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A<sc>bstract</sc> We study local, higher-spin conserved currents in integrable 2dsigma models that have been deformed via coupling to auxiliary fields. These currents generate integrability-preserving flows introduced by Smirnov and Zamolodchikov. For auxiliary field (AF) deformations of a free boson, we prove that local spin-ncurrents exist for allnand give recursion relations that characterize Smirnov-Zamolodchikov (SZ) flows driven by these currents. We then show how to construct spin-2ncurrents in a unified class of auxiliary field sigma models with common structure — including AF theories based on the principal chiral model (PCM), its non-Abelian T-dual, (bi-)Yang-Baxter deformations of the PCM, and symmetric space models — for interaction functions of one variable, and describe SZ flows driven by any function of the stress tensor in these cases. Finally, we give perturbative solutions for spin-3 SZ flows in any member of our unified class of AF models with underlying$$ \mathfrak{su} $$ $\mathrm{su}$(3) algebra. Part of our analysis shows that the class of AF deformations can be extended by allowing the interaction function to depend on a larger set of variables than has previously been considered. 

A<sc>bstract</sc> We generalize the auxiliary field deformations of the principal chiral model (PCM) introduced in [1] and [2] to sigma models whose target manifolds are symmetric or semi-symmetric spaces, including a Wess-Zumino term in the latter case. This gives rise to a new infinite family of classically integrable ℤ₂and ℤ₄coset models of the form which are of interest in applications of integrability to worldsheet string theory and holography. We demonstrate that every theory in this infinite class admits a zero-curvature representation for its equations of motion by exhibiting a Lax connection. 

We explore whether one can TT deform a collection of theories that are already TT deformed. This allows us to define classes of irrelevant deformations that know about subsystems. In some basic cases, we explore the spectrum that results from this procedure and we provide numerical evidence in favor of modular invariance. We also study the flow of the classical Lagrangian for free bosons and free fermions under successive deformations. Some of the models found by sequentially flowing are likely to have interesting holographic interpretations. 

The Dirac action describes the physics of the Nambu-Goldstone scalarsfound on branes. The Born-Infeld action defines a non-linear theory ofelectrodynamics. The combined Dirac-Born-Infeld (DBI) action describesthe leading interactions supported on a single D-brane in string theory.We define a non-abelian analogue of DBI using the T\bar{T} T T ‾ deformation in two dimensions. The resulting quantum theory iscompatible with maximal supersymmetry and such theories are quiterare.