This paper is mainly inspired by the conjecture about the existence of bound states for magnetic Neumann Laplacians on planar wedges of any aperture <i></i> (0, <i></i>). So far, a proof was only obtained for apertures <i></i> 0.511. The conviction in the validity of this conjecture for apertures <i></i> 0.511<i></i> mainly relied on numerical computations. In this paper we succeed to prove the existence of bound states for any aperture <i></i> 0.583 using a variational argument with suitably chosen test functions. Employing some more involved test functions and combining a variational argument with computer assistance, we extend this interval up to any aperture <i></i> 0.595<i></i>. Moreover, we analyse the same question for closely related problems concerning magnetic Robin Laplacians on wedges and for magnetic Schrdinger operators in the plane with <i></i>-interactions supported on broken lines.

We impose constraints on the odd coordinates of super-Teichmüller space in the uniformization picture for the monodromies around Ramond punctures, thus reducing the overall odd dimension to be compatible with that of the moduli spaces of super Riemann surfaces. Namely, the monodromy of a puncture must be a true parabolic element of the canonical subgroup SL(2 , R) of OSp(1\2).

Based on earlier work of the latter two named authors on the higher super-Teichmueller space with N=1, a component of the flat OSp(1\2) connections on a punctured surface, here we extend to the case N=2 of flat OSp(2\2) connections. Indeed, we construct here coordinates on the higher super-Teichmueller space of a surface F with at least one puncture associated to the supergroup OSp(2\2), which in particular specializes to give another treatment for N=1 simpler than the earlier work. The Minkowski space in the current case, where the corresponding super Fuchsian groups act, is replaced by the superspace R2,2\4, and the familiar lambda lengths are extended by odd invariants of triples of special isotropic vectors in R2,2\4 as well as extra bosonic parameters, which we call ratios, defining a flat R+-connection on F. As in the pure bosonic or N=1 cases, we derive the analogue of Ptolemy transformations for all these new variables.

We derive a universal formula for the asymptotic growth of the mean value of three-point coefficient for Warped Conformal Field Theories (WCFTs), and provide a holographic calculation in BTZ black holes. WCFTs are two dimensional quantum field theories featuring a chiral Virasoro and U(1) Kac-Moody algebra, and are conjectured to be holographically dual to quantum gravity on asymptotically AdS3 spacetime with Compere-Song-Strominger boundary conditions. The WCFT calculation amounts to the calculation of one-point functions on torus, whose high temperature limit can be approximated by using modular covariance of WCFT, similar to the derivation of Cardy formula. The bulk process is given by a tadpole diagram, with a massive spinning particle propagates from the infinity to the horizon, and splits into particle and antiparticle which annihilate after going around the horizon of BTZ black holes. The agreement between the bulk and WCFT calculations indicates that the black hole geometries in asymptotically AdS3 spacetimes can emerge upon coarse-graining over microstates in WCFTs, similar to the results of Kraus and Maloney in the context of AdS/CFT.

Warped conformal field theory (WCFT) is a two dimensional quantum field theory whose local symmetry algebra consists of a Virasoro algebra and a U(1) Kac-Moody algebra. In this paper, we study correlation functions for primary operators in WCFT. Similar to conformal symmetry, warped conformal symmetry is very constraining. The form of the two and three point functions are determined by the global warped conformal symmetry while the four point functions can be determined up to an arbitrary function of the cross ratio. The warped conformal bootstrap equation are constructed by formulating the notion of crossing symmetry. In the large central charge limit, four point functions can be decomposed into global warped conformal blocks, which can be solved exactly. Furthermore, we revisit the scattering problem in warped AdS spacetime (WAdS), and give a prescription on how to match the bulk result to a WCFT retarded Green’s function. Our result is consistent with the conjectured holographic dualities between WCFT and WAdS.