We exploit the critical structure on the Quot scheme Quot(A3) (O-circle plus r, n), in particular the associated symmetric obstruction theory, in order to study rank r K-theoretic Donaldson Thomas(DT) invariants of the local Calabi-Yau 3-fold A(3). We compute the associated partition function as a plethystic exponential, proving a conjecture proposed in string theory by Awata-Kanno and Benini-Bonelli-Poggi-Tanzini. A crucial step in the proof is the fact, nontrival if r > 1, that the invariants do not depend on the equivariant parameters of the framing torus (C*)(r). Reducing from K-theoretic to cohomological invariants, we compute the corresponding DT invariants, proving a conjecture of Szabo. Reducing further to enumerative DT invariants, we solve the higher rank DT theory of a pair (X, F), where F is an equivariant exceptional locally free sheaf on a projective toric 3-fold X.As a further refinement of the K-theoretic DT invariants, we formulate a mathematical definition of the chiral elliptic genus studied in physics. This allows us to define elliptic DT invariants of A(3) in arbitrary rank, which we use to tackle a conjecture of Benini-Bonelli-Poggi-Tanzini.

Higher rank K-theoretic Donaldson-Thomas Theory of points / Fasola, Nadir; Monavari, Sergej; Ricolfi, Andrea T.. - In: FORUM OF MATHEMATICS. SIGMA. - ISSN 2050-5094. - 9:(2021), pp. 1-51. [10.1017/fms.2021.4]

Higher rank K-theoretic Donaldson-Thomas Theory of points

Fasola, Nadir;Monavari, Sergej;Ricolfi, Andrea T.
2021-01-01

Abstract

We exploit the critical structure on the Quot scheme Quot(A3) (O-circle plus r, n), in particular the associated symmetric obstruction theory, in order to study rank r K-theoretic Donaldson Thomas(DT) invariants of the local Calabi-Yau 3-fold A(3). We compute the associated partition function as a plethystic exponential, proving a conjecture proposed in string theory by Awata-Kanno and Benini-Bonelli-Poggi-Tanzini. A crucial step in the proof is the fact, nontrival if r > 1, that the invariants do not depend on the equivariant parameters of the framing torus (C*)(r). Reducing from K-theoretic to cohomological invariants, we compute the corresponding DT invariants, proving a conjecture of Szabo. Reducing further to enumerative DT invariants, we solve the higher rank DT theory of a pair (X, F), where F is an equivariant exceptional locally free sheaf on a projective toric 3-fold X.As a further refinement of the K-theoretic DT invariants, we formulate a mathematical definition of the chiral elliptic genus studied in physics. This allows us to define elliptic DT invariants of A(3) in arbitrary rank, which we use to tackle a conjecture of Benini-Bonelli-Poggi-Tanzini.
2021
9
1
51
https://arxiv.org/abs/2003.13565
Fasola, Nadir; Monavari, Sergej; Ricolfi, Andrea T.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/135056
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