Question

can anyone can give me the mathmatical equation of 'STRING' theory?

Answer 1

NO SORRY I CANNOT GIVE U THE EQUATION OF STRING THEORY BECAUSE I M THE STUDENT OF CLASS
9TH BUT THIS QUESTION WHICH CLASS PREFERS FROM.

Answer 2

As Lenny Susskind explains in this and this lecture, how to describe the scattering behavior of particles is nearly the definition of string theory. So formulas for scattering amplitudes can in some way be considered as fundamental equations defining the theory. Very schematically, the equation to calculate the scattering amplitude AA can be written down as

A=∫perioddτ∫surfacesexp−iSΔXμ(σ,τ)A=∫perioddτ∫surfacesexp−iS⁡ΔXμ(σ,τ)

Considering for example the process of two strings joining and splitting again, one has to integrate over all world sheets ΔXμ(σ,τ)ΔXμ(σ,τ) that start and end with two distinct strings. A second integral has to be done over all possible periods of time dτdτ the strings join. The action SS may for example be given by

S=∫dτdσ[(∂Xν∂τ)2−(∂Xν∂σ)2]S=∫dτdσ[(∂Xν∂τ)2−(∂Xν∂σ)2]

The information about the incoming and outgoing particles themself is still missing in the first equation and has to be inserted by hand by including additional multiplicative factors (vertex operators)

∏jeik