Toda-like (0,2) mirrors to products of projective spaces

One of the open problems in understanding (0,2) mirror symmetry concerns the construction of toda-like landau-ginzburg mirrors to (0,2) theories on fano spaces. in this paper, we begin to fill this gap by making an ansatz for (0,2) toda-like theories mirror to (0,2) supersymmetric nonlinear sigma models on products of projective spaces, with deformations of the tangent bundle, generalizing a special case previously worked out for $$ {mathrm{mathbb{p}}}^1times {mathrm{mathbb{p}}}^1 $$ . we check this ansatz by matching correlation functions of the b/2-twisted toda-like theories to correlation functions of corresponding a/2-twisted nonlinear sigma models, computed primarily using localization techniques. these (0,2) landau-ginzburg models admit redundancies, which can lend themselves to multiple distinct-looking representatives of the same physics, which we discuss.