Consecutive holidays for faculty in the US
I can't really make much sense of the question, but I can explain how time off usually works in the US, though of course there are variations.
Professors aren't really typical employees. They likely technically have a set number of days they can take off and need to register them in some HR system, but usually no one is watching closely to make sure they are working on a work day (unless they don't show up for class), and even being absent from an office is not a very good sign a professor isn't working. Taking an extended vacation (a month or more) might be more noticeable, but even then, no one outside their lab is likely to even notice unless they are missing committee meetings or other responsibilities. Professors tend to be pretty self-motivated to work on their own research, and they won't be able to keep up with expectations for funding and publication if they take too much time off. Smart professors will still take some time off, though: however much they need to keep some balance in their life and remain productive during their working time.
Some days of the year are &quot;days off&quot; for everyone working for an employer (for employees in the entertainment/hospitality/retail sector this doesn't apply to them). These typically occur around secular or Christian holidays, and are usually just a single day or sometimes two consecutive days (for example, December 31st and January 1st). In practice, professors may work on these days anyways.
Academic calendars have some other breaks, most often a week in the spring for &quot;spring break&quot; and some time between semesters (often much of either December or January). However, these are mainly breaks for students, not employees. Professors could take this time off, but in practice those with teaching responsibilities often use that time to get caught up on grading and prep or focus on research.
The rest of time off is covered by &quot;vacation days&quot; allocated to individual employees (perhaps this is most similar to &quot;casual leave&quot; that you mention?). In principle these can be taken whenever an employee wants, but in practice their employer may designate days they can't be used. For someone teaching a course, it would be expected that no vacation days would be taken that conflict with being present to teach the course, except under exceptional circumstances (during which a professor would be expected to find their own substitute and communicate with their students unless they are physically incapacitated).
Some faculty under teaching contracts are only employed for 9 months of the year, during the typical fall/spring semesters, and are either not paid for the summer or have their 9-month salary prorated to give an income over the whole year. They don't have summer responsibilities directly, but this is the time they would have to devote to their own research, side projects like authoring books, and towards preparing courses for the next semester. Most will try to get these months covered by another salary source, however, and then do not have the time off.
If it was important to a professor on a 12-month contract to take a month-long vacation in some summer month, they can almost certainly do so assuming no conflicting responsibilities, but that would use up most/all of their annual leave. For an assistant professor on the tenure-track, there might be strong personal pressure to not take this sort of break as it might make it harder to achieve tenure, but that's really up to the individual. Longer leave in the form of &quot;sabbatical&quot; may be arranged, but typically professors on sabbatical still use this time to be productive in some way (for example, writing a book, travel related to their area of research, visiting collaborators at other institutions).