48 research outputs found
Reflecting magnons from D7 and D5 branes
We obtain the reflection matrices for the scattering of elementary magnons
from certain open boundaries, corresponding to open strings ending on D7 and D5
branes in . In each case we consider two possible orientations
for the vacuum state. We show that symmetry arguments are sufficient to
determine the reflection matrices up to at most two unknown functions. The D7
reflection matrices obey the boundary Yang Baxter-Equation. This is automatic
for one vacuum orientation, and requires a natural choice of ratio between two
unknowns for the other. In contrast, the D5 reflection matrices do not obey the
boundary Yang Baxter-Equation. In both cases we show consistency with the
existent weak and strong coupling results.Comment: 32 pages, 1 figure; v2: added references and minor changes; v3: error
in boundary Yang-Baxter equation for D5 reflection matrix note
Eigenvectors and scalar products for long range interacting spin chains II: the finite size effects
Long-Range Deformations for Integrable Spin Chains
We present a recursion relation for the explicit construction of integrable
spin chain Hamiltonians with long-range interactions. Based on arbitrary
short-range (e.g. nearest-neighbor) integrable spin chains, it allows to
construct an infinite set of conserved long-range charges. We explain the
moduli space of deformation parameters by different classes of generating
operators. The rapidity map and dressing phase in the long-range Bethe
equations are a result of these deformations. The closed chain asymptotic Bethe
equations for long-range spin chains transforming under a generic symmetry
algebra are derived. Notably, our construction applies to generalizations of
standard nearest-neighbor chains such as alternating spin chains. We also
discuss relevant properties for its application to planar D=4, N=4 and D=3, N=6
supersymmetric gauge theories. Finally, we present a map between long-range and
inhomogeneous spin chains delivering more insight into the structures of these
models as well as their limitations at wrapping order.Comment: 63 pages, v2: references added, v3: typos corrected in eqs (8.20) and
(8.24
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
All-mass n-gon integrals in n dimensions
We explore the correspondence between one-loop Feynman integrals and
(hyperbolic) simplicial geometry to describe the "all-mass" case: integrals
with generic external and internal masses. Specifically, we focus on
-particle integrals in exactly space-time dimensions, as these integrals
have particularly nice geometric properties and respect a dual conformal
symmetry. In four dimensions, we leverage this geometric connection to give a
concise dilogarithmic expression for the all-mass box in terms of the
Murakami-Yano formula. In five dimensions, we use a generalized Gauss-Bonnet
theorem to derive a similar dilogarithmic expression for the all-mass pentagon.
We also use the Schl\"afli formula to write down the symbol of these integrals
for all . Finally, we discuss how the geometry behind these formulas depends
on space-time signature, and we gather together many results related to these
integrals from the mathematics and physics literature.Comment: 49 pages, 8 figure