We show that 22d adjoint QCD, an SU(N)SU(N) gauge theory with one massless adjoint Majorana fermion, has a variety of mixed ’t Hooft anomalies. The anomalies are derived using a recent mod 22 index theorem and its generalization that incorporates ’t Hooft flux. Anomaly matching and dynamical considerations are used to determine the ground-state structure of the theory. The anomalies, which are present for most values of NN, are matched by spontaneous chiral symmetry breaking. We find that massless 22d adjoint QCD confines for N >2N>2, except for test charges of NN-ality N/2N/2, which are deconfined. In other words, \mathbb Z_NℤN center symmetry is unbroken for odd NN and spontaneously broken to \mathbb Z_{N/2}ℤN/2 for even NN. All of these results are confirmed by explicit calculations on small \mathbb{R}\times S^1ℝ×S1. We also show that this non-supersymmetric theory exhibits exact Bose-Fermi degeneracies for all states, including the vacua, when NN is even. Furthermore, for most values of NN, 22d massive adjoint QCD describes a non-trivial symmetry-protected topological (SPT) phase of matter, including certain cases where the number of interacting Majorana fermions is a multiple of 88. As a result, it fits into the classification of (1+1)(1+1)d SPT phases of interacting Majorana fermions in an interesting way.

We investigate the in-medium behavior of mesons at finite temperature and baryon chemical potential within a soft-wall model of AdS/QCD. We use a quartic scalar potential to obtain the correct form of chiral symmetry breaking. At zero quark mass the chiral phase transition is second-order, becoming a crossover at physical quark mass. At zero baryon chemical potential, we find a chiral transition temperature of 155 MeV in the chiral limit and a pseudo-transition temperature of 151 MeV at physical quark mass, consistent with lattice results. In the low-temperature limit, the second-order transition occurs at a baryon chemical potential of 566 MeV while the rapid crossover occurs at 559 MeV. A new parameterization of the dilaton profile results in improved meson spectra. Meson melting occurs at a lower temperature and chemical potential than the chiral phase transition, so the vector-axial vector mass splitting remains constant until the bound states melt.

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The phase transition from hadronic matter to chirally-symmetric quarkgluon plasma is expected to be a rapid crossover at zero quark chemical potential (µ), becoming first order at some finite value of µ, indicating the presence of a critical point. Using a three-flavor soft-wall model of AdS/QCD, we investigate the effect of varying the light and strange quark masses on the order of the chiral phase transition. At zero quark chemical potential, we reproduce the Columbia Plot, which summarizes the results of lattice QCD and other holographic models. We then extend this holographic model to examine the effects of finite quark chemical potential. We find that the the chemical potential does not affect the critical line that separates first-order from rapid crossover transitions. This excludes the possibility of a critical point in this model, suggesting that a different setup is necessary to reproduce all the features of the QCD phase diagram.