2.10 A spacetime orbifold in two dimensions, 4

A First Course in String Theory

(b) … the family of curves

$\displaystyle{x^+ x^- = a^2}$ ,

where $\displaystyle{a > 0}$ …

…

Show that the identification (2) relates points on each separate curve.

~~~

Identification (2):

$\displaystyle{(x^+, x^-) \sim \left( e^{-\lambda} x^+, e^{\lambda} x^- \right)}$ , where $\displaystyle{e^\lambda \equiv \sqrt{\frac{1+\beta}{1-\beta}}}$ .

$\displaystyle{ \begin{aligned} (x^+)' &= e^{- \lambda} x^+ \\ (x^-)' &= e^{\lambda} x^- \\ \end{aligned} }$

$\displaystyle{ \begin{aligned} (x^+)' (x^-)' &= e^{- \lambda} x^+ e^{\lambda} x^- \\ &= a^2 \\ \end{aligned} }$

— Me@2021-12-15 04:18:27 PM

Physics Town

continues

2.10 A spacetime orbifold in two dimensions, 4

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