# Comments on the temperature dependence of the gauge topology

## TL;DR

This paper discusses the temperature dependence of gauge topology, highlighting recent lattice and semiclassical findings on instantons and instanton-dyons, and proposes using sub-lattice topological susceptibility as a new investigative tool.

## Contribution

It introduces the idea of analyzing sub-lattice topological susceptibility to better understand gauge topology at different temperatures.

## Key findings

- High-temperature topological susceptibility aligns with instanton dominance.
- Instanton-dyon ensembles can reproduce deconfinement and chiral transitions.
- Proposes sub-lattice susceptibility as a new method for lattice studies.

## Abstract

Recent efforts in lattice evaluation of the topological susceptibility had shown that at high temperatures it is given by well-separated instantons (even in QCD with light fermions, where those are highly suppressed). Recent development of the semiclassical theory suggest that below $T_{max}\sim 2.5T_c$, where Polyakov line has values between one and zero, the topology ensemble can be represented by a plasma of instanton constituents (called instanton-dyons or instanton-monopoles). It has been shown that such ensemble undergoes deconfinement and chiral transitions, semi-qualitatively reproducing the lattice results. There are ongoing efforts to locate them on the lattice, or use (flavor-dependent) periodicity phases of the deformed versions of QCD on the lattice and semiclassically, in order to test this theory. We here propose another possibly useful tool: the topological susceptibility of a sub-lattice.