Blocking-inspired supersymmetric actions: A status report

Abstract

We provide a status report on the advances in blocking-inspired supersymmetric actions. This is done at the example of interacting supersymmetric quantum mechanics as well as the Wess-Zumino model. We investigate in particular the implications of a nontrivial realisation of translational symmetry on the lattice in this approach. We also discuss the locality of symmetry generators.

The nonperturbative functional renormalization group and its applications

“…In the formulation with the mSTI (76) this amounts to absorbing its right hand side in the symmetry transformations themselves. Typically then the generator of the symmetry looses its ultralocality, a well-studied problem for chiral symmetry transformations as well as supersymmetry in lattice formulation, for a point of view close to the FRG see [696]. Note that symmetries, and in particular the definition of (Noether) charges require locality (exponential decay in spacetime) of the generators of this symmetry.…”

“…Note that symmetries, and in particular the definition of (Noether) charges require locality (exponential decay in spacetime) of the generators of this symmetry. A well-studied example is chiral symmetry on the lattice: while chiral symmetry for Wilson fermions with explicit mass terms for the fermionic doublers can be formulated, the respective generator of chiral symmetry only has an algebraic decay in spacetime, see [696]. This leads to a slow convergence towards the continuum limit of observables with chiral properties.…”

Supersymmetry on the lattice and the status of the SYM simulations

“…Although it is possible to establish such an relation, it is hard to find a solution in the interacting case. Perhaps an approximation can lead to a useful lattice realization [17].…”

Functional flows in QED and the modified Ward–Takahashi identity

“…Still, even in the presence of the regulator the mWTI can be formulated as standard WTI with a modified generator of gauge transformations, [13,[16][17][18]. For more details on the properties of such a modified generator see [19]. This concise form of the mWTI as a symmetry identity is very useful for the construction of closed solutions of the mWTI.…”