Typos

Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>

sec/part2/divergences.tex

@@ -12,7 +12,7 @@ In fact in~\cite{Liu:2002:StringsTimeDependentOrbifold} the four tachyons amplit
 \begin{equation}
   A_4 \sim \int\limits_{q \sim \infty} \frac{\dd{q}}{\abs{q}} \ccA( q )
 \end{equation}
-where $\ccA_{\text{closed}}( q ) \sim q^{4 - \ap \norm{\vec{p}_{\perp}}^2}$ and $\ccA_{\text{closed}}( q ) \sim q^{1 - \ap \norm{\vec{p}_{\perp}}^2} \tr\qty( \liebraket{T_1}{T_2}_+ \liebraket{T_3}{T_4}_+ )$ ($T_i$ for $i = 1,\, 2,\, 3,\, 4$ are Chan-Paton matrices).
+where $\ccA_{\text{closed}}( q ) \sim q^{4 - \ap \norm{\vec{p}_{\perp}}^2}$ and $\ccA_{\text{open}}( q ) \sim q^{1 - \ap \norm{\vec{p}_{\perp}}^2} \tr\qty( \liebraket{T_1}{T_2}_+ \liebraket{T_3}{T_4}_+ )$ ($T_i$ for $i = 1,\, 2,\, 3,\, 4$ are Chan-Paton matrices).
 Moreover divergences in string amplitudes are not limited to four points: interestingly we show that the open string three point amplitude with two tachyons and the first massive state may be divergent when some \emph{physical} polarisations are chosen.
 The true problem is therefore not related to a gravitational issue but to the non existence of the effective field theory.
 In fact when we express the theory using the eigenmodes of the kinetic terms some coefficients do not exist, not even as a distribution.