Chiral primaries in the Leigh-Strassler deformed Script N = 4 SYM—a perturbative study

Abstract

We look for chiral primaries in the general Leigh-Strassler deformed N = 4 super Yang-Mills theory by systematically computing the planar one-loop anomalous dimension for single trace operators up to dimension six. The operators are organised into representations of the trihedral group, ∆(27), which is a symmetry of the Lagrangian. We find an interesting relationship between the U (1) R -charge of chiral primaries and the representation of ∆(27) to which the operator belongs. Up to scaling dimension ∆ 0 = 6 (and conjecturally to all dimensions) the following holds: The planar one-loop anomalous dimension vanishes only for operators that are in the singlet or three dimensional representations of ∆(27). For other operators, the vanishing of the one-loop anomalous dimension occurs only in a sub-locus in the space of couplings. *

Marginal deformations ofN=4SYMand open vs. closed string parameters

“…In this article, the same noncommutativity matrix was derived from a totally different perspective. Other interesting work on the ρ-deformation includes [100,101,102] in relation to generalized complex geometry and [103,104,105,103,106,107] regarding integrability and finitiness (see also [108] for some recent developments).…”

Quantum symmetries and marginal deformations

“…All these Z 3 's do not commute, rather they combine to produce a trihedral group with 27 elements (given by all combinations of the generators U , V and W up to the relations U 3 = V 3 = W 3 = 1 and U V = W V U ) known as ∆ 27 [31,76]. Some aspects of this discrete group have been investigated in [77,32], where it was shown that it is unbroken at the first few orders in perturbation theory. We should emphasise that the fact that these symmetries are preserved at the quantum level is a crucial consistency check, since in particular the cyclic symmetry is used as input in the Leigh-Strassler argument which equates the anomalous dimensions of the three scalars.…”

Bilocal phase operators inβ-deformed super Yang-Mills

“…Marginal deformations of conformally invariant supersymmetric gauge theories were first systematically studied by Leigh and Strassler [17], and have subsequently been analyzed extensively both perturbatively and at strong coupling in [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] just to mention a few.…”