Photometric Variability of Possible JWST Calibration Stars with TESS

We use data from the Transiting Exoplanet Survey Satellite (\tess) to search for, and set limits on, optical to near infrared photometric variability of the candidate \jwst\ spectrophotometric standards. This list is comprised of stars observed by the Hubble and Spitzer Space Telescopes and will be used to connect \jwst\ measurements to those from other observatories. Our search of 37 of these candidate standards has revealed measurable periodic variability in 15 stars. The majority of those that vary show low amplitudes below half a percent; however, 4 stars (\object{HD~38949}, \object{TIC~219114641}, \object{TIC~219897252}, \object{TIC~233095291}) are observed to vary photometrically by more than 1\%. At that level, the variability could impact the error budget in the spectrophotometric calibration of the science instruments aboard \jwst. For the other candidate standard stars that have \tess\ data we report upper limits on the observed changes in flux. Despite some systematic noise in some light curves, all stars brighter than $T<12$\,mag show a 3$\sigma$ upper limit on peak-to-peak variability less than half a percent for time scales between an hour and multiple weeks, confirming they will serve as reliable spectrophotometric standards.