# Refined geometric transition and $qq$-characters

## TL;DR

This paper refines the geometric transition in refined topological string theory and explores its application to describing $qq$-characters, revealing the impact of the preferred direction and proposing a string theory perspective on doubly quantized Seiberg--Witten curves.

## Contribution

It introduces a refined geometric transition formula accounting for the preferred direction and applies it to provide a string theory description of $qq$-characters.

## Key findings

- Modified formula for refined geometric transition including preferred direction effects
- Proposal of a string theory framework for $qq$-characters
- Insights into the structure of doubly quantized Seiberg--Witten curves

## Abstract

We show the refinement of the prescription for the geometric transition in the refined topological string theory and, as its application, discuss a possibility to describe $qq$-characters from the string theory point of view. Though the suggested way to operate the refined geometric transition has passed through several checks, it is additionally found in this paper that the presence of the preferred direction brings a nontrivial effect. We provide the modified formula involving this point. We then apply our prescription of the refined geometric transition to proposing the stringy description of doubly quantized Seiberg--Witten curves called $qq$-characters in certain cases.