Comments on Class S(YK)

We present a DSSYK-like interpretation of the Schur half-indices of N=2 $SU(2)$ gauge theories with matter, in the presence of fundamental Wilson lines. The Schur half-indices of these theories can be understood as transition amplitudes in a non-vacuum sector of ordinary DSSYK. In the language of chord diagrams, the half-indices are obtained by summing over diagrams with special segments, which correspond to coherent states of the q-oscillator algebra. In addition, we show that the Schur half-index of $SU(2)$ gauge theory with nF=4 fundamental half-hypermultiplets corresponds to the partition function of a particle on the quantum disk.