We study the regular surface defect in $$\Omega $$ -deformed four-dimensional supersymmetric gauge theory with group SU(N) 2N hypermultiplets fundamental representation. prove its vacuum expectation value obeys Knizhnik–Zamolodchikov equation for 4-point conformal block of $$\widehat{{\mathfrak {sl}}}_{N}$$ -current algebra, originally introduced context two-dimensional field theory. The level ...

A bstract We derive a generalized Knizhnik-Zamolodchikov equation for the correlation function of intertwiners vector and MacMahon representations Ding-Iohara-Miki algebra. These are cousins refined topological vertex which is regarded as intertwining operator Fock representation. The shift spectral parameter generated by constructed from universal R matrix. solutions to KZ factorized into rati...

An integral formula for the solutions of Knizhnik-Zamolodchikov (KZ) equation with values in an arbitrary irreducible representation of the symmetric group SN is presented for integer values of the parameter. The corresponding integrals can be computed effectively as certain iterated residues determined by a given Young diagram and give polynomials with integer coefficients. The derivation is b...

We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov–Zakharov (KZ) spectrum in weak 3-wave turbulence. In the finite capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a consequen...

The solutions of the slN Knizhnik-Zamolodchikov(KZ) equations at level 0 are studied. We present the integral formula which is obtained as a quasi-classical limit of the integral formula for form factors of the SU(N) invariant Thirring model due to F. Smirnov. A proof is given that those integrals satisfy slN KZ equation of level 0. The relation of the integral formulae with the chiral Szegö ke...

We present some new findings concerning branched covers in topos theory. Our discussion involves a particular subtopos of a given topos that can be described as the smallest subtopos closed under small coproducts in the including topos. Our main result is a description of the covers of this subtopos as a category of fractions of branched covers, in the sense of Fox [10], of the including topos....