Abstract
We ask the question of classical integrability for certain (classes of) supergravity vacua that contain an AdS3 factor arising in massive IIA and IIB theories and realizing various and different amounts of supersymmetry. Our approach is based on a well-established method of analytic non-integrability for Hamiltonian systems. To detect a non-integrable sector we consider a non-trivially wrapped string soliton and study its fluctuations. We answer in the negative for each and every one of the supergravity solutions. That is, of course, modulo very specific limits where the metrics reduce to the AdS3 × S3 × {tilde{S}}^3 × S1 and AdS3 × S3 × T4 solutions which are known to be integrable.
Highlights
We ask the question of classical integrability for certain supergravity vacua that contain an AdS3 factor arising in massive IIA and IIB theories and realizing various and different amounts of supersymmetry
Five dimensional superconformal field theories with various amounts of supersymmetry are investigated in [16,17,18,19,20,21,22,23], and an infinite class of six-dimensional N = (1, 0) theories was likewise inspected in the works [24,25,26,27,28,29,30,31,32,33,34,35]
The reason is that two dimensionalconformal field theories and three dimensional AdS spacetimes make their appearence in various places in theoretical physics; string theory, condensed matter physics, black holes to name a few
Summary
The method we adopt here is comprised out of the following steps: to begin with, we write an ansatz for a string embedding that extends in some dimensions and it wraps non-trivially some of the cyclic coordinates in a given background. We freeze all the dimensions on the values that solve their equations of motion and only consider fluctuations in the coordinate under examination In such a way, we arrive at second-order, ordinary differential equation that assumes the schematic form. If the coefficients of the NVE, Ai for = 1, 2, 3, are not rational functions we need to perform change of coordinates and/or perhaps other algebraic manipulations to bring them in an appropriate form In this kind of Hamiltonian dynamical systems, in order to make a statement for the analytic non-integrability of the structure of the aferementioned systems, one has to enforce differential Galois theory. The way that this occurs is that the NVEs will assuredly have simple solutions in terms of quadratures
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