Melnikov's method in String Theory

Melnikov's method is an analytical way to show the existence of classical chaos generated by a Smale horseshoe. It is a powerful technique, though its applicability is somewhat limited. In this paper, we present a solution of type IIB supergravity to which Melnikov's method is applicable. This is a brane-wave type deformation of the AdS$_5\times$S$^5$ background. By employing two reduction ans\"atze, we study two types of coupled pendulum-oscillator systems. Then the Melnikov function is computed for each of the systems by following the standard way of Holmes and Marsden and the existence of chaos is shown analytically.Comment: 37 pages, 5 figure

Chaotic strings in a near Penrose limit of AdS5×T1,1_5\times T^{1,1}

We study chaotic motions of a classical string in a near Penrose limit of AdS$_5\times T^{1,1}$. It is known that chaotic solutions appear on $R\times T^{1,1}$, depending on initial conditions. It may be interesting to ask whether the chaos persists even in Penrose limits or not. In this paper, we show that sub-leading corrections in a Penrose limit provide an unstable separatrix, so that chaotic motions are generated as a consequence of collapsed Kolmogorov-Arnold-Moser (KAM) tori. Our analysis is based on deriving a reduced system composed of two degrees of freedom by supposing a winding string ansatz. Then, we provide support for the existence of chaos by computing Poincare sections. In comparison to the AdS$_5\times T^{1,1}$ case, we argue that no chaos lives in a near Penrose limit of AdS$_5\times$S$^5$, as expected from the classical integrability of the parent system.Comment: 19 pages, 9 figures, LaTeX, v2: typos corrected and some clarifications adde

Lax pairs on Yang-Baxter deformed backgrounds

We explicitly derive Lax pairs for string theories on Yang-Baxter deformed backgrounds, 1) gravity duals for noncommutative gauge theories, 2) $\gamma$-deformations of S$^5$, 3) Schr\"odinger spacetimes and 4) abelian twists of the global AdS$_5$\,. Then we can find out a concise derivation of Lax pairs based on simple replacement rules. Furthermore, each of the above deformations can be reinterpreted as a twisted periodic boundary conditions with the undeformed background by using the rules. As another derivation, the Lax pair for gravity duals for noncommutative gauge theories is reproduced from the one for a $q$-deformed AdS$_5\times$S$^5$ by taking a scaling limit.Comment: 1+39 pages, v3: typos corrected and the reference [42] adde

Setting the Strategic Research Areas in the Government-funded Strategic Research in Japan

Atlanta Conference on Science and Innovation Policy 201