Exact results for the low energy AdS4 × $ \mathbb{C}\mathbb{P} $3 string theory

We derive the Thermodynamic Bethe Ansatz equations for the relativistic sigma model describing the AdS 4 × $ \mathbb{C}\mathbb{P} $ 3 string II A theory at strong coupling (i.e. in the Alday-Maldacena decoupling limit). The corresponding Y -system involves an infinite number of Y functions and is of a new type, although it shares a peculiar feature with the Y -system for AdS 4 × $ \mathbb{C}\mathbb{P} $ 3. A truncation of the equations at level p and a further generalisation to generic rank N allow us an alternative description of the theory as the N =4, p = ∞ representative in an infinite family of models corresponding to the conformal cosets ( $ \mathbb{C}\mathbb{P} $ N −1) p × U(1), perturbed by a relevant composite field ϕ (N,p) = ϕ[( $ \mathbb{C}\mathbb{P} $ N −1) p ] × ϕ [U(1)] that couples the two independent conformal field theories. The calculation of the ultraviolet central charge confirms the conjecture by Basso and Rej and the conformal dimension of the perturbing operator, at every N and p, is obtained using the Y-system periodicity. The conformal dimension of ϕ[( $ \mathbb{C}\mathbb{P} $ N −1) p ] matches that of the field identified by Fendley while discussing integrability issues for the purely bosonic $ \mathbb{C}\mathbb{P} $ N −1 sigma model.