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We study the domain walls in hot $4$-D $SU(N)$ super Yang-Mills theory andQCD(adj), with $n_f$ Weyl flavors. We find that the $k$-wall worldvolume theoryis $2$-D QCD with gauge group $SU(N-k)\times SU(k) \times U(1)$ and Diracfermions charged under $U(1)$ and transforming in the bi-fundamentalrepresentation of the nonabelian factors. We show that the DW theory has a$1$-form $\mathbb Z_{N}^{(1)}$ center symmetry and a $0$-form $\mathbbZ_{2Nn_f}^{d\chi}$ discrete chiral symmetry, with a mixed 't Hooft anomalyconsistent with bulk/wall anomaly inflow. We argue that $\mathbb Z_{N}^{(1)}$is broken on the wall, and hence, Wilson loops obey the perimeter law. Thebreaking of the worldvolume center symmetry implies that bulk $p$-strings canend on the wall, a phenomenon first discovered using string-theoreticconstructions. We invoke $2$-D bosonization and gauged Wess-Zumino-Wittenmodels to suggest that $\mathbb Z_{2Nn_f}^{d\chi}$ is also broken in the IR,which implies that the $0$-form/$1$-form mixed 't Hooft anomaly in the gapped$k$-wall theory is saturated by a topological quantum field theory. We alsofind interesting parallels between the physics of high-temperature domain wallsstudied here and domain walls between chiral symmetry breaking vacua in thezero temperature phase of the theory (studied earlier in the semiclassicallycalculable small spatial circle regime), arising from the similar mode ofsaturation of the relevant 't Hooft anomalies.

Domain walls in high-T SU(N) super Yang-Mills theory and QCD(adj)