The volume measure for flat connections as limit of the Yang–Mills measure

✍ Scribed by Ambar N. Sengupta

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 234 KB
• Volume: 47
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00229-2

✦ Synopsis

We prove that integration over the moduli space of flat connections can be obtained as a limit of integration with respect to the Yang-Mills measure defined in terms of the heat-kernel for the gauge group. In doing this we also give a rigorous proof of Witten's formula for the symplectic volume of the moduli space of flat connections. Our proof uses an elementary identity connecting determinants of matrices along with a careful accounting of certain dense subsets of full measure in the moduli space.