Exact results for the low energy AdS 4 × $ \mathbb{C}\mathbb{P} $ 3 string theory

We derive the Thermodynamic Bethe Ansatz equations for the relativistic sigma model describing the AdS4 × ℂℙ3 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 AdS4 × ℂℙ3. 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 (ℂℙN-1)p × U(1), perturbed by a relevant composite field φ(N,p) = φ[(ℂℙN-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[(ℂℙN-1)p] matches that of the field identified by Fendley while discussing integrability issues for the purely bosonic ℂℙN-1 sigma model.