Non-Integrability of Strings in $AdS_{6}\times S^{2}\timesΣ$ Background and its 5D Holographic Duals

Abstract

In this manuscript we study Liouvillian non-integrability of strings in AdS6 × S 2 × Σ background and its 5D Holographic Duals. For this we consider soliton strings and look for simple solutions in order to reduce our equations to only one linear second order differential equation called NVE(normal variation equation ). We show that, differently of previous studies, the correct truncation is given by η = 0 and not σ = 0. With this we are able to study many recent cases considered in the literature: the abelian and non-abelian T-duals, the (p, q)-five-brane system, the TN ,+MN theories and the TN,P and +P,N quivers. We show that all of them, and therefore the respective field theory duals, are not integrable. Finally, we consider the general case at the boundary η = 0 and show that we can get general conclusions about integrability. For example, beyond the above quivers, we show generically that long quivers are not integrable.

Wilson loops for 5d and 3d conformal linear quivers

“…(2. 19), (2.20) and (3.6) respectively. We focus on the cases of the T M,N and + M,N both in 3d and in 5d.…”

“…In the three dimensional case, the groups are unitary U(N). We calculate the Wilson loop for the l-gauge group (for l = 1, 2, 3, 4, ..., 19) in the k-antisymmetric representation for the values k = 2, 3, 4, 5. For this, we need to count N F 1 = 2, 3, 4, 5 fundamental strings extending between the probe and the stack of colour branes.…”

“…The case of N = 1 five dimensional linear quiver SCFTs (with eight Poincaré supercharges) was initially analysed holographically in [10]. A non-exhaustive list of papers testing the correspondence and analysing predictions derived for this case is [10][11][12][13][14][15][16][17][18][19][20].…”