Abstract
Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theory in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local and free of doublers and in the case of Yang-Mills theories also possess exact gauge invariance. In principle they form the basis for a truly non-perturbative definition of the continuum supersymmetric field theory. In this talk these ideas are reviewed with particular emphasis being placed on = 4 super Yang-Mills theory.
Highlights
The problem of formulating supersymmetric theories on lattices has a long history going back to the earliest days of lattice gauge theory
After initial efforts failed to produce useful supersymmetric lattice actions the topic languished for many years
A folklore developed that supersymmetry and the lattice were mutually incompatible
Summary
The problem of formulating supersymmetric theories on lattices has a long history going back to the earliest days of lattice gauge theory. From a practical point of view one can hope that some of the technology of lattice field theory such as strong coupling expansions and Monte Carlo simulation can be brought to bear on such supersymmetric theories In this talk I will outline some of the key ingredients that go into these constructions, the kinds of applications that have been considered so far and highlight the remaining difficulties. Kaplan and collaborators using ideas of orbifolding and deconstruction [4, 5, 6] These two seemingly independent approaches lead to the same lattice theories – see [11, 12, 13, 14] and the recent reviews [15, 16]. We will only have time to discuss the approach via topological twisting in this talk
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
