Nonperturbative Extra Dimensions

Project Coordinator: Edinburgh University

Partners: Wuppertal University, Queen Mary

Development of an efficient and flexible code for simulations of higher dimensional lattice gauge theories. Exploitation of this codebase for studying the Higgs mechanism and extended supersymmetry.

Task 1: Nonperturbative formulation of theories with extra-dimensions

We investigate five-dimensional gauge theories in order to understand the origin of confinement and of the Higgs mechanism in the SM in terms of the dynamics of the higher-dimensional theory. We formulate these theories on a Euclidean anisotropic lattice with either toroidal or orbifold boundary conditions. In these models, the Higgs is a relic of the extra dimensional gauge field and we search for a nonperturbative continuum limit where dimensional reduction can occur through localization or compactification and the Higgs potential can be predicted.

Task 2: Extended supersymmetry from dimensional reduction

It is well known that four dimensional gauge theories with extended supersymmetries can be obtained, in the continuum limit, from the dimensional reduction of a higher dimensional N=1 theory. There are indications that a similar approach can be efficiently implemented also within lattice gauge theory. Our goal is to develop this method into a concrete technique for simulating the N=2 super Yang-Mills theory on the lattice. This approach is complementary to the one explored in WP5, and we expect an intense synergy to develop between the two WPs.

Task 3: Supersymmetric theories with matter

We will consider the lattice version of supersymmetric gauge theories with matter. Going beyond the pure super Yang-Mills requires the development of both novel ideas and new algorithms. We will study the case of N=1 super QCD, and make contact with the large amount of analytic results accumulated for this theory over the last two decades.

Milestones:

  1. Codebase for simulations of pure gauge theories on higher dimensional asymmetric lattices. This will serve as a basis for all developments within this WP and provide a useful toolbox for many future simulations of gauge theories that differ from QCD in various respects. Timeframe: 12 m.
  2. Inclusion of fermions in higher dimensional simulations. Simulations with chiral fermions are now feasible in four dimensions. We will generalize the current available approaches to the higher dimensional case, with the application to N=2 Super-Yang Mills case as a main example. Timeframe: 24 m.