Integrable Fishnet from γ-Deformed N = 2 Quivers

Authors: Antonio Pittelli, Michelangelo Preti

Preprint Number: UUITP-21/19

We propose the γ-deformation of four-dimensional N = 2 quiver gauge theories, obtained by applying the Lunin-Maldacena deformation with respect to the U(1)r × SU(2)R R-symmetry. The resulting theory is supplied with double-trace counterterms and has a non-trivial RG-flow. We compute the one-loop β-function and identify the conformal fixed points of these theories. Furthermore, we study the double-scaling limit of large imaginary γ and weak ’t Hooft coupling. In this regime, both gauge fields and hypermultiplets decouple, leaving a non-supersymmetric, non-gauge theory where gluinos and vector multiplet scalars interact via Yukawa couplings. This model is integrable even though the original N = 2 theory is not. Indeed, the anomalous dimension of the BMN vacuum is dominated by fermionic wheel graphs, whose bulk constitutes an integrable fishnet known as brick-wall domain. Finally, we compute this scaling dimension to leading order directly from Feynman diagrams both for the general γ-deformation and the double-scaled theory.