Giant magnons

1
Giant magnons
in TsT-transformed
Dmitri Bykov
Trinity College Dublin Steklov Mathematical
Institute Moscow
Based on joint work arXiv0805.1070 with Sergey
Frolov
2
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 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
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 Lueschers approach
• to finite size corrections

(How can we obtain the in the
formula?)

• Solutions with several spins

• Loop corrections

• Nonsupersymmetric background