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

2. 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

3. 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

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

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

6. at fixed
The giant magnon ansatz
Independent parameters

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

8. The resulting system of equations:

9. Expansions in the decompactification limit
Modular parameter of the torus

10. 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

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

12. 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