1,819 research outputs found
Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM
In this paper we consider tree-level gauge invariant off-shell amplitudes
(Wilson line form factors) in SYM with arbitrary number of
off-shell gluons or equivalently Wilson line operator insertions. We make a
conjecture for the Grassmannian integral representation for such objects and
verify our conjecture on several examples. It is remarkable that in our
formulation one can consider situation when on-shell particles are not present
at all, i.e. we have Grassmannian integral representation for purely off-shell
object. In addition we show that off-shell amplitude with arbitrary number of
off-shell gluons could be also obtained using quantum inverse scattering method
for auxiliary super spin chain.Comment: 38 pages, 9 figures; v4: typos corrected, comment in section 3.2
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Conformal Invariance = Finiteness and Beta Deformed N=4 SYM Theory
We claim that if by a choice of the couplings the theory can be made
conformally invariant (vanishing of the beta functions) it is automatically
finite and vice versa. This is demonstrated by explicit example in
supersymmetric gauge theory. The formalism is then applied to the beta deformed
SYM theory and it is shown that the requirement of conformal
invariance = finiteness can be achieved for any complex parameter of
deformations.Comment: 15 pages, Latex, 1 figure axodraw styl
Ambitwistor strings and reggeon amplitudes in N=4 SYM
We consider the description of reggeon amplitudes (Wilson lines form factors)
in N=4 SYM within the framework of four dimensional ambitwistor string theory.
The latter is used to derive scattering equations representation for reggeon
amplitudes with multiple reggeized gluons present. It is shown, that
corresponding tree-level string correlation function correctly reproduces
previously obtained Grassmannian integral representation of reggeon amplitudes
in N=4 SYM.Comment: 18 page
Challenges of D=6 N=(1,1) SYM Theory
Maximally supersymmetric Yang-Mills theories have several remarkable
properties, among which are the cancellation of UV divergences, factorization
of higher loop corrections and possible integrability. Much attention has been
attracted to the N=4 D=4 SYM theory. The N=(1,1) D=6 SYM theory possesses
similar properties but is nonrenomalizable and serves as a toy model for
supergravity. We consider the on-shell four point scattering amplitude and
analyze its perturbative expansion within the spin-helicity and superspace
formalism. The integrands of the resulting diagrams coincide with those of the
N=4 D=4 SYM and obey the dual conformal invariance. Contrary to 4 dimensions,
no IR divergences on mass shell appear. We calculate analytically the leading
logarithmic asymptotics in all loops. Their summation leads to a Regge
trajectory which is calculated exactly. The leading powers of s are calculated
up to six loops. Their summation is performed numerically and leads to a smooth
function of s. The leading UV divergences are calculated up to 5 loops. The
result suggests the geometrical progression which ends up in a finite
expression. This leads us to a radical point of view on nonrenormalizable
theories.Comment: 11 pages, 2 figures, Late
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