Abstract
Baryonic matter is notoriously difficult to deal with in the large-N limit, as baryons become operators of very large dimension with N fields in the fundamental representation. This issue is also present in gauge/gravity duals as baryons are described by very heavy localized objects. There are however alternative large-N extrapolations of QCD where small baryonic operators exist and can be treated on an equal footing to mesons. We explore the possibility of turning on a finite density of “light” baryons in a theory with a hadronic mass gap using a gauge/gravity construction based on the D3/D7 intersection. We find a novel phase with spontaneous breaking of baryon symmetry at zero temperature.
Highlights
A holographic model with light baryonsThe model was originally introduced in [35], based on the usual D3/D7 intersection [9]
Since the structure of 2Nf × 2Nf matrices is preserved by the covariant derivative and the commutator, all the terms in the action can be written as the product of two block diagonal or two block off-diagonal matrices
Where we have used that Xd† = Xd
Summary
The model was originally introduced in [35], based on the usual D3/D7 intersection [9]. One can define an orbifold/orientifold action in the original theory that consists of a reflection, on the 6789 directions for the orbifold and the 45 directions for the orientifold, plus transformations acting on the Chan-Paton factors of the open strings ending on the branes. Since the orbifold and orientifold actions act on Chan-Paton factors, they can change the gauge group and the representation of the fields on the branes. The combined effect of the orbifold and the orientifold is to reduce by half the rank of the color and flavor groups, to U(Nc) and U(Nf ) respectively, and to turn the N = 2 adjoint hypermultiplet (constructed with the chiral multiplets X67, X89) into a hypermultiplet in a two-index antisymmetric representation of U(Nc) (details can be found in [35]). The lowest BPS operators, corresponding to relevant and marginal operators, are dual to the following modes (X45 is an adjoint chiral multiplet)
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