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We present the first gri-band period-luminosity (PL) and period-Wesenheit(PW) relations for 37 Type II Cepheids (hereafter TIIC) located in 18 globularclusters based on photometric data from the Zwicky Transient Facility. We alsoupdated BV IJHK-band absolute magnitudes for 58 TIIC in 24 globular clustersusing the latest homogeneous distances to the globular clusters. The slopes ofg/r/i and B/V/I band PL relations are found to be statistically consistent whenusing the same sample of distance and reddening. We employed the calibration ofri-band PL/PW relations in globular clusters to estimate a distance to M31based on a sample of ~270 TIIC from the PAndromeda project. The distancemodulus to M31, obtained using calibrated ri-band PW relation, agrees well withthe recent determination based on classical Cepheids. However, distance moduliderived using the calibrated r- and i-band PL relations are systematicallysmaller by ~0.2 mag, suggesting there are possible additional systematic erroron the PL relations. Finally, we also derive the period-color (PC) relationsand for the first time the period-Q-index (PQ) relations, where the Q-index isreddening-free, for our sample of TIIC. The PC relations based on (r-i) andnear-infrared colors and the PQ relations are found to be relativelyindependent of the pulsation periods.

Zwicky Transient Facility and Globular Clusters: The Period-Luminosity and Period-Wesenheit Relations for Type II Cepheids