6 research outputs found
Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM
We present the perturbative Yangian symmetry at next-to-leading order in the
su(2|1) sector of planar N=4 SYM. Just like the ordinary symmetry generators,
the bi-local Yangian charges receive corrections acting on several neighboring
sites. We confirm that the bi-local Yangian charges satisfy the necessary
conditions: they transform in the adjoint of su(2|1), they commute with the
dilatation generator, and they satisfy the Serre relations. This proves that
the sector is integrable at two loops.Comment: 13 pages, v2: minor correction
Algebra of Lax Connection for T-Dual Models
We study relation between T-duality and integrability. We develop the
Hamiltonian formalism for principal chiral model on general group manifold and
on its T-dual image. We calculate the Poisson bracket of Lax connections in
T-dual model and we show that they are non-local as opposite to the Poisson
brackets of Lax connection in original model. We demonstrate these calculations
on two specific examples: Sigma model on S(2) and sigma model on AdS(2).Comment: 24 pages, references adde
Open strings in relativistic ion traps
Electromagnetic plane waves provide examples of time-dependent open string
backgrounds free of corrections. The solvable case of open strings in
a quadrupolar wave front, analogous to pp-waves for closed strings, is
discussed. In light-cone gauge, it leads to non-conformal boundary conditions
similar to those induced by tachyon condensates. A maximum electric gradient is
found, at which macroscopic strings with vanishing tension are pair-produced --
a non-relativistic analogue of the Born-Infeld critical electric field. Kinetic
instabilities of quadrupolar electric fields are cured by standard atomic
physics techniques, and do not interfere with the former dynamic instability. A
new example of non-conformal open-closed duality is found. Propagation of open
strings in time-dependent wave fronts is discussed.Comment: 43 pages, 11 figures, Latex2e, JHEP3.cls style; v2: one-loop
amplitude corrected, open-closed duality proved, refs added, miscellaneous
improvements, see historical note in fil
Hidden Simplicity of Gauge Theory Amplitudes
These notes were given as lectures at the CERN Winter School on Supergravity,
Strings and Gauge Theory 2010. We describe the structure of scattering
amplitudes in gauge theories, focussing on the maximally supersymmetric theory
to highlight the hidden symmetries which appear. Using the BCFW recursion
relations we solve for the tree-level S-matrix in N=4 super Yang-Mills theory,
and describe how it produces a sum of invariants of a large symmetry algebra.
We review amplitudes in the planar theory beyond tree-level, describing the
connection between amplitudes and Wilson loops, and discuss the implications of
the hidden symmetries.Comment: 46 pages, 15 figures. v2 ref added, typos fixe