Seminar abstract: The period index problem has been suggested by Colliot-Thélène in early 2000s, and some of its low dimensional cases has been solved by de Jong, Lieblich and more recently Perry-Hotchkiss. We adapt the point of view of moduli of twisted sheaves, and by combining classical results in the theory of moduli of vector bundles, we realize the moduli of twisted vector bundles as the obstruction class of descending the determinantal line bundle; thus giving a bound on the period index problem for genus 2 curves over an arbitrary field.