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Register a new userSoft modes in $mathcal{N} = 2$ SYK model
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We study various properties of the soft modes in the $mathcal{N}=2$ supersymmetric SYK model.
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We study the SYK$_{2}$ model of $N$ Majorana fermions with random quadratic interactions through a detailed spectral analysis and by coupling the model to 2- and 4-point sources. In particular, we define the generalized spectral form factor and level spacing distribution function by generalizing from the partition function to the generating function. For $N=2$, we obtain an exact solution of the generalized spectral form factor. It exhibits qualitatively similar behavior to the higher $N$ case with a source term. The exact solution helps understand the behavior of the generalized spectral form factor. We calculate the generalized level spacing distribution function and the mean value of the adjacent gap ratio defined by the generating function. For the SYK$_2$ model with a 4-point source term, we find a Gaussian unitary ensemble behavior in the near-integrable region of the theory, which indicates a transition to chaos. This behavior is confirmed by the connected part of the generalized spectral form factor with an unfolded spectrum. The departure from this Gaussian random matrix behavior as the relative strength of the source term is increased is consistent with the observation that the 4-point source term alone, without the SYK$_2$ couplings turned on, exhibits an integrable spectrum from the spectral form factor and level spacing distribution function in the large $N$ limit.
The gravitational part of the holographic dual to the SYK model has been conjectured to be Jackiw-Teitelboim (JT) gravity. In this paper we construct an AdS2 background in N = (2,2) JT gravity and show that the gravitational dynamics are - as in the N = 0 and N = 1 cases - fully captured by the extrinsic curvature as an effective boundary action. This boundary term is given by the super-Schwarzian of the N = 2 SYK model, thereby providing further evidence of the JT/SYK duality. The chirality of this SYK model is reproduced by the inherent chirality of axial N = (2,2) supergravity.
We propose a generalization of S-folds to 4d $mathcal{N}=2$ theories. This construction is motivated by the classification of rank one 4d $mathcal{N}=2$ super-conformal field theories (SCFTs), which we reproduce from D3-branes probing a configuration of $mathcal{N}=2$ S-folds combined with 7-branes. The main advantage of this point of view is that realizes both Coulomb and Higgs branch flows and allows for a straight forward generalization to higher rank theories.
Using supersymmetric localization, we consider four-dimensional $mathcal{N}=2$ superconformal quiver gauge theories obtained from $mathbb{Z}_n$ orbifolds of $mathcal{N}=4$ Super Yang-Mills theory in the large $N$ limit at weak coupling. In particular, we show that: 1) The partition function for arbitrary couplings can be constructed in terms of universal building blocks. 2) It can be computed in perturbation series, which converges uniformly for $|lambda_I|<pi^2$, where $lambda_I$ are the t Hooft coupling of the gauge groups. 3) The perturbation series for two-point functions can be explicitly computed to arbitrary orders. There is no universal effective coupling by which one can express them in terms of correlators of the $mathcal{N}=4$ theory. 4) One can define twisted and untwisted sector operators. At the perturbative orbifold point, when all the couplings are the same, the correlators of untwisted sector operators coincide with those of $mathcal{N}=4$ Super Yang-Mills theory. In the twisted sector, we find remarkable cancellations of a certain number of planar loops, determined by the conformal dimension of the operator.
We construct several novel examples of 3d $mathcal{N}=2$ models whose free energy scales as $N^{3/2}$ at large $N$. This is the first step towards the identification of field theories with an M-theory dual. Furthermore, we match the volumes extracted from the free energy with the ones computed from the Hilbert series. We perform a similar analysis for the 4d parents of the 3d models, matching the volume extracted from the $a$ conformal anomaly to that obtained from the Hilbert series. For some of the 4d models, we show the existence of a Sasaki-Einstein metric on the internal space of the candidate type IIB gravity dual.
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