Refined stable pair invariants for E-, M- and [p, q]-strings

By Min-xin Huang, A. Klemm, Maximilian Poretschkin. 2013

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A bstractWe use mirror symmetry, the refined holomorphic anomaly equation and modularity properties of elliptic singularities to calculate the refined BPS invariants of stable pairs on non-compact Calabi-Yau manifolds, based on del Pezzo surfaces and elliptic surfaces, in particular the half K3. The BPS numbers contribute naturally to the fivedimensional N =1 supersymmetric index of M-theory, but they can be also interpreted in terms of the superconformal index in six dimensions and upon dimensional reduction the generating functions count N = 2 Seiberg-Witten gauge theory instantons in four dimensions. Using the M/F-theory uplift the additional information encoded in the spin content can be used in an essential way to obtain information about BPS states in physical systems associated to small instantons, tensionless strings, gauge symmetry enhancement in F-theory by [p, q]-strings as well as M-strings.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/7603dba0dc4ba42b2be6a2a8c4a87f2091c4207f

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In Nuclear and High Energy Physics

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Topological Strings from Quantum Mechanics (2014, background): “In the current case it is given by the third order differential operator [33] L = (−12m(2) + 9ũ− 18mũ(2) + 8m(2)ũ(3))∂(3) ũ + (−108m− 128m(4) + 144m(2)ũ+ 27ũ(2) − 64m(3)ũ(2) − 52mũ(3) + 24m(2)ũ(4))∂(2) ũ + (−9 + 8mũ)(−27 + 16m(3) + 36mũ − 8m(2)ũ(2) − ũ(3) +mũ(4))∂ũ, (5.”