# T-system on T-hook : Grassmannian solution and twisted Quantum Spectral Curve

* Corresponding author
Abstract : We propose an efficient grassmannian formalism for solution of bi-linear finite-difference Hirota equation (T-system) on T-shaped lattices related to the space of highest weight representations of $gl(K_1,K_2|M)$ superalgebra. The formalism is inspired by the quantum fusion procedure known from the integrable spin chains and is based on exterior forms of Baxter-like Q-functions. We find a few new interesting relations among the exterior forms of Q-functions and reproduce, using our new formalism, the Wronskian determinant solutions of Hirota equations known in the literature. Then we generalize this construction to the twisted Q-functions and demonstrate the subtleties of untwisting procedure on the examples of rational quantum spin chains with twisted boundary conditions. Using these observations, we generalize the recently discovered, in our paper with N. Gromov, AdS/CFT Quantum Spectral Curve for exact planar spectrum of AdS/CFT duality to the case of arbitrary Cartan twisting of $AdS_5\times S^5$ string sigma model. Finally, we successfully probe this formalism by reproducing the energy of gamma-twisted BMN vacuum at single-wrapping orders of weak coupling expansion.
Keywords :
Document type :
Journal articles
Domain :

https://hal.sorbonne-universite.fr/hal-01522682
Contributor : Gestionnaire Hal-Upmc <>
Submitted on : Monday, May 15, 2017 - 1:15:20 PM
Last modification on : Friday, May 24, 2019 - 5:25:15 PM
Long-term archiving on : Thursday, August 17, 2017 - 12:51:45 AM

### File

tsystem.pdf
Publication funded by an institution

### Citation

Vladimir Kazakov, Sébastien Leurent, Dmytro Volin. T-system on T-hook : Grassmannian solution and twisted Quantum Spectral Curve. Journal of High Energy Physics, Springer, 2016, pp.044. ⟨10.1007/JHEP12(2016)044⟩. ⟨hal-01522682⟩

Record views