80 research outputs found
Self-Dual Fields on Self-Dual Backgrounds and the Double Copy
We explore the double copy for self-dual gauge and gravitational fields on
self-dual background spacetimes. We consider backgrounds associated to
solutions of the second Plebanski equation and describe results with different
gauge-fixing conditions. Finally we discuss the kinematic and -algebras and
the double copy, identifying modified Poisson structures and kinematic
structure constants in the presence of the self-dual background. The self-dual
plane wave and Eguchi-Hanson spacetimes are studied as examples and their
respective -algebras derived.Comment: 23 page
Conformal topological Yang-Mills theory and de Sitter holography
A new topological conformal field theory in four Euclidean dimensions is
constructed from N=4 super Yang-Mills theory by twisting the whole of the
conformal group with the whole of the R-symmetry group, resulting in a theory
that is conformally invariant and has two conformally invariant BRST operators.
A curved space generalisation is found on any Riemannian 4-fold. This
formulation has local Weyl invariance and two Weyl-invariant BRST symmetries,
with an action and energy-momentum tensor that are BRST-exact. This theory is
expected to have a holographic dual in 5-dimensional de Sitter space.Comment: 34 pages, AMSTex, Reference adde
Integrals of Motion in the Two Killing Vector Reduction of General Relativity
We apply the inverse scattering method to the midi-superspace models that are
characterized by a two-parameter Abelian group of motions with two spacelike
Killing vectors. We present a formulation that simplifies the construction of
the soliton solutions of Belinski\v i and Zakharov. Furthermore, it enables us
to obtain the zero curvature formulation for these models. Using this, and
imposing periodic boundary conditions corresponding to the Gowdy models when
the spatial topology is a three torus , we show that the equation of
motion for the monodromy matrix is an evolution equation of the Heisenberg
type. Consequently, the eigenvalues of the monodromy matrix are the generating
functionals for the integrals of motion. Furthermore, we utilise a suitable
formulation of the transition matrix to obtain explicit expressions for the
integrals of motion. This involves recursion relations which arise in solving
an equation of Riccati type. In the case when the two Killing vectors are
hypersurface orthogonal the integrals of motion have a particularly simple
form.Comment: 20 pages, plain TeX, SU-GP-93/7-8, UM-P-93/7
Non-Supersymmetric Loop Amplitudes and MHV Vertices
We show how the MHV diagram description of Yang-Mills theories can be used to
study non-supersymmetric loop amplitudes. In particular, we derive a compact
expression for the cut-constructible part of the general one-loop MHV
multi-gluon scattering amplitude in pure Yang-Mills theory. We show that in
special cases this expression reduces to known amplitudes - the amplitude with
adjacent negative-helicity gluons, and the five gluon non-adjacent amplitude.
Finally, we briefly discuss the twistor space interpretation of our result.Comment: 31 pages, 5 figures, Typos Correcte
Stable Non--Perturbative Minimal Models Coupled to 2D Quantum Gravity
A generalisation of the non--perturbatively stable solutions of string
equations which respect the KdV flows, obtained recently for the
conformal minimal models coupled to two--dimensional quantum gravity, is
presented for the models. These string equations are the most general
string equations compatible with the --th generalised KdV flows. They
exhibit a close relationship with the bi-hamiltonian structure in these
hierarchies. The Ising model is studied as a particular example, for which a
real non-singular numerical solution to the string susceptibility is presented.Comment: (35 pp; two figures not included; plain TEX
One-Loop Gauge Theory Amplitudes in N=4 Super Yang-Mills from MHV Vertices
We propose a new, twistor string theory inspired formalism to calculate loop
amplitudes in N=4 super Yang-Mills theory. In this approach, maximal helicity
violating (MHV) tree amplitudes of N=4 super Yang-Mills are used as vertices,
using an off-shell prescription introduced by Cachazo, Svrcek and Witten, and
combined into effective diagrams that incorporate large numbers of conventional
Feynman diagrams. As an example, we apply this formalism to the particular
class of MHV one-loop scattering amplitudes with an arbitrary number of
external legs in N=4 super Yang-Mills. Remarkably, our approach naturally leads
to a representation of the amplitudes as dispersion integrals, which we
evaluate exactly. This yields a new, simplified form for the MHV amplitudes,
which is equivalent to the expressions obtained previously by Bern, Dixon,
Dunbar and Kosower using the cut-constructibility approach.Comment: Latex, 35 pages, 3 figures. v2: remarks on gauge invariance added.
Published version to appear in Nuclear Physics
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