Q: What tenses should be used in the literature write-up?

By ‘literature write-up,’ we understand you mean ‘literature review.’ Now, do you mean an entire paper that is a literature review or only the literature review section of the paper that typically comes in the Introduction?

Anyway, the answer is: it depends, and it’s quite possible to have multiple tenses in the literature review. (That’s why your basic question is right: What tenses should be used… rather than What tense should be used…) To know more, you may go through these resources (one of which is a similar question):

• What tense should I use when writing a literature review?
• The secret to using tenses in scientific writing

And in case you are writing a literature review, you may find these articles helpful:

• A young researcher's guide to writing a literature review
• How to write the literature review of your research paper

Hope that helps!