TFPT scientific source excerpt
Original repository path: documents/archive--tfpt-45--source_extracts--00_orientation_source/sections/002-section-big-picture-what-tfpt-actually-claims.tex
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000071 |     title={TFPT master equation and closed indices}, colbacktitle=tfptblue]
000072 | \begin{equation}
000073 | \label{eq:tfpt-master}
000074 | \begin{aligned}
000075 | S_{\mathrm{TFPT}}
000076 | =
000077 | \operatorname{Tr}f\!\left(\frac{D_{\mathrm{rel}}+A_{\Sigma}^{\mathrm{seed}}}{\chiseed}\right)
000078 | -
000079 | \operatorname{Tr}f\!\left(\frac{D_{\mathrm{ref}}}{\chiseed}\right)
000080 | +\frac{i\pi}{2}\Delta\eta_\Sigma,
000081 | \qquad
000082 | A_{\Sigma}^{\mathrm{seed}}:=\mathcal B_{\mathrm{rel}}\oplus\nabla_{\chiseed}.
000083 | \end{aligned}
000084 | \end{equation}
000085 | \begin{equation}
000086 | \label{eq:tfpt-selectors}
000087 | \begin{aligned}
000088 | \operatorname*{Stat}_{\alpha,\chiseed,e,\wspin}S_{\mathrm{TFPT}}=0,
000089 | \qquad
000090 | \Padm:=\Pi_{\ker\Delta_{\mathrm{adm}}},
000091 | \qquad
000092 | \partial_\alpha\Gamma_{U(1)}(\alpha)=0,
000093 | \\
000094 | \operatorname{Ind}(D^+_{\mathrm{fam}})=3,
000095 | \qquad
000096 | \operatorname{Ind}(\mathcal B^+_{E_2})=1,
000097 | \qquad
000098 | \operatorname{Ind}(\mathcal B^+_{E_3})=0.
000099 | \end{aligned}
000100 | \end{equation}
000101 | \end{tcolorbox}
000102 | 
000103 | The hard carrier theorems below do not require the full theorem stack behind
000104 | \TFPTxref{eq:tfpt-master,eq:tfpt-selectors}. In the present paper the master equation is the
000105 | organizing closed form: the carrier theorems are hard, the later closure theorems are internal