Question

What is U-duality? and Why U-duality is important?

Answer 1

In string theory, we know three dualities.

S-duality: Extension of Electric-magnetic duality, Duality between strongly coupled qft and weakly coupled qft. (One of the typical example is Seiberg duality in sqft)

T-duality: In short R↔1RR↔1R

U-duality: In M theory perspective, U-duality usually means T+S duality.(???)

But I am wondering about the last part, U-duality.

What is U-duality and why it is important in string theory

Answer 2

,U-duality (short for unified duality) is a symmetry of string theory or M-theory combining S-duality and T-duality transformations. The term is most often met in the context of the "U-duality (symmetry) group" of M-theory as defined on a particular background space (topological manifold). This is the union of all the S-duality and T-duality available in that topology. The narrow meaning of the word "U-duality" is one of those dualities that can be classified neither as an S-duality, nor as a T-duality - a transformation that exchanges a large geometry of one theory with the strong coupling of another theory