56,811 research outputs found
From Trees to Loops and Back
We argue that generic one-loop scattering amplitudes in supersymmetric
Yang-Mills theories can be computed equivalently with MHV diagrams or with
Feynman diagrams. We first present a general proof of the covariance of
one-loop non-MHV amplitudes obtained from MHV diagrams. This proof relies only
on the local character in Minkowski space of MHV vertices and on an application
of the Feynman Tree Theorem. We then show that the discontinuities of one-loop
scattering amplitudes computed with MHV diagrams are precisely the same as
those computed with standard methods. Furthermore, we analyse collinear limits
and soft limits of generic non-MHV amplitudes in supersymmetric Yang-Mills
theories with one-loop MHV diagrams. In particular, we find a simple explicit
derivation of the universal one-loop splitting functions in supersymmetric
Yang-Mills theories to all orders in the dimensional regularisation parameter,
which is in complete agreement with known results. Finally, we present concrete
and illustrative applications of Feynman's Tree Theorem to one-loop MHV
diagrams as well as to one-loop Feynman diagrams.Comment: 52 pages, 17 figures. Some typos in Appendix A correcte
Generalized string theory mapping relations between gravity and gauge theory
A previous study of the Kawai, Lewellen and Tye (KLT) relations between
gravity and gauge theories, imposed by the relationship of closed and open
strings, are here extended in the light of general relativity and Yang-Mills
theory as effective field theories. We discuss the possibility of generalizing
the traditional KLT mapping in this effective setting. A generalized mapping
between the effective Lagrangians of gravity and Yang-Mills theory is
presented, and the corresponding operator relations between gauge and gravity
theories at the tree level are further explored. From this generalized mapping
remarkable diagrammatic relations are found, -- linking diagrams in gravity and
Yang-Mills theory, -- as well as diagrams in pure effective Yang-Mills theory.
Also the possibility of a gravitational coupling to an antisymmetric field in
the gravity scattering amplitude is considered, and shown to allow for mixed
open-closed string solutions, i.e., closed heterotic strings.Comment: 10 pages, 7 figures, format ReVTeX, comments and ref. added, typos
correcte
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
Parity Invariance For Strings In Twistor Space
Topological string theory with twistor space as the target makes visible some
otherwise difficult to see properties of perturbative Yang-Mills theory. But
left-right symmetry, which is obvious in the standard formalism, is highly
unclear from this point of view. Here we prove that tree diagrams computed from
connected -instanton configurations are parity-symmetric. The main point in
the proof also works for loop diagrams.Comment: 18 p
Diagrammatic proof of the BCFW recursion relation for gluon amplitudes in QCD
We present a proof of the Britto-Cachazo-Feng-Witten tree-level recursion
relation for gluon amplitudes in QCD, based on a direct equivalence between
BCFW decompositions and Feynman diagrams. We demonstrate that this equivalence
can be made explicit when working in a convenient gauge. We exhibit that gauge
invariance and the particular structure of Yang-Mills vertices guarantees the
validity of the BCFW construction.Comment: 24 pages, 33 figure
Towards Field Theory Amplitudes From the Cohomology of Pure Spinor Superspace
A simple BRST-closed expression for the color-ordered super-Yang-Mills
5-point amplitude at tree-level is proposed in pure spinor superspace and shown
to be BRST-equivalent to the field theory limit of the open superstring 5-pt
amplitude. It is manifestly cyclic invariant and each one of its five terms can
be associated to the five Feynman diagrams which use only cubic vertices. Its
form also suggests an empirical method to find superspace expressions in the
cohomology of the pure spinor BRST operator for higher-point amplitudes based
on their kinematic pole structure. Using this method, Ansaetze for the 6- and
7-point 10D super-Yang-Mills amplitudes which map to their 14 and 42
color-ordered diagrams are conjectured and their 6- and 7-gluon expansions are
explicitly computed.Comment: 14 pages, harvmac, v4: trivial edits in the text to comply with JHEP
refere
The Kinematic Algebra From the Self-Dual Sector
We identify a diffeomorphism Lie algebra in the self-dual sector of
Yang-Mills theory, and show that it determines the kinematic numerators of
tree-level MHV amplitudes in the full theory. These amplitudes can be computed
off-shell from Feynman diagrams with only cubic vertices, which are dressed
with the structure constants of both the Yang-Mills colour algebra and the
diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour
algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We
further study perturbative gravity, both in the self-dual and in the MHV
sectors, finding that the kinematic numerators of the theory are the BCJ
squares of the Yang-Mills numerators.Comment: 29 pages, 5 figures. v2: references added, published versio
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