The other topological twisting of N = 4 Yang-Mills

Abstract

We present the alternative topological twisting of N = 4 Yang-Mills, in which the path integral is dominated not by instantons, but by flat connections of the complexified gauge group. The theory is nontrivial on compact orientable four-manifolds with nonpositive Euler number, which are necessarily not simply connected. On such manifolds, one finds a single topological invariant, analogous to the Casson invariant of three-manifolds.

Real space renormalization group for twisted lattice N $$ \mathcal{N} $$ =4 super Yang-Mills

“…In flat space this corresponds merely to an exotic change of variables -one more suited to discretization. In the case of N = 4 SYM there are three independent topological twists of the theory and the one that is employed in the lattice work is the Marcus or GeometricLanglands twist [13,14]. The resulting lattice action takes the form …”

Twisted supersymmetric gauge theories and orbifold lattices

“…In four dimensions, the twist of N = 4 is introduced by Marcus [6]. The three dimensional N = 4 and N = 8 and two dimensional N = (8,8), N = (4, 4) theories are presented by Blau and Thompson [7] and are examined in more detail in [33,34].…”

“…There are various possible twists of the N = 4 SYM theory in four dimensions [3,4,6]. The one we will consider and which emerges out of the orbifold lattice naturally is due to Marcus.…”

“…Here, we use the spin zero supercharge associated with λ (motivated by the orbifold lattice). This produces the transformations given by [6].…”

Twisted $ \mathcal{N} $ = 4 super Yang-Mills theory in Ω-background

“…In the undeformed case, when u 2 + v 2 = 0, the action is shown to be the Q-exact form up to the topological term [14]. When u 2 + v 2 = 0, the action is not written in the Q-exact form but it is Q-closed [13]. In the following, we show that this property also holds in the deformed theory.…”