Abstract
We introduce bi-fermion fishnet theories, a class of models describing integrable sectors of four-dimensional gauge theories with non-maximal supersymmetry. Bi-fermion theories are characterized by a single complex scalar field and two Weyl fermions interacting only via chiral Yukawa couplings. The latter generate oriented Feynman diagrams forming hexagonal lattices, whose fishnet structure signals an underlying integrability that we exploit to compute anomalous dimensions of BMN-vacuum operators. Furthermore, we investigate Lunin-Maldacena deformations of N=2 superconformal field theories with deformation parameter γ and prove that bi-fermion models emerge in the limit of large imaginary γ and vanishing 't Hooft coupling g, with ge−i2γ fixed. Finally, we explicitly find non-trivial conformal fixed points and compute the scaling dimensions of operators for any γ and in presence of double-trace deformations.
Highlights
Introduction and conclusionsRevealing integrable sectors of a given quantum field theory (QFT) is an extremely compelling problem
We investigate Lunin-Maldacena deformations of N = 2 superconformal field theories with deformation parameter γ and prove that bi-fermion models emerge in the limit of large imaginary γ and vanishing ’t Hooft coupling g, with g e
Similar γ -deformations and DS limits were introduced for ABJM. Both χ CFT4 and its 3d companion descend from integrable QFTs, N = 4 SYM and ABJM respectively
Summary
Revealing integrable sectors of a given quantum field theory (QFT) is an extremely compelling problem. A novel integrable 4d QFT was proposed [7] This theory, called χ CFT4, was obtained by considering the double-scaling (DS) limit [8] of γ -deformed N = 4 SYM, namely the regime o√f strong imaginary twists γ and weak ’t Hooft coupling g = gYM Nc/4π. Similar γ -deformations and DS limits were introduced for ABJM theory [11] Both χ CFT4 and its 3d companion descend from integrable QFTs, N = 4 SYM and ABJM respectively. The action of the DS limit on a γ -deformed quiver is dramatic: matter multiplets decouple, leaving a collection of disjoint nodes captured by bi-fermion theories with couplings ξi. In the DS limit (1), LγHM becomes the Lagrangian of a free theory and decouples from the vector multiplet
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