Holography for QCD with fermionic matter in the adjoint and fundamental representations

We discuss confinement and chiral symmetry breaking in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>SU</a:mi> <a:mo stretchy="false">(</a:mo> <a:msub> <a:mrow> <a:mi>N</a:mi> </a:mrow> <a:mrow> <a:mi>c</a:mi> </a:mrow> </a:msub> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> gauge theories with fermions in the adjoint representation. There has been considerable work on studying these theories compactified on a small circle (with compactification scale <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mn>1</e:mn> <e:mo>/</e:mo> <e:mi>L</e:mi> </e:math> large relative to the strong coupling scale of the theory). The weakly coupled IR theory of photons exhibits confinement through a density of magnetically charged instanton configurations. As the compactification scale <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mn>1</g:mn> <g:mo>/</g:mo> <g:mi>L</g:mi> </g:math> approaches the strong coupling scale, the IR theory becomes strongly coupled. In this regime we propose a holographic description of the IR degrees of freedom. The instanton condensation scale can be associated with a scale at which the Brietenlohner-Freedman (BF) bound is violated in the model and the glueball spectrum is computed. We can also introduce the adjoint fermions which holographically display a BF bound violation associated with their running anomalous dimension. Very naively extending the perturbative results to the nonperturbative regime suggests that chiral symmetry breaking might occur ahead of confinement, but equally they may be joined phenomena. If the two phenomena are separate, then it would be useful to be able to enlarge the gap in scales. We propose adding fermions in the fundamental representation as well, which in a holographic model (that favors this separation) can greatly enlarge the gap to an order of magnitude. These results challenge the lattice community to seek such scale gaps (or their absence) to further understand the confining and chiral symmetry breaking dynamics.