Closed strings and CY

Signed-off-by: Riccardo Finotello <riccardo.finotello@gmail.com>
This commit is contained in:
2020-09-03 18:26:02 +02:00
parent 6bfebc26dd
commit 0818345375
5 changed files with 695 additions and 190 deletions

View File

@@ -47,176 +47,179 @@
%---- remap greek letters
\renewcommand{\alpha}{\upalpha}
\renewcommand{\beta}{\upbeta}
\renewcommand{\gamma}{\upgamma}
\renewcommand{\delta}{\updelta}
\renewcommand{\epsilon}{\upepsilon}
\renewcommand{\zeta}{\upzeta}
\renewcommand{\eta}{\upeta}
\renewcommand{\theta}{\uptheta}
\renewcommand{\iota}{\upiota}
\renewcommand{\kappa}{\upkappa}
\renewcommand{\lambda}{\uplambda}
\renewcommand{\mu}{\upmu}
\renewcommand{\nu}{\upnu}
\renewcommand{\xi}{\upxi}
\renewcommand{\pi}{\uppi}
\renewcommand{\rho}{\uprho}
\renewcommand{\sigma}{\upsigma}
\renewcommand{\tau}{\uptau}
\renewcommand{\upsilon}{\upupsilon}
\renewcommand{\phi}{\upphi}
\renewcommand{\chi}{\upchi}
\renewcommand{\psi}{\uppsi}
\renewcommand{\omega}{\upomega}
\renewcommand{\varepsilon}{\upvarepsilon}
\renewcommand{\vartheta}{\upvartheta}
\renewcommand{\varpi}{\upvarpi}
\renewcommand{\varphi}{\upvarphi}
\renewcommand{\Gamma}{\Upgamma}
\renewcommand{\Delta}{\Updelta}
\renewcommand{\Theta}{\Uptheta}
\renewcommand{\Lambda}{\Uplambda}
\renewcommand{\Xi}{\Upxi}
\renewcommand{\Pi}{\Uppi}
\renewcommand{\Sigma}{\Upsigma}
\renewcommand{\Upsilon}{\Upupsilon}
\renewcommand{\Phi}{\Upphi}
\renewcommand{\Psi}{\Uppsi}
\renewcommand{\Omega}{\Upomega}
\renewcommand{\alpha}{\upalpha\xspace}
\renewcommand{\beta}{\upbeta\xspace}
\renewcommand{\gamma}{\upgamma\xspace}
\renewcommand{\delta}{\updelta\xspace}
\renewcommand{\epsilon}{\upepsilon\xspace}
\renewcommand{\zeta}{\upzeta\xspace}
\renewcommand{\eta}{\upeta\xspace}
\renewcommand{\theta}{\uptheta\xspace}
\renewcommand{\iota}{\upiota\xspace}
\renewcommand{\kappa}{\upkappa\xspace}
\renewcommand{\lambda}{\uplambda\xspace}
\renewcommand{\mu}{\upmu\xspace}
\renewcommand{\nu}{\upnu\xspace}
\renewcommand{\xi}{\upxi\xspace}
\renewcommand{\pi}{\uppi\xspace}
\renewcommand{\rho}{\uprho\xspace}
\renewcommand{\sigma}{\upsigma\xspace}
\renewcommand{\tau}{\uptau\xspace}
\renewcommand{\upsilon}{\upupsilon\xspace}
\renewcommand{\phi}{\upphi\xspace}
\renewcommand{\chi}{\upchi\xspace}
\renewcommand{\psi}{\uppsi\xspace}
\renewcommand{\omega}{\upomega\xspace}
\renewcommand{\varepsilon}{\upvarepsilon\xspace}
\renewcommand{\vartheta}{\upvartheta\xspace}
\renewcommand{\varpi}{\upvarpi\xspace}
\renewcommand{\varphi}{\upvarphi\xspace}
\renewcommand{\Gamma}{\Upgamma\xspace}
\renewcommand{\Delta}{\Updelta\xspace}
\renewcommand{\Theta}{\Uptheta\xspace}
\renewcommand{\Lambda}{\Uplambda\xspace}
\renewcommand{\Xi}{\Upxi\xspace}
\renewcommand{\Pi}{\Uppi\xspace}
\renewcommand{\Sigma}{\Upsigma\xspace}
\renewcommand{\Upsilon}{\Upupsilon\xspace}
\renewcommand{\Phi}{\Upphi\xspace}
\renewcommand{\Psi}{\Uppsi\xspace}
\renewcommand{\Omega}{\Upomega\xspace}
%---- numerical sets
\providecommand{\1}{\ensuremath{\mathds{1}}}
\providecommand{\N}{\ensuremath{\mathds{N}}}
\providecommand{\Q}{\ensuremath{\mathds{Q}}}
\providecommand{\R}{\ensuremath{\mathds{R}}}
\providecommand{\Z}{\ensuremath{\mathds{Z}}}
\providecommand{\C}{\ensuremath{\mathds{C}}}
\providecommand{\1}{\ensuremath{\mathds{1}}\xspace}
\providecommand{\N}{\ensuremath{\mathds{N}}\xspace}
\providecommand{\Q}{\ensuremath{\mathds{Q}}\xspace}
\providecommand{\R}{\ensuremath{\mathds{R}}\xspace}
\providecommand{\Z}{\ensuremath{\mathds{Z}}\xspace}
\providecommand{\C}{\ensuremath{\mathds{C}}\xspace}
%---- calligraphic letters
\providecommand{\cA}{\ensuremath{\mathcal{A}}}
\providecommand{\cB}{\ensuremath{\mathcal{B}}}
\providecommand{\cC}{\ensuremath{\mathcal{C}}}
\providecommand{\cD}{\ensuremath{\mathcal{D}}}
\providecommand{\cE}{\ensuremath{\mathcal{E}}}
\providecommand{\cF}{\ensuremath{\mathcal{F}}}
\providecommand{\cG}{\ensuremath{\mathcal{G}}}
\providecommand{\cH}{\ensuremath{\mathcal{H}}}
\providecommand{\cI}{\ensuremath{\mathcal{I}}}
\providecommand{\cJ}{\ensuremath{\mathcal{J}}}
\providecommand{\cK}{\ensuremath{\mathcal{K}}}
\providecommand{\cL}{\ensuremath{\mathcal{L}}}
\providecommand{\cM}{\ensuremath{\mathcal{M}}}
\providecommand{\cN}{\ensuremath{\mathcal{N}}}
\providecommand{\cO}{\ensuremath{\mathcal{O}}}
\providecommand{\cP}{\ensuremath{\mathcal{P}}}
\providecommand{\cQ}{\ensuremath{\mathcal{Q}}}
\providecommand{\cR}{\ensuremath{\mathcal{R}}}
\providecommand{\cS}{\ensuremath{\mathcal{S}}}
\providecommand{\cT}{\ensuremath{\mathcal{T}}}
\providecommand{\cU}{\ensuremath{\mathcal{U}}}
\providecommand{\cV}{\ensuremath{\mathcal{V}}}
\providecommand{\cW}{\ensuremath{\mathcal{W}}}
\providecommand{\cX}{\ensuremath{\mathcal{X}}}
\providecommand{\cY}{\ensuremath{\mathcal{Y}}}
\providecommand{\cZ}{\ensuremath{\mathcal{Z}}}
\providecommand{\cA}{\ensuremath{\mathcal{A}}\xspace}
\providecommand{\cB}{\ensuremath{\mathcal{B}}\xspace}
\providecommand{\cC}{\ensuremath{\mathcal{C}}\xspace}
\providecommand{\cD}{\ensuremath{\mathcal{D}}\xspace}
\providecommand{\cE}{\ensuremath{\mathcal{E}}\xspace}
\providecommand{\cF}{\ensuremath{\mathcal{F}}\xspace}
\providecommand{\cG}{\ensuremath{\mathcal{G}}\xspace}
\providecommand{\cH}{\ensuremath{\mathcal{H}}\xspace}
\providecommand{\cI}{\ensuremath{\mathcal{I}}\xspace}
\providecommand{\cJ}{\ensuremath{\mathcal{J}}\xspace}
\providecommand{\cK}{\ensuremath{\mathcal{K}}\xspace}
\providecommand{\cL}{\ensuremath{\mathcal{L}}\xspace}
\providecommand{\cM}{\ensuremath{\mathcal{M}}\xspace}
\providecommand{\cN}{\ensuremath{\mathcal{N}}\xspace}
\providecommand{\cO}{\ensuremath{\mathcal{O}}\xspace}
\providecommand{\cP}{\ensuremath{\mathcal{P}}\xspace}
\providecommand{\cQ}{\ensuremath{\mathcal{Q}}\xspace}
\providecommand{\cR}{\ensuremath{\mathcal{R}}\xspace}
\providecommand{\cS}{\ensuremath{\mathcal{S}}\xspace}
\providecommand{\cT}{\ensuremath{\mathcal{T}}\xspace}
\providecommand{\cU}{\ensuremath{\mathcal{U}}\xspace}
\providecommand{\cV}{\ensuremath{\mathcal{V}}\xspace}
\providecommand{\cW}{\ensuremath{\mathcal{W}}\xspace}
\providecommand{\cX}{\ensuremath{\mathcal{X}}\xspace}
\providecommand{\cY}{\ensuremath{\mathcal{Y}}\xspace}
\providecommand{\cZ}{\ensuremath{\mathcal{Z}}\xspace}
\providecommand{\ccA}{\ensuremath{\mathscr{A}}}
\providecommand{\ccB}{\ensuremath{\mathscr{B}}}
\providecommand{\ccC}{\ensuremath{\mathscr{C}}}
\providecommand{\ccD}{\ensuremath{\mathscr{D}}}
\providecommand{\ccE}{\ensuremath{\mathscr{E}}}
\providecommand{\ccF}{\ensuremath{\mathscr{F}}}
\providecommand{\ccG}{\ensuremath{\mathscr{G}}}
\providecommand{\ccH}{\ensuremath{\mathscr{H}}}
\providecommand{\ccI}{\ensuremath{\mathscr{I}}}
\providecommand{\ccJ}{\ensuremath{\mathscr{J}}}
\providecommand{\ccK}{\ensuremath{\mathscr{K}}}
\providecommand{\ccL}{\ensuremath{\mathscr{L}}}
\providecommand{\ccM}{\ensuremath{\mathscr{M}}}
\providecommand{\ccN}{\ensuremath{\mathscr{N}}}
\providecommand{\ccO}{\ensuremath{\mathscr{O}}}
\providecommand{\ccP}{\ensuremath{\mathscr{P}}}
\providecommand{\ccQ}{\ensuremath{\mathscr{Q}}}
\providecommand{\ccR}{\ensuremath{\mathscr{R}}}
\providecommand{\ccS}{\ensuremath{\mathscr{S}}}
\providecommand{\ccT}{\ensuremath{\mathscr{T}}}
\providecommand{\ccU}{\ensuremath{\mathscr{U}}}
\providecommand{\ccV}{\ensuremath{\mathscr{V}}}
\providecommand{\ccW}{\ensuremath{\mathscr{W}}}
\providecommand{\ccX}{\ensuremath{\mathscr{X}}}
\providecommand{\ccY}{\ensuremath{\mathscr{Y}}}
\providecommand{\ccZ}{\ensuremath{\mathscr{Z}}}
\providecommand{\ccA}{\ensuremath{\mathscr{A}}\xspace}
\providecommand{\ccB}{\ensuremath{\mathscr{B}}\xspace}
\providecommand{\ccC}{\ensuremath{\mathscr{C}}\xspace}
\providecommand{\ccD}{\ensuremath{\mathscr{D}}\xspace}
\providecommand{\ccE}{\ensuremath{\mathscr{E}}\xspace}
\providecommand{\ccF}{\ensuremath{\mathscr{F}}\xspace}
\providecommand{\ccG}{\ensuremath{\mathscr{G}}\xspace}
\providecommand{\ccH}{\ensuremath{\mathscr{H}}\xspace}
\providecommand{\ccI}{\ensuremath{\mathscr{I}}\xspace}
\providecommand{\ccJ}{\ensuremath{\mathscr{J}}\xspace}
\providecommand{\ccK}{\ensuremath{\mathscr{K}}\xspace}
\providecommand{\ccL}{\ensuremath{\mathscr{L}}\xspace}
\providecommand{\ccM}{\ensuremath{\mathscr{M}}\xspace}
\providecommand{\ccN}{\ensuremath{\mathscr{N}}\xspace}
\providecommand{\ccO}{\ensuremath{\mathscr{O}}\xspace}
\providecommand{\ccP}{\ensuremath{\mathscr{P}}\xspace}
\providecommand{\ccQ}{\ensuremath{\mathscr{Q}}\xspace}
\providecommand{\ccR}{\ensuremath{\mathscr{R}}\xspace}
\providecommand{\ccS}{\ensuremath{\mathscr{S}}\xspace}
\providecommand{\ccT}{\ensuremath{\mathscr{T}}\xspace}
\providecommand{\ccU}{\ensuremath{\mathscr{U}}\xspace}
\providecommand{\ccV}{\ensuremath{\mathscr{V}}\xspace}
\providecommand{\ccW}{\ensuremath{\mathscr{W}}\xspace}
\providecommand{\ccX}{\ensuremath{\mathscr{X}}\xspace}
\providecommand{\ccY}{\ensuremath{\mathscr{Y}}\xspace}
\providecommand{\ccZ}{\ensuremath{\mathscr{Z}}\xspace}
%---- roman letters
\providecommand{\rA}{\ensuremath{\mathrm{A}}}
\providecommand{\rB}{\ensuremath{\mathrm{B}}}
\providecommand{\rC}{\ensuremath{\mathrm{C}}}
\providecommand{\rD}{\ensuremath{\mathrm{D}}}
\providecommand{\rE}{\ensuremath{\mathrm{E}}}
\providecommand{\rF}{\ensuremath{\mathrm{F}}}
\providecommand{\rG}{\ensuremath{\mathrm{G}}}
\providecommand{\rH}{\ensuremath{\mathrm{H}}}
\providecommand{\rI}{\ensuremath{\mathrm{I}}}
\providecommand{\rJ}{\ensuremath{\mathrm{J}}}
\providecommand{\rK}{\ensuremath{\mathrm{K}}}
\providecommand{\rL}{\ensuremath{\mathrm{L}}}
\providecommand{\rM}{\ensuremath{\mathrm{M}}}
\providecommand{\rN}{\ensuremath{\mathrm{N}}}
\providecommand{\rO}{\ensuremath{\mathrm{O}}}
\providecommand{\rP}{\ensuremath{\mathrm{P}}}
\providecommand{\rQ}{\ensuremath{\mathrm{Q}}}
\providecommand{\rR}{\ensuremath{\mathrm{R}}}
\providecommand{\rS}{\ensuremath{\mathrm{S}}}
\providecommand{\rT}{\ensuremath{\mathrm{T}}}
\providecommand{\rU}{\ensuremath{\mathrm{U}}}
\providecommand{\rV}{\ensuremath{\mathrm{V}}}
\providecommand{\rW}{\ensuremath{\mathrm{W}}}
\providecommand{\rX}{\ensuremath{\mathrm{X}}}
\providecommand{\rY}{\ensuremath{\mathrm{Y}}}
\providecommand{\rZ}{\ensuremath{\mathrm{Z}}}
\providecommand{\rA}{\ensuremath{\mathrm{A}}\xspace}
\providecommand{\rB}{\ensuremath{\mathrm{B}}\xspace}
\providecommand{\rC}{\ensuremath{\mathrm{C}}\xspace}
\providecommand{\rD}{\ensuremath{\mathrm{D}}\xspace}
\providecommand{\rE}{\ensuremath{\mathrm{E}}\xspace}
\providecommand{\rF}{\ensuremath{\mathrm{F}}\xspace}
\providecommand{\rG}{\ensuremath{\mathrm{G}}\xspace}
\providecommand{\rH}{\ensuremath{\mathrm{H}}\xspace}
\providecommand{\rI}{\ensuremath{\mathrm{I}}\xspace}
\providecommand{\rJ}{\ensuremath{\mathrm{J}}\xspace}
\providecommand{\rK}{\ensuremath{\mathrm{K}}\xspace}
\providecommand{\rL}{\ensuremath{\mathrm{L}}\xspace}
\providecommand{\rM}{\ensuremath{\mathrm{M}}\xspace}
\providecommand{\rN}{\ensuremath{\mathrm{N}}\xspace}
\providecommand{\rO}{\ensuremath{\mathrm{O}}\xspace}
\providecommand{\rP}{\ensuremath{\mathrm{P}}\xspace}
\providecommand{\rQ}{\ensuremath{\mathrm{Q}}\xspace}
\providecommand{\rR}{\ensuremath{\mathrm{R}}\xspace}
\providecommand{\rS}{\ensuremath{\mathrm{S}}\xspace}
\providecommand{\rT}{\ensuremath{\mathrm{T}}\xspace}
\providecommand{\rU}{\ensuremath{\mathrm{U}}\xspace}
\providecommand{\rV}{\ensuremath{\mathrm{V}}\xspace}
\providecommand{\rW}{\ensuremath{\mathrm{W}}\xspace}
\providecommand{\rX}{\ensuremath{\mathrm{X}}\xspace}
\providecommand{\rY}{\ensuremath{\mathrm{Y}}\xspace}
\providecommand{\rZ}{\ensuremath{\mathrm{Z}}\xspace}
%---- frak letters
\providecommand{\fA}{\ensuremath{\mathfrak{A}}}
\providecommand{\fB}{\ensuremath{\mathfrak{B}}}
\providecommand{\fC}{\ensuremath{\mathfrak{C}}}
\providecommand{\fD}{\ensuremath{\mathfrak{D}}}
\providecommand{\fE}{\ensuremath{\mathfrak{E}}}
\providecommand{\fF}{\ensuremath{\mathfrak{F}}}
\providecommand{\fG}{\ensuremath{\mathfrak{G}}}
\providecommand{\fH}{\ensuremath{\mathfrak{H}}}
\providecommand{\fI}{\ensuremath{\mathfrak{I}}}
\providecommand{\fJ}{\ensuremath{\mathfrak{J}}}
\providecommand{\fK}{\ensuremath{\mathfrak{K}}}
\providecommand{\fL}{\ensuremath{\mathfrak{L}}}
\providecommand{\fM}{\ensuremath{\mathfrak{M}}}
\providecommand{\fN}{\ensuremath{\mathfrak{N}}}
\providecommand{\fO}{\ensuremath{\mathfrak{O}}}
\providecommand{\fP}{\ensuremath{\mathfrak{P}}}
\providecommand{\fQ}{\ensuremath{\mathfrak{Q}}}
\providecommand{\fR}{\ensuremath{\mathfrak{R}}}
\providecommand{\fS}{\ensuremath{\mathfrak{S}}}
\providecommand{\fT}{\ensuremath{\mathfrak{T}}}
\providecommand{\fU}{\ensuremath{\mathfrak{U}}}
\providecommand{\fV}{\ensuremath{\mathfrak{V}}}
\providecommand{\fW}{\ensuremath{\mathfrak{W}}}
\providecommand{\fX}{\ensuremath{\mathfrak{X}}}
\providecommand{\fY}{\ensuremath{\mathfrak{Y}}}
\providecommand{\fZ}{\ensuremath{\mathfrak{Z}}}
\providecommand{\fA}{\ensuremath{\mathfrak{A}}\xspace}
\providecommand{\fB}{\ensuremath{\mathfrak{B}}\xspace}
\providecommand{\fC}{\ensuremath{\mathfrak{C}}\xspace}
\providecommand{\fD}{\ensuremath{\mathfrak{D}}\xspace}
\providecommand{\fE}{\ensuremath{\mathfrak{E}}\xspace}
\providecommand{\fF}{\ensuremath{\mathfrak{F}}\xspace}
\providecommand{\fG}{\ensuremath{\mathfrak{G}}\xspace}
\providecommand{\fH}{\ensuremath{\mathfrak{H}}\xspace}
\providecommand{\fI}{\ensuremath{\mathfrak{I}}\xspace}
\providecommand{\fJ}{\ensuremath{\mathfrak{J}}\xspace}
\providecommand{\fK}{\ensuremath{\mathfrak{K}}\xspace}
\providecommand{\fL}{\ensuremath{\mathfrak{L}}\xspace}
\providecommand{\fM}{\ensuremath{\mathfrak{M}}\xspace}
\providecommand{\fN}{\ensuremath{\mathfrak{N}}\xspace}
\providecommand{\fO}{\ensuremath{\mathfrak{O}}\xspace}
\providecommand{\fP}{\ensuremath{\mathfrak{P}}\xspace}
\providecommand{\fQ}{\ensuremath{\mathfrak{Q}}\xspace}
\providecommand{\fR}{\ensuremath{\mathfrak{R}}\xspace}
\providecommand{\fS}{\ensuremath{\mathfrak{S}}\xspace}
\providecommand{\fT}{\ensuremath{\mathfrak{T}}\xspace}
\providecommand{\fU}{\ensuremath{\mathfrak{U}}\xspace}
\providecommand{\fV}{\ensuremath{\mathfrak{V}}\xspace}
\providecommand{\fW}{\ensuremath{\mathfrak{W}}\xspace}
\providecommand{\fX}{\ensuremath{\mathfrak{X}}\xspace}
\providecommand{\fY}{\ensuremath{\mathfrak{Y}}\xspace}
\providecommand{\fZ}{\ensuremath{\mathfrak{Z}}\xspace}
%---- groups
\providecommand{\O}[1]{\ensuremath{\mathrm{O}(#1)}}
\providecommand{\SO}[1]{\ensuremath{\mathrm{SO}(#1)}}
\providecommand{\U}[1]{\ensuremath{\mathrm{U}(#1)}}
\providecommand{\SU}[1]{\ensuremath{\mathrm{SU}(#1)}}
\providecommand{\SL}[2]{\ensuremath{\mathrm{SL}_{#1}(#2)}}
\providecommand{\GL}[2]{\ensuremath{\mathrm{GL}_{#1}(#2)}}
\providecommand{\OO}[1]{\ensuremath{\mathrm{O}(#1)}\xspace}
\providecommand{\SO}[1]{\ensuremath{\mathrm{SO}(#1)}\xspace}
\providecommand{\U}[1]{\ensuremath{\mathrm{U}(#1)}\xspace}
\providecommand{\SU}[1]{\ensuremath{\mathrm{SU}(#1)}\xspace}
\providecommand{\SL}[2]{\ensuremath{\mathrm{SL}_{#1}(#2)}\xspace}
\providecommand{\GL}[2]{\ensuremath{\mathrm{GL}_{#1}(#2)}\xspace}
%---- algebras
\providecommand{\liebraket}[2]{\ensuremath{\left[ #1,\, #2 \right]}}
%---- inline partial derivatives (use $\ipd{s}$ for $\partial_s$)