Twisted supersymmetric sigma model on the lattice

Abstract

In this paper we conduct a numerical study of the supersymmetric O(3) non-linear sigma model. The lattice formulation we employ was derived in \cite{sigma1} and corresponds to a discretization of a {\it twisted} form of the continuum action. The twisting process exposes a {\it nilpotent} supercharge $Q$ and allows the action to be rewritten in $Q$-exact form. These properties may be maintained on the lattice. We show how to deform the theory by the addition of potential terms which preserve the supersymmetry. A Wilson mass operator may be introduced in this way with a minimal breaking of supersymmetry. We additionally show how to rewrite the theory in the language of Kähler-Dirac fields and explain why this avenue does not provide a good route to discretization. Our numerical results provide strong evidence for a restoration of full supersymmetry in the continuum limit {\it without} fine tuning. We also observe a non-vanishing chiral condensate as expected from continuum instanton calculations.

33 pages, 12 figures. Two references added and minor typos corrected. Expanded discussion of renormalization issues. Version to be published in JHEP

References in corpus (44)

• Supergravity and The Large N Limit of Theories With Sixteen Supercharges
• Gluino Condensate and Magnetic Monopoles in Supersymmetric Gluodynamics
• Supersymmetry on a Spatial Lattice
• Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with Four Supercharges
• A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories with Sixteen Supercharges
• A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
• Supersymmetry on a Euclidean Spacetime Lattice II: Theories with Eight Supercharges
• Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle
• Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry
• Exact 2+1 flavour RHMC simulations
• Exact Lattice Supersymmetry: the Two-Dimensional N=2 Wess-Zumino Model
• Krylov space solvers for shifted linear systems
• Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions
• Twisted Supersymmetric Gauge Theories and Orbifold Lattices
• A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice
• Lattice Supersymmetry and Topological Field Theory
• Twisted Superspace on a Lattice
• Exact Extended Supersymmetry on a Lattice: Twisted N=2 Super Yang-Mills in Two Dimensions
• Topological Matter in Two Dimensions
• Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice
• Lattice formulation of $\mathcal{N}=4$ super Yang-Mills theory
• Two-Dimensional Compact N=(2,2) Lattice Super Yang-Mills Theory with Exact Supersymmetry
• Black Holes and the Super Yang-Mills diagram. II
• Non-positive fermion determinants in lattice supersymmetry
• A lattice path integral for supersymmetric quantum mechanics
• Simulations of $\mathcal{N}=2$ super Yang-Mills theory in two dimensions
• The fermion determinant in (4,4) 2d lattice super-Yang-Mills
• Lattice Sigma Models with Exact Supersymmetry
• Breakdown of Cluster Decomposition in Instanton Calculations of the Gluino Condensate
• Deconstruction, Lattice Supersymmetry, Anomalies and Branes
• Noncommutativity Approach to Supersymmetry on the Lattice: SUSY Quantum Mechanics and an Inconsistency
• Twisted Superspace for N=D=2 Super BF and Yang-Mills with Dirac-Kähler Fermion Mechanism
• Compact Gauge Fields for Supersymmetric Lattices
• Matrix Theory Black Holes and the Gross Witten Transition
• N=4 Twisted Superspace from Dirac-Kahler Twist and Off-shell SUSY Invariant Actions in Four Dimensions
• Supersymetry on the Noncommutative Lattice
• Exact Lattice Supersymmetry from Topological Field Theory
• The Exact Mass-Gap of the Supersymmetric CP^{n-1} Sigam Model
• N=(1,1) Super Yang-Mills on a (2+1) Dimensional Transverse Lattice with one Exact Supersymmetry
• N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one exact supersymmetry
• A solution to the fermion doubling problem for supersymmetric theories on the transverse lattice
• Lattice Supersymmetry via Twisting
• Notes on (twisted) lattice supersymmetry
• Lattice Study of the O(3) Supersymmetric Sigma Model

Cited by in corpus (16)

• Exact lattice supersymmetry
• Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions
• Towards lattice simulation of the gauge theory duals to black holes and hot strings
• Lattice Formulation of Two-Dimensional N=(2,2) SQCD with Exact Supersymmetry
• Generalized supersymmetry and sigma models
• Ginsparg-Wilson Formulation of 2D N =(2,2) SQCD with Exact Lattice Supersymmetry
• 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
• Matrix formulation of superspace on 1D lattice with two supercharges
• Supersymmetric Nonlinear O(3) Sigma Model on the Lattice
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• On the Continuum and Lattice Formulations of N=4 D=3 Twisted Super Yang-Mills
• Advances and applications of lattice supersymmetry
• Particle Dark Matter Candidates
• A deconstruction lattice description of the D1/D5 brane world-volume gauge theory