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Correction of typos in sez. 2

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Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
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Riccardo
2020-11-06 19:40:31 +01:00
parent dde9c3d05f
commit 334b7613c5
1 changed files with 6 additions and 6 deletions
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12
sec/part1/dbranes.tex
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@@ -349,16 +349,16 @@ One way to deal with them is to introduce the \emph{doubling trick} by gluing th
Let then $\cU_{(t,\, t+1)} = U_{(t+1)}\, U_{(t)}$ and $\tcU_{(t,\, t+1)} = U_{(\bart)}\, U_{(t)}\, U_{(t+1)}\, U_{(\bart)}$. Let then $\cU_{(t,\, t+1)} = U_{(t+1)}\, U_{(t)}$ and $\tcU_{(t,\, t+1)} = U_{(\bart)}\, U_{(t)}\, U_{(t+1)}\, U_{(\bart)}$.
The boundary conditions in terms of the doubling field are: The boundary conditions in terms of the doubling field are:
\begin{eqnarray} \begin{eqnarray}
\ipd{z} \cX( x_t + e^{2 \pi i}( \eta + i\, 0^+ ) ) \ipd{z} \cX( x_{(t)} + e^{2 \pi i}( \eta + i\, 0^+ ) )
& = & & = &
\cU_{(t,\, t+1)} \cU_{(t,\, t+1)}\,
\ipd{z} \cX( x_t + \eta + i\, 0^+ ), \ipd{z} \cX( x_{(t)} + \eta + i\, 0^+ ),
\label{eq:top_monodromy} \label{eq:top_monodromy}
\\ \\
\partial \cX( x_t + e^{2 \pi i}( \eta - i\, 0^+ ) ) \ipd{z} \cX( x_{(t)} + e^{2 \pi i}( \eta - i\, 0^+ ) )
& = & & = &
\tcU_{(t,\, t+1)} \tcU_{(t,\, t+1)}\,
\ipd{z} \cX( x_t + \eta - i\, 0^+ ), \ipd{z} \cX( x_{(t)} + \eta - i\, 0^+ ),
\label{eq:bottom_monodromy} \label{eq:bottom_monodromy}
\end{eqnarray} \end{eqnarray}
for $0 < \eta < \min\qty( \abs{x_{(t-1)} - x_{(t)}}, \abs{x_{(t)} - x_{(t+1)}} )$ in order to consider only the two adjacent D-branes $D_{(t)}$ and $D_{(t+1)}$. for $0 < \eta < \min\qty( \abs{x_{(t-1)} - x_{(t)}}, \abs{x_{(t)} - x_{(t+1)}} )$ in order to consider only the two adjacent D-branes $D_{(t)}$ and $D_{(t+1)}$.