Bootstrapping ADE M-strings

Abstract

We study elliptic genera of ADE-type M-strings in 6d (2,0) SCFTs from their modularity and explore the relation to topological string partition functions. We find a novel kinematical constraint that elliptic genera should follow, which determines elliptic genera at low base degrees and helps us to conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of related geometries. Using this, we can bootstrap the elliptic genera to arbitrary base degree, including D/E-type theories for which explicit formulas are only partially known. We utilize our results to obtain the 6d Cardy formulas and the superconformal indices for (2,0) theories.

Weyl invariant Jacobi forms along Higgsing trees

“…In [66,67,3,98], these boundary conditions are imposed in the form of so-called vanishing conditions: the constraint that Gopakumar-Vafa invariants of a given curve class must vanish at sufficiently high genus. In [66], it was argued that imposing generic vanishing conditions (i.e.…”

Holomorphic Anomalies, Fourfolds and Fluxes

“…All in all we therefore find 20) where (2.58) was used after the second equality. To evaluate this further, note that the topological intersection number in the first term,…”

“…Nearly tensionless non-critical strings decoupled from gravity are known to arise at finite distances in moduli space [1,2]. The modular behaviour of their partition function, or elliptic genus [3], was crucial in understanding the physics of the associated superconformal theories [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], or other nonperturbative phenomena such as the formation of bound states of non-critical strings to yield the heterotic string [21,22]. Recently [23][24][25][26][27], the role of nearly tensionless critical strings at infinite distance points has been clarified in the context of quantum gravity conjectures such as the Weak Gravity Conjecture [28] or the Swampland Distance Conjecture [29]; the modularity of the partition function of these strings lies at the heart of the proof of the Weak Gravity Conjecture in such theories [23,[30][31][32].…”

Weyl invariant Jacobi forms along Higgsing trees

“…In [22,23,25,56], these boundary conditions are imposed in the form of so-called vanishing conditions: the constraint that Gopakumar-Vafa invariants of a given curve class must vanish at sufficiently high genus. In [22], it was argued that imposing generic vanishing conditions (i.e.…”