321 research outputs found
A Grassmannian Etude in NMHV Minors
Arkani-Hamed, Cachazo, Cheung and Kaplan have proposed a Grassmannian
formulation for the S-matrix of N=4 Yang-Mills as an integral over link
variables. In parallel work, the connected prescription for computing tree
amplitudes in Witten's twistor string theory has also been written in terms of
link variables. In this paper we extend the six- and seven-point results of
arXiv:0909.0229 and arXiv:0909.0499 by providing a simple analytic proof of the
equivalence between the two formulas for all tree-level NMHV superamplitudes.
Also we note that a simple deformation of the connected prescription integrand
gives directly the ACCK Grassmannian integrand in the limit when the
deformation parameters equal zero.Comment: 17 page
The Grassmannian and the Twistor String: Connecting All Trees in N=4 SYM
We present a new, explicit formula for all tree-level amplitudes in N=4 super
Yang-Mills. The formula is written as a certain contour integral of the
connected prescription of Witten's twistor string, expressed in link variables.
A very simple deformation of the integrand gives directly the Grassmannian
integrand proposed by Arkani-Hamed et al. together with the explicit contour of
integration. The integral is derived by iteratively adding particles to the
Grassmannian integral, one particle at a time, and makes manifest both parity
and soft limits. The formula is shown to be related to those given by Dolan and
Goddard, and generalizes the results of earlier work for NMHV and N^2MHV to all
N^(k-2)MHV tree amplitudes in N=4 super Yang-Mills.Comment: 26 page
Conformal Fixed Points of Unidentified Gauge Theories
In this article we discuss gauge/strings correspondence based on the
non-critical strings. With this goal we present several remarkable sigma models
with the AdS target spaces. The models have kappa symmetry and are completely
integrable. The radius of the AdS space is fixed and thus they describe
isolated fixed points of gauge theories in various dimensionsComment: 14 page
General Split Helicity Gluon Tree Amplitudes in Open Twistor String Theory
We evaluate all split helicity gluon tree amplitudes in open twistor string
theory. We show that these amplitudes satisfy the BCFW recurrence relations
restricted to the split helicity case and, hence, that these amplitudes agree
with those of gauge theory. To do this we make a particular choice of the
sextic constraints in the link variables that determine the poles contributing
to the contour integral expression for the amplitudes. Using the residue
theorem to re-express this integral in terms of contributions from poles at
rational values of the link variables, which we determine, we evaluate the
amplitudes explicitly, regaining the gauge theory results of Britto et al.Comment: 30 pages, minor misprints correcte
Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
We continue the investigation of two-loop string corrections to the energy of
a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the
scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We
compute the generalized scaling function at two-loop order f_2(ell) both for
small and large values of ell matching the predictions based on the asymptotic
Bethe ansatz. In particular, in the small ell expansion, we derive an exact
integral form for the ell-dependent coefficient of the Catalan's constant term
in f_2(ell). Also, by resumming a certain subclass of multi-loop Feynman
diagrams we obtain an exact expression for the leading (ln ell) part of
f(lambda^(1/2), ell) which is valid to any order in the alpha'~1/lambda^(1/2)
expansion. At large ell the string energy has a BMN-like expansion and the
first few leading coefficients are expected to be the same at weak and at
strong coupling. We provide a new example of this non-renormalization for the
term which is generated at two loops in string theory and at one-loop in gauge
theory (sub-sub-leading in 1/J). We also derive a simple algebraic formula for
the term of maximal transcendentality in f_2(ell) expanded at large ell. In the
second part of the paper we initiate the study of 2-loop finite size
corrections to the string energy by formally compactifying the spatial
world-sheet direction in the string action expanded near long fast-spinning
string. We observe that the leading finite-size corrections are of "Casimir"
type coming from terms containing at least one massless propagator. We consider
in detail the one-loop order (reproducing the leading Landau-Lifshitz model
prediction) and then focus on the two-loop contributions to the (1/ln S) term
(for J=0). We find that in a certain regularization scheme used to discard
power divergences the two-loop coefficient of the (1/ln S) term appears to
vanish.Comment: 50 pages, 4 figures v2: typos corrected, references adde
Yangian in the Twistor String
We study symmetries of the quantized open twistor string. In addition to
global PSL(4|4) symmetry, we find non-local conserved currents. The associated
non-local charges lead to Ward identities which show that these charges
annihilate the string gluon tree amplitudes, and have the same form as
symmetries of amplitudes in N=4 super conformal Yang Mills theory. We describe
how states of the open twistor string form a realization of the PSL(4|4)
Yangian superalgebra.Comment: 37 pages, 4 figure
One-loop corrections to AdS_5 x S^5 superstring partition function via Pohlmeyer reduction
We discuss semiclassical expansions around a class of classical string
configurations lying in AdS_3 x S^1 using the Pohlmeyer-reduced from of the
AdS_5 x S^5 superstring theory. The Pohlmeyer reduction of the AdS_5 x S^5
superstring theory is a gauged Wess-Zumino-Witten model with an integrable
potential and two-dimensional fermionic fields. It was recently conjectured
that the quantum string partition function is equal to the quantum reduced
theory partition function. Continuing the previous paper (arXiv:0906.3800)
where arbitrary solutions in AdS_2 x S^2 and homogeneous solutions were
considered, we provide explicit demonstration of this conjecture at the
one-loop level for several string solutions in AdS_3 x S^1 embedded into AdS_5
x S^5. Quadratic fluctuations derived in the reduced theory for inhomogeneous
strings are equivalent to respective fluctuations found from the Nambu action
in the original string theory. We also show the equivalence of fluctuation
frequencies for homogeneous strings with both the orbital momentum and the
winding on a big circle of S^5.Comment: 45 pages, references added, minor correction
Three-Loop Superfiniteness of N=8 Supergravity
We construct the three-loop four-point amplitude of N=8 supergravity using
the unitarity method. The amplitude is ultraviolet finite in four dimensions.
Novel cancellations, not predicted by traditional superspace power-counting
arguments, render its degree of divergence in D dimensions to be no worse than
that of N=4 super-Yang-Mills theory -- a finite theory in four dimensions.
Similar cancellations can be identified at all loop orders in certain unitarity
cuts, suggesting that N=8 supergravity may be a perturbatively finite theory of
quantum gravity.Comment: 5 pages, 4 figures. In v2 references and minor clarifications adde
Gluon Tree Amplitudes in Open Twistor String Theory
We show how the link variables of Arkani-Hamed, Cachazo, Cheung and Kaplan
(ACCK), can be used to compute general gluon tree amplitudes in the twistor
string. They arise from instanton sectors labelled by d, with d=n-1, where n is
the number of negative helicities. Read backwards, this shows how the various
forms for the tree amplitudes studied by ACCK can be grouped into contour
integrals whose structure implies the existence of an underlying string theory.Comment: 36 page
The Ultraviolet Behavior of N=8 Supergravity at Four Loops
We describe the construction of the complete four-loop four-particle
amplitude of N=8 supergravity. The amplitude is ultraviolet finite, not only in
four dimensions, but in five dimensions as well. The observed extra
cancellations provide additional non-trivial evidence that N=8 supergravity in
four dimensions may be ultraviolet finite to all orders of perturbation theory.Comment: 5 pages, 4 figures. v2 contains minor corrections, including flipping
sign of eq. (1). Complete results, including mathematica readable form,
presented in the directory aux/ included in the source of this manuscript. As
certain computer operating systems (e.g. Windows) preclude the naming of
directories "aux" we also host this data at:
http://www.physics.ucla.edu/~jjmc/auxiliaryData.tg
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