Lattice supersymmetry, superfields and renormalization

Abstract

We study Euclidean lattice formulations of non-gauge supersymmetric models with up to four supercharges in various dimensions. We formulate the conditions under which the interacting lattice theory can exactly preserve one or more nilpotent anticommuting supersymmetries. We introduce a superfield formalism, which allows the enumeration of all possible lattice supersymmetry invariants. We use it to discuss the formulation of Q-exact lattice actions and their renormalization in a general manner. In some examples, one exact supersymmetry guarantees finiteness of the continuum limit of the lattice theory. As a consequence, we show that the desired quantum continuum limit is obtained without fine tuning for these models. Finally, we discuss the implications and possible further applications of our results to the study of gauge and non-gauge models.

44 pages, 1 figure

References in corpus (21)

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• Supersymmetry on a Spatial Lattice
• Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with Four Supercharges
• A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
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• Lattice Supersymmetry and Topological Field Theory
• Super Yang-Mills on the lattice with domain wall fermions
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• Non-positive fermion determinants in lattice supersymmetry
• A lattice path integral for supersymmetric quantum mechanics
• Nicolai mapping vs. exact chiral symmetry on the lattice
• The fermion determinant in (4,4) 2d lattice super-Yang-Mills
• Lattice Sigma Models with Exact Supersymmetry
• Lattice Formulation of Supersymmetric Yang-Mills Theories without Fine-Tuning
• SDLCQ: Supersymmetric Discrete Light Cone Quantization
• Exact Lattice Supersymmetry from Topological Field Theory
• Phase diagram of the lattice Wess-Zumino model from rigorous lower bounds on the energy
• Deconstruction, 2d lattice Yang-Mills, and the dynamical lattice spacing
• Improved results for N=(2,2) super Yang-Mills theory using supersymmetric discrete light-cone quantization

Cited by in corpus (43)

• A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories with Sixteen Supercharges
• Exact lattice supersymmetry
• Twisted Supersymmetric Gauge Theories and Orbifold Lattices
• A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice
• Simulating Wess-Zumino Supersymmetry Model in Optical Lattices
• Deconstruction and other approaches to supersymmetric lattice field theories
• Low-dimensional Supersymmetric Lattice Models
• Two-Dimensional Compact N=(2,2) Lattice Super Yang-Mills Theory with Exact Supersymmetry
• Less naive about supersymmetric lattice quantum mechanics
• Tensor network formulation for two-dimensional lattice $\mathcal{N}=1$ Wess-Zumino model
• Two-dimensional N=(2,2) super Yang-Mills theory on the lattice via dimensional reduction
• Simulations of $\mathcal{N}=2$ super Yang-Mills theory in two dimensions
• Progress in four-dimensional lattice supersymmetry
• Two-Dimensional Wess-Zumino Models at Intermediate Couplings
• A Critique of the Link Approach to Exact Lattice Supersymmetry
• Compact Gauge Fields for Supersymmetric Lattices
• Lattice formulation of (2,2) supersymmetric gauge theories with matter fields
• R-symmetry in the Q-exact (2,2) 2d lattice Wess-Zumino model
• Supersymmetry Breaking in Low Dimensional Models
• Supersymmetric nonperturbative formulation of the WZ model in lower dimensions
• Chiral Lattice Gauge Theories from Warped Domain Walls and Ginsparg-Wilson Fermions
• Supersymmetric Deformations of Type IIB Matrix Model as Matrix Regularization of N=4 SYM
• Supersymmetric QCD on the Lattice: An Exploratory Study
• Spontaneous supersymmetry breaking in matrix models from the viewpoints of localization and Nicolai mapping
• N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one exact supersymmetry
• A local formulation of lattice Wess-Zumino model with exact $\U(1)_R$ symmetry
• A criterion for lattice supersymmetry: cyclic Leibniz rule
• Supersymmetric quantum mechanics on the lattice: I. Loop formulation
• Warped Domain Wall Fermions
• Supersymmetric QCD: Renormalization and Mixing of Composite Operators
• Direct computational approach to lattice supersymmetric quantum mechanics
• Supersymmetry restoration in lattice formulations of 2D $\mathcal{N}=(2,2)$ WZ model based on the Nicolai map
• Gauge-invariant Renormalization of the Gluino-Glue operator
• Exact Results in Discretized Gauge Theories
• Advances and applications of lattice supersymmetry
• Renormalization and Mixing of the Gluino-Glue Operator on the Lattice
• Lattice study of supersymmetry breaking in N=2 supersymmetric quantum mechanics
• A lattice formulation of N=2 supersymmetric SYK model
• Numerical study of the $\mathcal{N}=2$ Landau--Ginzburg model
• Continuum limit in numerical simulations of the $\mathcal{N}=2$ Landau--Ginzburg model
• A deconstruction lattice description of the D1/D5 brane world-volume gauge theory
• Symmetry and scaling in the Q-exact lattice (2,2) 2d Wess-Zumino model
• One-loop calculations in Supersymmetric Lattice QCD