Orientifold planar equivalence

Project Coordinator: Swansea University

Partners: CP3-Origins, Edinburgh University

1) Determine the large-N equivalence between the bosonic sectors of the two theories by computing the spectrum at various N and extrapolating to infinite N. 2) Compute the corrections in 1/N to establish whether the theory at N=3 (which has the same colour content as real-world QCD) is close to the large-N limit. 3) Compare the lattice results with predictions coming from supersymmetric yang-Mills (e.g. degeneracy of the scalar and of the pseudoscalar) in the large-N limit.

Task 1: Lattice explorations of orientifold planar equivalence

The highest impact result of Orientifold Planar Equivalence is the transcription of results derived fom N=1 Super Yang-Mills to QCD-like theory through the equivalence at large N. This is more straightforward when the matter content of the QCD theory is one flavor of Dirac fermions. An open questions in Orientifold Planar Equivalence is the size of the 1/N corrections: were they to be so large that the N=3 case can not be described by a simple power series, the relevance of the equivalence for QCD will be seriously questionable. In order to understand the size of the corrections, we need calculations from first principles, and the lattice is the ideal tool for those. However, putting one flavour of Dirac fermions in the (anti-)symmetric or one Majorana flavour in the adjoint spoils the positive-definiteness of the Boltzmann weight in the Euclidean partition function of the system, making the problem technically more complicated. Hence, working on this aspect of Orientifold Planar Equivalence requires an initial coding effort to adapt our simulation codes for the one flavour case. Since the study of the adjoint theory with one Majorana flavour is a core part of this package, there is a natural connection between this work package and WP5 on lattice supersymmetry.


  1. Development and testing of a simulation code for the case of one flavour of matter fields. Timeframe: 12 m.
  2. Explore the lattice phase structure of the theory on a 16×83 for N=2,3,4,6 to locate the regime connected to the physical case. Timeframe: 4 m.
  3. For each gauge group, perform calculations at three values of the couplings for masses extrapolating to the chiral limit and scaling the lattice size in such a way that the physical volume is constant. Timeframe: 18 m.
  4. Evaluate the large-N limit of the observables and the size of the 1/N corrections. Timeframe: 2 m.