We study two-dimensional conformal field theories in the semiclassical limit. In this limit, the four-point function is dominated by intermediate primaries of particular weights along with their descendants, and the crossing equations simplify drastically. For a four-point function receiving sufficiently small contributions from the light primaries, the structure constants involving heavy primaries follow a universal formula. Applying our results to the four-point function of the Z_2 twist field in the symmetric product orbifold, we produce the Hellerman bound and the logarithmically corrected Cardy formula that is valid for h ≥ c/12.

No abstract uploaded!

No abstract uploaded!

Statistical and machine learning theory has developed several conditions ensuring that popular estimators such as the Lasso or the Dantzig selector perform well in high-dimensional sparse regression, including the restricted eigenvalue, compatibility, and q sensitivity properties. However, some of the central aspects of these conditions are not well understood. For instance, it is unknown if these conditions can be checked efficiently on any given dataset. This is problematic, because they are at the core of the theory of sparse regression. Here we provide a rigorous proof that these conditions are NP-hard to check. This shows that the conditions are computationally infeasible to verify, and raises some questions about their practical applications. However, by taking an average-case perspective instead of the worst-case view of NP-hardness, we show that a particular condition, q sensitivity, has certain

The study of Rényi mutual information (RMI) sheds light on the AdS/CFT correspondence beyond classical order. In this article, we study the Rényi mutual information between two intervals at large distance in two-dimensional holographic warped conformal field theory, which is conjectured to be dual to the gravity on AdS3 or warped AdS3 spacetime under the Dirichlet-Newman boundary conditions. By using the operator product expansion of twist operators up to level 3, we read the leading oder and the next-toleading order RMI in the large central charge and small cross-ratio limits. The leading order result is furthermore confirmed using the conformal block expansion. Finally, we match the next-to-leading result by a 1-loop calculation in the bulk.