Yang–Mills existence and mass gap

Construct four-dimensional quantum Yang–Mills theory for every compact simple gauge group and prove that it has a positive mass gap.

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1	{
2	"domain": "physics-astronomy",
3	"topics": [
4	"mathematical-physics"
5	],
6	"type": "proof",
7	"source": {
8	"key": "clay",
9	"name": "Clay Millennium Prize Problems",
10	"url": "https://www.claymath.org/millennium/yang-mills-the-maths-gap/",
11	"curator": "Clay Mathematics Institute",
12	"poser": "Clay Mathematics Institute, with the problem description by Arthur Jaffe and Edward Witten",
13	"status": "unsolved",
14	"as_of": "2026-10-20",
15	"prize": "$1,000,000",
16	"catalog": "0521c19bbd38"
17	},
18	"review": true,
19	"approval": "first-time"
20	}