# Imaginary time and string theory

Is imaginary time an extra dimension? In other words, are time and imaginary time considered two separate dimensions? If so, does imaginary time appear (as a separate dimension) in string theory (thus contributing to the 11 dimensions in M-theory)?

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In physics, it is often possible/meaningful to analytically continue various real quantities into a corresponding complex variable.

In case of time, such analytical continuation allows us to wick-rotate a real time integration contour into an imaginary integration contour if we avoid singularities in the complex plane.

Wick-rotation is a mathematical procedure that doesn't count/qualify as an extra physical space-time dimension.

That said, there exists a branch of string theory, known as F-theory, that formally operates with two time-dimensions, cf. this Phys.SE post.

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