Semiclassical spectrum of a Jordanian deformation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>AdS</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>5</mml:mn></mml:msup></mml:math>
Riccardo Borsato, Sibylle Driezen, Juan Miguel Nieto García, Leander Wyss
Abstract
We study a Jordanian deformation of the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ superstring that preserves 12 superisometries. It is an example of homogeneous Yang-Baxter deformations, a class that generalizes TsT deformations to the non-Abelian case. Many of the attractive features of TsT carry over to this more general class, from the possibility of generating new supergravity solutions to the preservation of world sheet integrability. In this paper, we exploit the fact that the deformed $\ensuremath{\sigma}$-model with periodic boundary conditions can be reformulated as an undeformed one with twisted boundary conditions and discuss the construction of the classical spectral curve and its semiclassical quantization. First, we find global coordinates for the deformed background and identify the global time corresponding to the energy that should be computed in the spectral problem. Using the curve of the twisted model, we obtain the one-loop correction to the energy of a particular solution, and we find that the charge encoding the twisted boundary conditions does not receive an anomalous correction. Finally, we give evidence suggesting that the unimodular version of the deformation (giving rise to a supergravity background) and the nonunimodular one (whose background does not solve the supergravity equations) have the same spectrum at least to one-loop.