I am a Physics undergrad aspiring to pursue mathematical physics(string theory etc) as a future career. How much importance is given to your GPA by grad schools in the US or Europe for admitting students to PhD programs. A comprehensive account of the importance given by universities of different tiers would be appreciated. Example what are the guidelines followed by unis like harvard, princeton in comparision to something like texas, rochester, UCLA, etc. Also, what GPA is considered 'good' by a uni like princeton compared to the lower tier universities.
The importance of any single metric is binary and its value (important or not) depends on the size of the department. If the department is big admissions committees use metrics to weed out candidates. Basically anyone with GPA/GRE below X is triaged (doesn't matter what school you went to, how good your references are, etc). Smaller departments generally look at all applications. Once your applications is looked at, it is considered as a whole. There is no formula by which good GRE scores can offset a bad GPA. Obviously a better GPA doesn't hurt, but you really want to worry about the things you can control. For example, good research experience tends to trump everything else.