Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds

We compute the contribution of Euclidean D-branes in type IIB string theory on Calabi-Yau threefolds to the metric on the hypermultiplet moduli space in the large volume, weak coupling limit. Our results are in perfect agreement with the predictions based on S-duality, mirror symmetry and supersymmetry.

On the Lyapunov–Perron reducible Markovian Master Equation

We consider an open quantum system in [Formula: see text] governed by quasiperiodic Hamiltonian with rationally independent frequencies and under the assumption of Lyapunov–Perron reducibility of the associated Schrödinger equation. We construct the Markovian Master Equation and the resulting CP-divisible evolution in the weak coupling limit regime, generalizing our previous results from the periodic case. The analysis is conducted with the application of projection operator techniques and concluded with some results regarding stability of solutions and existence of quasiperiodic global steady state.

Using phase dynamics to study partial synchrony: three examples

Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to analyze coupled oscillatory systems. Typically, the phase dynamics description is obtained in the weak coupling limit, i.e., in the first-order in the coupling strength. The extension beyond the first-order represents an unsolved problem and is an active area of research. In this paper, three partially synchronous states are investigated and presented in order of increasing complexity. First, the usage of the phase response curve for the description of macroscopic oscillators is analyzed. To achieve this, the response of the mean-field oscillations in a model of all-to-all coupled limit-cycle oscillators to pulse stimulation is measured. The next part treats a two-group Kuramoto model, where the interaction of one attractive and one repulsive group results in an interesting solitary state, situated between full synchrony and self-consistent partial synchrony. In the last part, the phase dynamics of a relatively simple system of three Stuart-Landau oscillators are extended beyond the weak coupling limit. The resulting model contains triplet terms in the high-order phase approximation, though the structural connections are only pairwise. Finally, the scaling of the new terms with the coupling is analyzed.

A Wronskian method for elastic waves propagating along a tube

A technique involving the higher Wronskians of a differential equation is presented for analysing the dispersion relation in a class of wave propagation problems. The technique shows that the complicated transcendental-function expressions which occur in series expansions of the dispersion function can, remarkably, be simplified to low-order polynomials exactly, with explicit coefficients which we determine. Hence simple but high-order expansions exist which apply beyond the frequency and wavenumber range of widely used approximations based on kinematic hypotheses. The new expansions are hypothesis-free, in that they are derived rigorously from the governing equations, without approximation. Full details are presented for axisymmetric elastic waves propagating along a tube, for which stretching and bending waves are coupled. New approximate dispersion relations are obtained, and their high accuracy confirmed by comparison with the results of numerical computations. The weak coupling limit is given particular attention, and shown to have a wide range of validity, extending well into the range of strong coupling.

Uniform and Completely Nonequilibrium Invariant States for Weak Coupling Limit Type Quantum Markov Semigroups Associated with Eulerian Cycles

We define the uniform and completely nonequilibrium invariant states, which are associated with Eulerian cycles; once we did this, we use the Hierholzer’s algorithm to obtain a canonical Euler-Hierholzer cycle, and for it, characterize the invariant state. For the simplest case of nonequilibrium, we give sufficient conditions for these states to be invariant and write its eigenvalues explicitly.

Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials

We improve results by Frank, Hainzl, Naboko, and Seiringer (J Geom Anal 17(4):559–567, 2007) and Hainzl and Seiringer (Math Nachr 283(3):489–499, 2010) on the weak coupling limit of eigenvalues for Schrödinger-type operators whose kinetic energy vanishes on a codimension one submanifold. The main technical innovation that allows us to go beyond the potentials considered in Frank, Hainzl, Naboko, and Seiringer (2007), Hainzl and Seiringer (2010) is the use of the Tomas–Stein theorem.

An obstacle to sub-AdS holography for SYK-like models

We argue that “stringy” effects in a putative gravity-dual picture for SYK-like models are related to the branching time, a kinetic coefficient defined in terms of the retarded kernel. A bound on the branching time is established assuming that the leading diagrams are ladders with thin rungs. Thus, such models are unlikely candidates for sub-AdS holography. In the weak coupling limit, we derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime using two different approximations.

Quantum corrections in 4d N = 1 infinite distance limits and the weak gravity conjecture

We study quantum corrections in four-dimensional theories with N = 1 supersymmetry in the context of Quantum Gravity Conjectures. According to the Emergent String Conjecture, infinite distance limits in quantum gravity either lead to decompactification of the theory or result in a weakly coupled string theory. We verify this conjecture in the framework of N = 1 supersymmetric F-theory compactifications to four dimensions including perturbative α′ as well as non-perturbative corrections. After proving uniqueness of the emergent critical string at the classical level, we show that quantum corrections obstruct precisely those limits in which the scale of the emergent critical string would lie parametrically below the Kaluza-Klein scale. Limits in which the tension of the asymptotically tensionless string sits at the Kaluza-Klein scale, by contrast, are not obstructed.In the second part of the paper we study the effect of quantum corrections for the Weak Gravity Conjecture away from the strict weak coupling limit. We propose that gauge threshold corrections and mass renormalisation effects modify the super-extremality bound in four dimensions. For the infinite distance limits in F-theory the classical super-extremality bound is generically satisfied by a sublattice of states in the tower of excitations of an emergent heterotic string. By matching the F-theory α′-corrections to gauge threshold corrections of the dual heterotic theory we predict how the masses of this tower must be renormalised in order for the Weak Gravity Conjecture to hold at the quantum level.