On the dual symmetry of the non-linear sigma models

On elliptic string solutions in AdS3 and dS3

“…Having set up the notation, the equations of motion for the field Y are 6) whereas the equation of motion for the Lagrange multiplier λ yields the constraint (2.1),…”

“…Since then, the understanding of Pohlmeyer reduction has significantly advanced. The connection between the JHEP07(2016)070 target space being a symmetric space and the integrability of the sigma model has been understood [6,7] and interpreted geometrically as Gauss-Codazzi equations for the embedding of the submanifold of the NLSM solution within the target space [8]. Although Pohlmeyer reduction leads to an integrable Hamiltonian system, it is a non-trivial question whether the dynamics of this system can be derived from a local Lagrangian.…”

Master symmetry in the AdS 5 × S 5 pure spinor string

“…As argued in [30], χ µ generates an infinite tower of non-local symmetries of a Z 2 coset. The analogous statement for the pure spinor string for any value of µ will be proved at the end of this paper.…”

Two-dimensional gravities and supergravities as integrable systems

“…This fact can be exploited by taking the three-dimensional Lagrangian as one's point of departure in analyzing the reduction to two dimensions rather than starting from the higher-dimensional theory. In this section, I will first summarize the general formalism for the bosonic a-models, which was invented by particle physicists long ago [30] (see also [31] for a more recent treatment) and then present N = 2 supergravity in three dimensions, which is the locally supersymmetric extension of (2.1.6). The limitation to the N = 2 theory is mainly for pedagogical reasons, as this is the simplest supersymmetrie model to be studied in the present context.…”

“…To formulate the bosonic a-models in a general way [31], consider a maximally symmetric space G/H with the associated Lie algebra decomposition…”