Giant magnons in TsT-transformed Dmitri Bykov Trinity College Dublin

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Presentation transcript:

Giant magnons in TsT-transformed Dmitri Bykov Trinity College Dublin Steklov Mathematical Institute Moscow Based on joint work arXiv:0805.1070 with Sergey Frolov

Super-Yang-Mills theory AdS/CFT conjecture Super-Yang-Mills theory Maldacena ‘97 IIB strings on Conformal group in 4 dimensions Isometry group of -symmetry of Isometry group of Scaling dimension in gauge theory Energy of string

The TsT transformation The deformed space Lunin, Maldacena ‘05 The TsT transformation 3-torus in formed by Three 2-tori TsT TsT TsT Frolov ‘05

The dual superconformal theory superpotential: Leigh, Strassler ‘95 Action for strings propagating in in the conformal gauge Twisted boundary conditions:

Dispersion relation on the infinite world-sheet Hofman, Maldacena ‘06 Giant magnons Dispersion relation on the infinite world-sheet

at fixed The giant magnon ansatz Independent parameters

Equations of motion and Virasoro conditions Torus Cylinder We label the roots of r.h.s. as

The resulting system of equations:

Expansions in the decompactification limit Modular parameter of the torus

The dispersion relation Relation not modified in the infinite limit contrary to Chu, Georgiou, Khoze ‘06 No shift Relation between world-sheet and spin-chain momenta – coincides with Arutyunov, Frolov, Zamaklar ‘06

Energy of the solution in deformed theory is higher Solution exists if and only if all values of Unique

Summary and prospects Obtained the dispersion relation for giant magnons in -deformed theory A challenge for Luescher’s approach to finite size corrections (How can we obtain the in the formula?) Solutions with several spins Loop corrections Nonsupersymmetric background