Supersymmetric Lattice Gauge Theories via Orbifolding
• Supersymmetric Deformations of Type IIB Matrix Model as Matrix Regularization of N=4 SYM
• A Computer Test of Holographic Flavour Dynamics
• Ginsparg-Wilson Formulation of 2D N =(2,2) SQCD with Exact Lattice Supersymmetry
• Two-dimensional N=(2,2) super Yang-Mills theory on computer
• Lattice Gerbe Theory
• Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice
• Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping
• Lattice formulation of 2D $\mathcal{N}=(2,2)$ SQCD based on the B model twist
• Lattice formulation of three-dimensional $\mathcal{N}=4$ gauge theory with fundamental matter fields
• On the restoration of supersymmetry in twisted two-dimensional lattice Yang-Mills theory
• Lattice Formulation for 2d N=(2,2), (4,4) Super Yang-Mills Theories without Admissibility Conditions
• An object oriented code for simulating supersymmetric Yang--Mills theories
• Lattice Actions for Yang-Mills Quantum Mechanics with Exact Supersymmetry
• Exact Lattice Supersymmetry at the Quantum Level for $N=2$ Wess-Zumino Models in 1- and 2-Dimensions
• What lattice theorists can do for superstring/M-theory
• Nonperturbative study of dynamical SUSY breaking in $\mathcal{N}=(2,2)$ Yang-Mills
• Restoration of supersymmetry in two-dimensional SYM with sixteen supercharges on the lattice
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• Three Dimensional N=2 Supersymmetry on the Lattice
• Two-dimensional $\mathcal{N}=(2,2)$ Lattice Gauge Theories with Matter in Higher Representations
• Exact Vacuum Energy of Orbifold Lattice Theories
• On the Continuum and Lattice Formulations of N=4 D=3 Twisted Super Yang-Mills
• Supersymmetric quiver gauge theories on the lattice
• The Large N Reduction in Matrix Quantum Mechanics -- a Bridge between BFSS and IKKT --
• Technicolor and Beyond: Unification in Theory Space
• General solution of cyclic Leibniz rule
• Deformed matrix models, supersymmetric lattice twists and N=1/4 supersymmetry
• Real Time Quantum Gravity Dynamics from Classical Statistical Yang-Mills Simulations
• Vafa-Witten Theory on N=2 and N=4 Twisted Superspace in Four Dimensions
• Exact Ward-Takahashi identity for the lattice N=1 Wess-Zumino model
• 3d N=4 Super-Yang-Mills on a Lattice
• On the removal of the trace mode in lattice $\mathcal{N}=4$ super Yang-Mills theory
• Lattice Formulation of $\mathcal{N}=2^{\ast }$ Yang-Mills