Sewing Yang–Mills Measures and Moduli Spaces over Compact Surfaces

✍ Scribed by Claas Becker; Ambar Sengupta

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 445 KB
• Volume: 152
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1997.3161

✦ Synopsis

Consider a closed surface 7 obtained by pasting two surfaces 7 1 and 7 2 along some of their boundary components. A formula is derived expressing quantum Yang Mills functional integrals for 7 in terms of the corresponding integrals for the surfaces 7 i . Using this, a formula is derived which expresses the symplectic volume measure on the moduli space of flat SU(2) connections over a closed Riemann surface 7 in terms of the corresponding volume measures for the surfaces 7 1 and 7 2 , when the latter have one boundary component each.