Positivity, low twist dominance and CSDR for CFTs

We consider a crossing symmetric dispersion relation (CSDR) for CFT four point correlation with identical scalar operators, which is manifestly under the cross-ratios $u,v$ interchange. This representation has several features in common CSDR quantum field theories. It enables study of expansion function around $u=v=1/4$, used numerical conformal bootstrap program. elucidate remarkable dispersive using $\Phi_{1,2}$ operators 2d minimal models as test-bed. When dimension external operator ($\Delta_\sigma$) less than $\frac{1}{2}$, gets contribution from only single tower global primary second being projected out. find that there notion low twist dominance (LTD) which, $\Delta_\sigma$, maximized near Ising model well non-unitary Yang-Lee model. The and LTD further explain positivity Taylor coefficients lead to universal predictions specific ratios these coefficients. These results carry over epsilon $4-\epsilon$ dimensions. also conduct preliminary investigation geometric theory ideas, namely Bieberbach-Rogosinski bounds.