Abstract:We study extremal correlation functions of chiral primary operators in the large-N SU(N ) N = 2 superconformal QCD theory and present new results based on supersymmetric localization. We discuss extensively the basis-independent data that can be extracted from these correlators using the leading order large-N matrix model free energy given by the four-sphere partition function. Special emphasis is given to singletrace 2-and 3-point functions as well as a new class of observables that are scalars on the conformal manifold. These new observables are particular quadratic combinations of the structure constants of the chiral ring. At weak 't Hooft coupling we present perturbative results that, in principle, can be extended to arbitrarily high order. We obtain closed-form expressions up to the first subleading order. At strong coupling we provide analogous results based on an approximate Wiener-Hopf method.
It was demonstrated in [2], [14] that d = 4 unitary CFT's satisfy a special property: if a scalar operator with conformal dimension ∆ exists in the operator spectrum, then the conformal bootstrap demands that large spin primary operators have to exist in the operator spectrum of the CFT with a conformal twist close to 2∆ + 2N for any integer N . In this paper the conformal bootstrap methods in [1] that were used to find the anomalous dimension of the N = 0 operators have been generalized to recursively find the anomalous dimension of all large spin operators of this class. In AdS these operators can be interpreted as the excited states of the product states of objects that were found in other works.
In the framework of the AdS 3 / CFT 2 correspondence, we present a systematic analysis of the late time thermalization of a two dimensional CFT state created by insertion of small number of heavy operators on the vacuum. We show that at late Lorentzian time, the universal features of this thermalization are solely captured by the eigenvalues of the monodromy matrix corresponding to the solutions of the uniformization equation. We discuss two different ways to extract the monodromy eigenvalues while bypassing the need for finding explicitly the full monodromy matrix -first, using a monodromy preserving diffeomorphism and second using Chen-Simons formulation of gravity in AdS 3 . Both of the methods yield the same precise relation between the eigenvalues and the final black hole temperature at late Lorentzian time.
The universal nature of black hole collapse in asymptotically AdS 3 gravitational theories suggests that its holographic dual process, thermalization, should similarly be fixed by the universal features of 2d CFT with large central charge c. It is known that non-equilibrium states with scaling dimensions of order c can be sorted into states that eventually thermalize and those that fail to do so. By proving an equivalence between bounded Virasoro coadjoint orbits and certain (in)stability intervals of Hill's equation it is shown that a state that fails to thermalize can be promoted to a thermalizing state by preparing the system beforehand with an energy greater than an appropriate threshold energy. It is generally a difficult problem to ascertain whether a state will thermalize or not. As partial progress to this problem a set of lower bounds are presented for the threshold energy, which can alternatively be interpreted as criteria for thermalization.
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