Instantons in N=2 4d Theories with Defects and Integrability
by
Andrey Zayakin(Universidade de Santiago de Compostella)
→
Europe/Stockholm
122:026
122:026
Description
We consider an extension of the duality between N=2 field theories in
4d and integrable theories in 2d by adding a codimension 2 defect,
described by its Gukov-Witten parameters. Viewed from the
Alday-Gaiotto-Tachikawa prospective, the duality relates now the
correlators in an affine SL(N)-algebra CFT (Wess-Zumino-Witten model)
rather than those of a W_N (Toda/Liouville model) to the partition
function and observables in 4d. Viewed from the sigma-model
prospective, the theory with defect is dual now to a Bethe Ansatz with
some extra twist parameters. We consider the extended duality from
these both points of view. A nice represenation-theoretic
understanding of the instantonic partition function with the extra
parameters is suggested. We comment on the relation between the
localization calculation of a Wilson loop in 4d with defects and the
CFT calculation thereof. We suggest a modified Yang-Yang function for
the 2d-4d duality, where twists are simply related to Gukov-Witten
parameters. Basing on the modified Yang-Yang function, we study the
marginal stability curves for N=2 SQCD with defects. All these
findings point out a fruitful and interesting direction in the studies
of the 4d-2d duality.
