Abstract
We investigate the integrable Yang-Baxter deformation of the 2d Principal Chiral Model with a Wess-Zumino term. For arbitrary groups, the one-loop β-functions are calculated and display a surprising connection between classical and quantum physics: the classical integrability condition is necessary to prevent new couplings being generated by renormalisation. We show these theories admit an elegant realisation of Poisson-Lie T-duality acting as a simple inversion of coupling constants. The self-dual point corresponds to the Wess-Zumino-Witten model and is the IR fixed point under RG. We address the possibility of having supersymmetric extensions of these models showing that extended supersymmetry is not possible in general.
Highlights
A surprising feature of the η-deformed theory in the context of the AdS5 × S5 superstring is that it appears to describe a scale invariant but not Weyl invariant theory
We investigate the integrable Yang-Baxter deformation of the 2d Principal Chiral Model with a Wess-Zumino term
We address the possibility of having supersymmetric extensions of these models showing that extended supersymmetry is not possible in general
Summary
We present the Yang-Baxter Wess-Zumino model (YB-WZ) as constructed in [26], which will be the main topic of the remainder of this paper. The canonical realization of R is most seen in a Cartan-Weyl basis for the Lie algebra where it maps generators belonging to the CSA to zero and where it acts diagonally on generators corresponding to positive (negative) roots with eigenvalue +i (−i) Equipped with this structure, we define the YB-WZ action in worldsheet light-cone coordinates as,. We conclude that the currents K± are on-shell flat provided eq (2.8) holds This is sufficient to guarantee classical integrability as the equations of motion follow from the flatness of the standard gC-valued Zakharov-Mikhailov Lax connection [42],. The right acting G symmetry is broken to its Cartan in the action eq (2.2), but is enhanced by non-local charges to form a classical version of a quantum group Uq(g) [3] ( further extended to an affine Uq(g) [36]).
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