Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
149 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Topological strings, quiver varieties and Rogers-Ramanujan identities (1707.00831v2)

Published 4 Jul 2017 in math.AG, math-ph, math.MP, and math.NT

Abstract: Motivated by some recent works on BPS invariants of open strings/knot invariants, we guess there may be a general correspondence between the Ooguri-Vafa invariants of toric Calabi-Yau 3-folds and cohomologies of Nakajima quiver varieties. In this short note, we provide a toy model to explain this correspondence. More precisely, we study the topological open string model of $\mathbb{C}3$ with one Aganagic-Vafa brane $\mathcal{D}_\tau$, and we show that, when $\tau\leq 0$, its Ooguri-Vafa invariants are given by the Betti numbers of certain quiver variety. Moreover, the existence of Ooguri-Vafa invariants implies an infinite product formula. In particular, we find that the $\tau=1$ case of such infinite product formula is closely related to the celebrated Rogers-Ramanujan identities.

Summary

We haven't generated a summary for this paper yet.