From 4fa9c980d9d793bdb3a2ad676346f8f3a0bbc476 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 4 Sep 2024 23:34:11 +0200
Subject: A bit of writing.

---
 topology.tex | 10 ++++++++--
 1 file changed, 8 insertions(+), 2 deletions(-)

(limited to 'topology.tex')

diff --git a/topology.tex b/topology.tex
index 4120cef..daacab2 100644
--- a/topology.tex
+++ b/topology.tex
@@ -1176,7 +1176,7 @@ to before. Alongside those in \eqref{eq:ops.bos} and \eqref{eq:ops.ferm}, we als
 These come with a volume term in the action
 \begin{equation}
   \begin{aligned}
-    \frac12\log\det\left(
+    \mathcal V=\frac12\log\det\left(
       \begin{bmatrix}
         C   & iR        & X_+       & X_-       \\
         iR  & D         & i\hat X_+ & i\hat X_- \\
@@ -1246,7 +1246,13 @@ and likewise a Gaussian integral in the Grassmann variables with kernel
     -G_{21} & -\bar J & -G_{22} & 0
   \end{bmatrix}
 \end{equation}
-\
+The effective action then has the form
+\begin{equation}
+  \mathcal S
+  =-\frac\alpha2\left(
+    \log\det K-\log\det K'+V_0^2(K^{-1})_{22}
+  \right)+\mathcal V
+\end{equation}
 
 
 
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