New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM

TL;DR

The authors construct a new class of 4D integrable QFTs by a double-scaling limit of the γ-deformed ${\cal N}=4$ SYM in which gauge fields decouple and the theory reduces to a chiral, non-supersymmetric system with fixed couplings $\xi_j$ (with $\xi_j^2 = g^2 e^{-i \gamma_j}$). In the planar limit the model remains integrable and many correlators are conformal, allowing exact treatment of BMN-type operators whose anomalous dimensions are governed by wheel graph periods; they provide explicit two-wrapping results in terms of multiple zeta values, including $\gamma^{(2)}_{\mathrm{vac}}(3)$ and a new $L=4$ formula. The integrable structure is exposed via a conformal spin-chain transfer matrix with $SL(2,2)$ symmetry, and the work points toward an all-loop DS version of the twisted QSC as a computational framework. The theory is non-unitary due to imaginary twists and, at finite $N_c$, conformality is broken by double-trace terms, but in the large-$N_c$ limit many observables remain tractable and the results offer a promising route to exact graph-level computations in non-supersymmetric 4D QFTs.

Abstract

We consider the $γ$-deformed $\mathcal{N}=4$ SYM in the double scaling limit of large imaginary twists and small coupling, which discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the 't~Hooft limit, these 4D theories are integrable, with most of the correlators being conformal such that the whole arsenal of AdS/CFT integrability remains applicable. In particular, for one non-zero effective coupling, we obtain a QFT of two complex scalars with a chiral, quartic interaction. The BMN vacuum anomalous dimension is dominated in each non-zero loop order by a single "wheel" graph, in principle computable by integrability. Thus we also provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes.

Figures (2)

• Figure 1: The single possible Feynman graph contributing to the correlator of two the BMN vacuum operators in the model \ref{['Lthree']} at a given order (given number $M$ of wrappings): a) On the "globe" graph, ${\text{Tr}} \phi_1^{\dagger L}(x)$ and ${\text{Tr}} \phi_1^L(0)$ are placed at the north and south pole, respectively. $L$ solid lines of $\phi_1$ particles can be only crossed at the interaction vertices in one direction by $M$ dashed lines of $\phi_2$ particles. b) The divergence of this graph is captured by the "wheel" graph, obtained by removing the vicinity of one of the poles.
• Figure 2: A graph of torus topology contributing to the two-point function of two BMN vacuum operators