I happened to get my hands on a string theory book where its been said that the universe's fundamental particle i.e. the string, takes about ten dimensions for specifying itself under symmetry. What are those?
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It depends on what theory are you useing, in theory of relativity there are only four dimensions $x^{\mu}$ but in another theory like general relativity there is a higher dimension which there is a constraint to eliminate the artifical 5th dimension (schwartzchild metric).
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