Blowup Equations for Little Strings

TL;DR

This paper introduces blowup equations for 6d little string theories, extending previous equations for 4d/5d theories, and demonstrates their use in calculating elliptic genera by incorporating auxiliary flux sums and modular properties.

Contribution

It generalizes Nakajima-Yoshioka's blowup equations to 6d little string theories, including new flux summations to handle anomaly cancellation.

Findings

Blowup equations for little strings are established.

Explicit examples show how to solve these equations for elliptic genera.

Modular properties aid in solving the blowup equations.

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.