I. S. Faliakhov | Searcharxiv

arXiv2026

Self-dual higher spin theory: Poincaré invariance and new solutions

In this paper we study the self-dual higher spin theory in $4d$ recently proposed in arXiv:2209.01966. The typical vacuum of higher spin theories is an empty AdS space-time. We consider solutions of special form: space-time geometry associated with spin $S=2$ field is an AdS, and other fields may have nonzero values, such that the global space-time symmetry of the vacuum is broken to $3d$ Poincaré. We show that the only field possessing this property is a two-parametric scalar vacuum. We also provide a new family of solutions that generalize this scalar vacuum. In addition to the scalar, the family consists of a fermion $S = 1/2$ in the bulk propagating along the radial direction in Poincaré coordinates and trivial fields of all spins. Fields are trivial in the sense that they do not have gauge fields in the bulk and correspond to trivially conserved currents (i.e. constants) on the conformal boundary.

hep-th↗

arXiv2025

On symmetry breaking in the self-dual higher-spin theory

We explore the symmetry-broken phase of the self-dual (chiral) sector of higher-spin theory in four dimensions. To that end, we construct a two-parameter vacuum that breaks the AdS symmetry but remains symmetric under the leftover Poincaré algebra in three dimensions. The vacuum non-zero fields include spin-two AdS frame fields and a scalar, which has a profile that extends along the AdS radial direction. The two free parameters correspond to two scalar branches of conformal dimensions $Δ=1$ and $Δ=2$. Focusing on the $Δ=1$ branch, we analyze the dynamics of free fields around this vacuum and examine its holographic dual. We observe that certain higher spin states decouple in the broken phase. This is illustrated by a set of gauge fluctuations, which acquire no source from higher-spin currents, leading to their complete decoupling, except for the gauge field associated with spin one. The dual higher-spin currents appear to be disentangled from the gauge fields and generally do not conserve; however, their lower-spin components with helicities $s = -1, 0$, and $\pm 1/2$ remain unaffected by the symmetry breaking. Notably, the helicity $s=+1$ current, while deformed, remains conserved.

hep-th↗