385 research outputs found
Boundary scattering in the principal chiral model
An informal introduction to our recent work on the principal chiral model
with boundary. We found that both classically integrable boundary conditions
and quantum boundary S-matrices were classified by the symmetric spaces G/H.
The connection is explained by the presence of a twisted Yangian algebra of
non-local charges.Comment: Updated v2 based on talk at 'IFTs, Solitons and Duality', Sao Paulo
2002; v1 appeared in Proc. QGIS Prague 200
Affine Toda Solitons and Automorphisms of Dynkin Diagrams
Using Hirota's method, solitons are constructed for affine Toda field
theories based on the simply-laced affine algebras. By considering
automorphisms of the simply-laced Dynkin diagrams, solutions to the remaining
algebras, twisted as well as untwisted, are deduced.Comment: 21 page
Yangian symmetry of the Y=0 maximal giant graviton
We study the remnants of Yangian symmetry of AdS/CFT magnons reflecting from
boundaries with no degrees of freedom. We present the generalized twisted
boundary Yangian of open strings ending on boundaries which preserve only a
subalgebra h of the bulk algebra g, where (g,h) is a symmetric pair. This is
realized by open strings ending on the D3 brane known as the Y=0 maximal giant
graviton in AdS_5 x S^5. We also consider the Yangian symmetry of the boundary
which preserves an su(1|2) subalgebra only.Comment: 17 pages, v2: minor correction made, accepted for publication in JHE
On the algebraic structure of factorized S-matrices
This thesis investigates the algebraic structure of certain quantum field theories in one space and one time dimension. These theories are integrable - essentially, highly constrained and therefore soluble. Thus, instead of having to use perturbative techniques, it is possible to conjecture their exact 5-matrices, which have the property that they are factorized into two-particle 5-matrices. In particular, there are two types of such theory: in one, scattering is purely elastic, whilst in the other, there is additional structure dictated by the Yang-Baxter equation. This thesis explores the algebraic structure of the latter and its links with the former. We begin, in chapter one, with an informal summary of the development of the subject, followed by a more mathematical exposition in chapter two. Chapter three constructs explicitly some exact factorized 5-matrices with Yang-Baxter structure, and comments on their features, both intrinsic and in relation to purely elastic 5-matrices. In particular, there is an unexplained close correspondence between the mass spectra and particle fusings in the two types of theory. The next three chapters attempt to shed some light on these features. Chapter four constructs similar 5-matrices, but based on quantum-deformed algebras rather than classical algebras. In chapter five we describe the structure of the 5-matrices when the particles they describe transform in irreducible representations of classical algebras. This leads us to consider the Yangian algebra, the representation theory of which underlies Yang-Baxter dependent 5-matrices, and which we therefore review briefly. We begin chapter six by reviewing the work which shows that the Yangian is also the charge algebra of the integrable quantum field theory, and subsequently show that the Yangian is also to a great extent present in the corresponding classical theory. We conclude with a brief seventh chapter describing the outlook for further research, followed by appendices containing respectively details of the Lagrangians of some integrable quantum field theories, a continuum formulation of the quantum inverse problem, explicit expressions for some of the R-matrices computed in the text, and a summary of known solutions of the Yang-Baxter equation
Achiral boundaries and the twisted Yangian of the D5-brane
We consider integrable field theories with achiral boundary conditions and
uncover the underlying achiral twisted Yangian algebra. This construction
arises from old work on the bosonic principal chiral model on a half-line, but
finds a modern realization as the hidden symmetry in the planar limit of the
scattering of worldsheet excitations of the AdS/CFT light-cone superstring off
a D5-brane.Comment: 21 pages, 6 figures; v2: typos corrected, refs added; v3: minor
corrections made, published versio
The Attrition Dynamics of Multilateral War
We extend classical force-on-force combat models to study the attrition dynamics of three-way and multilateral war. We introduce a new multilateral combat model (the multiduel) which generalizes the Lanchester models, and solve it under an objective function which values one's own surviving force minus that of one's enemies. The outcome is stark: either one side is strong enough to destroy all the others combined, or all sides are locked in a stalemate which results in collective mutual annihilation. The situation in Syria fits this paradigm
Targeting, deployment and loss-tolerance in Lanchester engagements
Existing Lanchester combat models focus on two force parameters: numbers (force size) and per-capita effectiveness (attrition rate). While these two parameters are central in projecting a battle’s outcome, there are other important factors that affect the battlefield: (1) targeting capability, the capacity to identify live enemy units and not dissipate fire on non-targets; (2) tactical restrictions preventing full deployment of forces; and (3) morale and tolerance of losses, the capacity to endure casualties. In the spirit of Lanchester theory, we derive, for the first time, force-parity equations for various combinations of these effects, and obtain general implications and trade-offs. We show that more units and better weapons (higher attrition rate) are preferred over improved targeting capability and relaxed deployment restrictions unless these are poor. However, when facing aimed fire and unable to deploy more than half one’s force it is better to be able to deploy more existing units than to have either additional reserve units or the same increase in attrition effectiveness. Likewise more relaxed deployment constraints are preferred over enhanced loss-tolerance when initial reserves are greater than the force level at which withdrawal occurs
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