TTbar deformation and the light-cone gauge

TL;DR

The paper interprets the spectrum of TTbar-deformed two-dimensional theories as a gauge-invariance condition for target-space energy and momentum in a non‑critical string quantised in a generalized uniform light-cone gauge, with the deformation parameter tied to the gauge parameter $a$ via $a = \tfrac{1}{2}+α$ and the deformation encoded by the homogeneous Burgers equation $∂_α E_α(R) + E_α(R) ∂_R E_α(R) = 0$. It develops a general, gauge-based construction that yields TTbar-deformed actions for systems with any number of scalars, fermions and chiral bosons, showing the deformation is governed by the canonical Noether stress-energy tensor and, in scalar cases, yields a square-root Nambu-Goto form. For fermions, the approach extends to Green-Schwarz-type sigma models, producing an explicit AAF-like Lagrangian ${\cal L}_{\rm AAF} = (i K^+_+ + i K^-_- + α(K^+_- K^-_+ - K^+_+ K^-_- ) - V)/(1 + α V)$ and clarifying the distinction between canonical and covariant stress-energy tensors. The framework unifies TTbar with multi-field and non-Lorentz-invariant deformations, connects to CDD factors in the S-matrix, and points to promising directions such as multi-parameter deformations (e.g., $J\bar{T}$), JT gravity relations, and quantum aspects of TTbar.

Abstract

The homogeneous inviscid Burgers equation which determines the spectrum of a TTbar deformed model has a natural interpretation as the condition of the gauge invariance of the target space-time energy and momentum of a (non-critical) string theory quantised in a generalised uniform light-cone gauge which depends on the deformation parameter. As a simple application of the light-cone gauge interpretation we derive the TTbar deformed Lagrangian for a system of any number of scalars, fermions and chiral bosons with an arbitrary potential. We find that the TTbar deformation is driven by the canonical Noether stress-energy tensor but not the covariant one.