The Aesthetic Contract. Statutes of Art and Intellectual Work in Modernity

A note on Wilson–ʼt Hooft operators

“…These bundles take into account electric degrees of freedom present in dyonic operators in the OPE (1). We will compute the right side of (1) for N = 4 SYM and N = 2 SYM with N f = 0 in the future [19] and hope to compare with the forthcoming results from the alternative method [18] based on the connection with 2d CFT.…”

“…Then from the holomorphic Euler characteristic χ(P 2 ,Ṽ 1 ) = 1 we find H 1 (P 2 ,Ṽ 1 ) = 0. We will use this information in [19] to identifyṼ 1 as a certain wellknown holomorphic vector bundle on P 2 . If one would like to compute the OPE (1), the bundles V on M and V bulk on M bulk , which appear in (2), are the pull-back of the vector bundle V a,b over the base P 2 U to M and M bulk correspondingly.…”

“…Since M is compact we can take a connection on V to be the pull-back of the connection on the base P 2 U . We will clarify how to define a connection V bulk on the non-compact M bulk in [19] where we will present the computation of the OPE (1).…”

“…Finally, in Section 6, we construct bundles V over M and V bulk over M bulk corresponding to ν = aw 1 + bw 2 with a + 2b = 0 mod 3. We will use the geometry of M and M bulk together with these bundles to determine the right side of (1) in N = 4 SYM theory and in N = 2 SYM with N f = 0 in the future [19].…”