Exact computation of one-loop correction to energy of spinning folded string in AdS_5 x S^5

We consider the 1-loop correction to the energy of folded spinning string solution in the AdS_3 part of AdS_5 x S^5. The classical string solution is expressed in terms of elliptic functions so an explicit computation of the corresponding fluctuation determinants for generic values of the spin appears to be a non-trivial problem. We show how it can be solved exactly by using the static gauge expression for the string partition function (which we demonstrate to be equivalent to the conformal gauge one) and observing that all the corresponding second order fluctuation operators can be put into the standard (single-gap) Lam\'e form. We systematically derive the small spin and large spin expansions of the resulting expression for the string energy and comment on some of their applications.Comment: 52 pp, 12 figures; v3: footnote 9 adde

Semiclassical Strings in AdS_5 x S^5 and Automorphic Functions

Using AdS/CFT we derive from the folded spinning string ordinary differential equations for the anomalous dimension of the dual N=4 SYM twist-two operators at strong coupling. We show that for large spin the asymptotic solutions have the Gribov-Lipatov recirocity property. To obtain this result we use a hidden modular invariance of the energy-spin relation of the folded spinning string. Further we identify the Moch-Vermaseren-Vogt (MVV) relations, which were first recognized in plain QCD calculations, as the recurrence relations of the asymptotic series ansatz.Comment: 4 page

Quasi-doubly periodic solutions to a generalized Lame equation

We consider the algebraic form of a generalized Lame equation with five free parameters. By introducing a generalization of Jacobi's elliptic functions we transform this equation to a 1-dim time-independent Schroedinger equation with (quasi-doubly) periodic potential. We show that only for a finite set of integral values for the five parameters quasi-doubly periodic eigenfunctions expressible in terms of generalized Jacobi functions exist. For this purpose we also establish a relation to the generalized Ince equation.Comment: 15 pages,1 table, accepted for publication in Journal of Physics

Quantum mass correction for the twisted kink

We present an analytic result for the 1-loop quantum mass correction in semiclassical quantization for the twisted \phi^4 kink on S^1 without explicit knowledge of the fluctuation spectrum. For this purpose we use the contour integral representation of the spectral zeta function. By solving the Bethe ansatz equations for the n=2 Lame equation we obtain an analytic expression for the corresponding spectral discriminant. We discuss the renormalization issues of this model. An energetically preferred size for the compact space is finally obtained.Comment: 18 pages, 2 figures;v2:references and discussion added, typos correcte

YETI observations of the young transiting planet candidate CVSO 30 b

CVSO 30 is a unique young low-mass system, because, for the first time, a close-in transiting and a wide directly imaged planet candidates are found around a common host star. The inner companion, CVSO 30 b, is the first possible young transiting planet orbiting a previously known weak-lined T-Tauri star. With five telescopes of the 'Young Exoplanet Transit Initiative' (YETI) located in Asia, Europe and South America we monitored CVSO 30 over three years in a total of 144 nights and detected 33 fading events. In two more seasons we carried out follow-up observations with three telescopes. We can confirm that there is a change in the shape of the fading event between different observations and that the fading event even disappears and reappears. A total of 38 fading event light curves were simultaneously modelled. We derived the planetary, stellar, and geometrical properties of the system and found them slightly smaller but in agreement with the values from the discovery paper. The period of the fading event was found to be 1.36 s shorter and 100 times more precise than the previous published value. If CVSO 30 b would be a giant planet on a precessing orbit, which we cannot confirm, yet, the precession period may be shorter than previously thought. But if confirmed as a planet it would be the youngest transiting planet ever detected and will provide important constraints on planet formation and migration time-scales.Comment: 14 pages (20 with appendix), 7 figures (16 with appendix), 6 tables (7 with appendix

Stirring in massive, young debris discs from spatially resolved Herschel images

A significant fraction of main-sequence stars are encircled by dusty debris discs, where the short-lived dust particles are replenished through collisions between planetesimals. Most destructive collisions occur when the orbits of smaller bodies are dynamically stirred up, either by the gravitational effect of locally formed Pluto-sized planetesimals (self-stirring scenario), or via secular perturbation caused by an inner giant planet (planetary stirring). The relative importance of these scenarios in debris systems is unknown. Here we present new Herschel Space Observatory imagery of 11 discs selected from the most massive and extended known debris systems. All discs were found to be extended at far-infrared wavelengths, five of them being resolved for the first time. We evaluated the feasibility of the self-stirring scenario by comparing the measured disc sizes with the predictions of the model calculated for the ages of our targets. We concluded that the self-stirring explanation works for seven discs. However, in four cases, the predicted pace of outward propagation of the stirring front, assuming reasonable initial disc masses, was far too low to explain the radial extent of the cold dust. Therefore, for HD 9672, HD 16743, HD 21997, and HD 95086, another explanation is needed. We performed a similar analysis for {\ss} Pic and HR 8799, reaching the same conclusion. We argue that planetary stirring is a promising possibility to explain the disk properties in these systems. In HR 8799 and HD 95086 we may already know the potential perturber, since their known outer giant planets could be responsible for the stirring process. Our study demonstrates that among the largest and most massive debris discs self-stirring may not be the only active scenario, and potentially planetary stirring is responsible for destructive collisions and debris dust production in a number of systems.Comment: Accepted for publication in MNRAS, 22 pages, 7 figures, 6 tables (abstract abridged due to arXiv requirements

Quantum kink and its excitations

We show how detailed properties of a kink in quantum field theory can be extracted from field correlation functions. This makes it possible to study quantum kinks in a fully non-perturbative way using Monte Carlo simulations. We demonstrate this by calculating the kink mass as well as the spectrum and approximate wave functions of its excitations. This way of measuring the kink mass has clear advantages over the existing approaches based on creation and annihilation operators or the kink free energy. Our methods are straightforward to generalise to more realistic theories and other defect types.Comment: 21 pages, 11 figures, v2: typos corrected, references adde

One-loop spectroscopy of semiclassically quantized strings: bosonic sector

We make a further step in the analytically exact quantization of spinning string states in semiclassical approximation, by evaluating the exact one-loop partition function for a class of two-spin string solutions for which quadratic fluctuations form a non-trivial system of coupled modes. This is the case of a folded string in the SU(2) sector, in the limit described by a quantum Landau–Lifshitz model. The same applies to the full bosonic sector of fluctuations over the folded spinning string in AdS5 with an angular momentum J in S5. Fluctuations are governed by a special class of fourth-order differential operators, with coefficients being meromorphic functions on the torus, which we are able to solve exactly