Glossary of string theory

${\displaystyle \alpha ^{\prime }}$

${\displaystyle \alpha ^{\prime }}$

${\displaystyle l_{s}={\sqrt {\alpha ^{\prime }}}}$

${\displaystyle {\frac {1}{2\pi \alpha ^{\prime }}}.}$

Tension is energy or work per unit length. In natural units ${\displaystyle c=1}$ and ${\displaystyle \hbar =1}$, and hence ${\displaystyle \alpha ^{\prime }}$ has dimension of length/energy or length/mass. Since ${\displaystyle \hbar }$ has the dimension of action, i.e. momentum times length, it follows that in natural units mass =1/length, and so ${\displaystyle \alpha ^{\prime }}$ has the unit of area. The slope ${\displaystyle \alpha ^{\prime }}$ of a Regge trajectory ${\displaystyle \alpha (M^{2})}$ in Regge theory is the derivative of spin ${\displaystyle S}$ or angular momentum with respect to mass-squared, i.e.

${\displaystyle {\frac {dS}{dM^{2}}}.}$

Since angular momentum is moment of momentum ${\displaystyle p}$, i.e. length times mass with ${\displaystyle c=1}$, ${\displaystyle S}$ is dimensionless in natural units, and ${\displaystyle \alpha ^{\prime }}$ has units of ${\displaystyle 1/M^{2}}$ or area like the inverse string tension.