Higher rank K-theoretic Donaldson-Thomas Theory of points

We exploit the critical locus structure on Quot scheme $\mathrm{Quot}_{\mathbb A^3}(\mathscr O^{\oplus r},n)$, in particular associated symmetric obstruction theory, order to define rank $r$ K-theoretic Donaldson-Thomas invariants of Calabi-Yau $3$-fold $\mathbb A^3$. compute partition function as a plethystic exponential, proving conjecture proposed string theory by Awata-Kanno and Benini-Bonelli-Poggi-Tanzini. A crucial step proof is fact that do not depend equivariant parameters framing torus $(\mathbb C^\ast)^r$. Reducing from cohomological invariants, we corresponding DT Szabo. further enumerative solve higher pair $(X,F)$, where $F$ an exceptional vector bundle projective toric $X$. Finally, give mathematical definition chiral elliptic genus studied physics This allows us A^3$ arbitrary rank, study their first properties.