Modified Gamma conjecture I (strong form)

Establish that for any Fano manifold X there exist T in C and ε>0 such that the Γ-flat section e^{T/z}S(z)z^{-µ}z^{−c1(X)}ΓX has moderate growth as z→0 within the angular sector |arg z|<π/2+ε, and show that this T equals the A-model conifold value TA,con.

Background

The authors propose a strengthened modification of Gamma conjecture I that does not assume Property OA. It requires global control of the Γ-flat section on a sector wider than π and identifies the exponential rate with TA,con. This version implies the weak form and is verified for toric Fano manifolds by mirror symmetry.