N=4 SUPERSYMMETRIC YANG–MILLS THEORY ON ORBIFOLD-T⁴/Z₂

Abstract

We derive the partition function of N = 4 supersymmetric Yang-Mills theory on orbifold-T 4 /Z 2 . In classical geometry, K3 surface is constructed from the orbifold-T 4 /Z 2 . Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-T 4 /Z 2 . The partition function is given by the product of the contribution of the untwisted sector of T 4 /Z 2 , and that of the twisted sector of T 4 /Z 2 i.e., O(−2) curve blow-up formula.

The M5-brane on K3 and del Pezzo's and multi-loop string amplitudes

“…This is naturally interpreted as a multi-instanton toric amplitude in the heterotic string. Notice also that the same results follow from the application of orbifold techniques [15].…”

An Approach to Script N = 4 ADE Gauge Theory onK3

“…Vafa and Witten combined the conjecture of strong/week duality to this 't Hooft's result. Their conjecture is summarized by the following formula: 6) where ζ G = exp( 2πi N G ). We conjecture that this duality relation is also valid for the general ADE partition function (2.5).…”

GAP CONDITION AND SELF-DUALIZED ${\mathcal N}=4$ SUPER-YANG–MILLS THEORY FOR ADE GAUGE GROUP ON K3

“…We tried to reproduce the above geometrical processes in the partition function level for SU (N ) [6,7]. The trial was successful, that is, SU (N ) partition on K3 has the product of two factors.…”

“…We reproduced the above geometrical processes in the partition function level for SU (N ) [7,8],where it is shown that the SU (N ) partition function on K3 has a sum of the product of two factors. The first one is the contribution from S 0 and is described by Hecke transformation of order N of 1/η 8 (τ ).…”