Lattice Supersymmetry and Topological Field Theory
نویسنده
چکیده
We discuss the connection between supersymmetric field theories and topological field theories and show how this connection may be used to construct local lattice field theories which maintain an exact supersymmetry. It is shown how metric independence of the continuum topological field theory allows us to derive the lattice theory by blocking out of the continuum in a deformed geometry. This, in turn allows us to prove the cut-off independence of certain supersymmetric Ward identities.
منابع مشابه
Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry
We construct super Yang-Mills theories with N = 2, 4 supersymmetries on the two-dimensional square lattice keeping one or two supercharges exactly. Along the same line as the previous paper [1], the construction is based on topological field theory formulation. We present two kinds of modifications of the action which preserve the exact supersymmetry and resolve the problem of degenerate classi...
متن کاملNo-Go Theorem of Leibniz Rule and Supersymmetry on the Lattice
An obstacle to realize supersymmetry on a lattice is the breakdown of Leibniz rule. We give a proof of a no-go theorem that it is impossible to construct a lattice field theory in an infinite lattice volume with any nontrivial field products and difference operators that satisfy the following three properties: (i) translation invariance, (ii) locality and (iii) Leibniz rule. We then propose a w...
متن کاملar X iv : h ep - t h / 93 11 13 8 v 1 2 3 N ov 1 99 3 Lattice models and N = 2 supersymmetry
We review the construction of exactly solvable lattice models whose continuum limits are N = 2 supersymmetric models. Both critical and off-critical models are discussed. The approach we take is to first find lattice models with natural topological sectors, and then identify the continuum limits of these sectors with topologically twisted N = 2 supersymmetric field theories. From this, we then ...
متن کاملCategorically-algebraic topology and its applications
This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...
متن کاملSuper Yang-Mills on the lattice with domain wall fermions
The dynamical N = 1, SU(2) Super Yang-Mills theory is studied on the lattice using a new lattice fermion regulator, domain wall fermions. This formulation even at non-zero lattice spacing does not require fine-tuning, has improved chiral properties and can produce topological zero-mode phenomena. Numerical simulations of the full theory on lattices with the topology of a torus indicate the form...
متن کامل