Non-integrability on AdS3 supergravity backgrounds

We investigate classical integrability on two recently discovered classes of backgrounds in massive IIA supergravity. These vacua are of the form AdS$_3\times\,$S$^2\times\mathbb{R}\times\,$CY$_2$, they preserve small $\mathcal{N}=(0,4)$ supersymmetry and are associated with D8$-$D6$-$D4$-$D2 Hanany-Witten brane set-ups. We choose an appropriate string embedding and use differential Galois theory on its associated Hamiltonian system, intending to produce the conditions under which Liouvillian solutions may occur. By constraining the parameters of the system according to the consistency of the associate brane set-ups we prove that no such conditions exist, yielding the complete non-integrability of these vacua. That is, up to the trivial cases where the background reduces to the Abelian and non-Abelian T-dual of AdS$_3\times\,$S$^3\times\,$T$^4$.Comment: 22 pages plus appendices. Added references, corrected typos, corrected/added comments, improved titl

Integrability and non-integrability in N=2 SCFTs and their holographic backgrounds N = 2 N=2 \mathcal{N}=2 SCFTs and their holographic backgrounds

We show that the string worldsheet theory of Gaiotto-Maldacena holographic duals to N=2 superconformal field theories generically fails to be classically integrable. We demonstrate numerically that the dynamics of a winding string configuration possesses a non-vanishing Lyapunov exponent. Furthermore an analytic study of the Normal Variational Equation fails to yield a Liouvillian solution. An exception to the generic non-integrability of such backgrounds is provided by the non-Abelian T-dual of $AdS_5 \times S^5$. Here by virtue of the canonical transformation nature of the T-duality classical integrability is known to be present.Comment: 20 pages plus appendices. Various figures. References adde

The non-integrability of strings in massive type IIA and their holographic duals

In this work we study various aspects of six-dimensional ${\cal N}=(1,0)$ SCFTs. We consider the construction of their string duals in Massive IIA and discuss some observables in given examples. We study the dynamics of string solitons wrapping and rotating on the Massive IIA background and show that the associated Hamiltonian system is both non-integrable and chaotic, implying the non-integrability of the dual CFT. Our procedure is analytic, using well developed mathematical techniques, and numerical, by the explicit calculation of power spectra, Lyapunov coefficients and Poincar\'e sections.Comment: 28 pages plus appendices. Various figures. Some clarifications and references adde

Higgs decay into massive b-quarks at NNLO QCD in the nested soft-collinear subtraction scheme

We present a fully differential description of a decay of a scalar Higgs boson into massive b-quarks valid at next-to-next-to-leading order (NNLO) in perturbative quan- tum chromodynamics (QCD). We work within the nested soft-collinear subtraction scheme extended to accommodate massive partons. We include the loop-induced contribution in- volving a Higgs coupling to a top quark. We test our calculation against results existing in the literature, comparing the predictions for the total decay width and jet rates