Blowup Equations for Little Strings

Abstract

We propose blowup equations for 6d little string theories which generalize Nakajima-Yoshioka's blowup equations for the 4d/5d instanton partition functions on Omega background. We find that unlike the blowup equations for standard SQFTs, we need to sum over auxiliary magnetic fluxes on the blown-up ${\mathbb{P}}^1$ for a non-dynamical 2-form gauge field which plays a role in canceling the mixed anomalies of the gauge symmetries. We demonstrate with explicit examples that the blowup equations, when combined with the modular properties, can be solved in order to determine the elliptic genera of little strings.

arXiv comment71 pages, 6 figures

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Cited by in corpus (3)

• E-strings, $F_4$, and $D_4$ triality
• Probing Quantum Curves and Transitions in 5d SQFTs via Defects and Blowup Equations
• More on 5d Wilson Loops in Higher-Rank Theories and Blowup Equations