27 research outputs found
A note on NMHV form factors from the Gra{\ss}mannian and the twistor string
In this note we investigate Gra{\ss}mannian formulas for form factors of the
chiral part of the stress-tensor multiplet in superconformal
Yang-Mills theory. We present an all- contour for the
Gra{\ss}mannian integral of NMHV form factors derived from on-shell diagrams
and the BCFW recursion relation. In addition, we study other
formulas obtained from the connected prescription introduced recently. We find
a recursive expression for all and study its properties. For ,
our formula has the same recursive structure as its amplitude counterpart,
making its soft behaviour manifest. Finally, we explore the connection between
the two Gra{\ss}mannian formulations, using the global residue theorem, and
find that it is much more intricate compared to scattering amplitudes.Comment: 21 pages, 3 figures; v2: JHEP version + minor correction
Elliptic Feynman integrals and pure functions
We propose a variant of elliptic multiple polylogarithms that have at most
logarithmic singularities in all variables and satisfy a differential equation
without homogeneous term. We investigate several non-trivial elliptic two-loop
Feynman integrals with up to three external legs and express them in terms of
our functions. We observe that in all cases they evaluate to pure combinations
of elliptic multiple polylogarithms of uniform weight. This is the first time
that a notion of uniform weight is observed in the context of Feynman integrals
that evaluate to elliptic polylogarithms.Comment: 47 page
All two-loop MHV remainder functions in multi-Regge kinematics
We introduce a method to extract the symbol of the coefficient of of MHV remainder functions in planar N=4 Super Yang-Mills in multi-Regge
kinematics region directly from the symbol in full kinematics. At two loops
this symbol can be uplifted to the full function in a unique way, without any
beyond-the-symbol ambiguities. We can therefore determine all two-loop MHV
amplitudes at function level in all kinematic regions with different energy
signs in multi-Regge kinematics. We analyse our results and we observe that
they are consistent with the hypothesis of a contribution from the exchange of
a three-Reggeon composite state starting from two loops and eight points in
certain kinematic regions.Comment: 36 pages, 4 figure
On-shell methods for off-shell quantities in N = 4 Super Yang-Mills: From scattering amplitudes to form factors and the dilatation operator
PhDPlanar maximally supersymmetric Yang-Mills theory (N = 4 SYM) is a special quantum
fi eld theory. A few of its remarkable features are conformal symmetry at the quantum
level, evidence of integrability and, moreover, it is a prime example of the AdS/CFT duality.
Triggered by Witten's twistor string theory [1], the past 15 years have witnessed
enormous progress in reformulating this theory to make as many of these special features
manifest, from the choice of convenient variables to recursion relations that allowed new
mathematical structures to appear, like the Grassmannian [2]. These methods are collectively
referred to as on-shell methods. The ultimate hope is that, by understanding
N = 4 SYM in depth, one can learn about other, more realistic quantum fi eld theories.
The overarching theme of this thesis is the investigation of how on-shell methods can aid
the computation of quantities other than scattering amplitudes. In this spirit we study
form factors and correlation functions, said to be partially and completely off-shell quantities,
respectively. More explicitly, we compute form factors of half-BPS operators up
to two loops, and study the dilatation operator in the SO(6) and SU(2j3) sectors using
techniques originally designed for amplitudes. A second part of the work is dedicated
to the study of scattering amplitudes beyond the planar limit, an area of research which
is still in its infancy, and not much is known about which special features of the planar
theory survive in the non-planar regime. In this context, we generalise some aspects of the
on-shell diagram formulation of Arkani-Hamed et al. [3] to take into account non-planar
corrections
A note on NMHV form factors from the Graßmannian and the twistor string
In this note we investigate Graßmannian formulas for form factors of the chiral part of the stress-tensor multiplet in N=4 superconformal Yang-Mills theory. We present an all-n contour for the G(3, n + 2) Graßmannian integral of NMHV form factors derived from on-shell diagrams and the BCFW recursion relation. In addition, we study other G(3, n + 2) formulas obtained from the connected prescription introduced recently. We find a recursive expression for all n and study its properties. For n ≥ 6, our formula has the same recursive structure as its amplitude counterpart, making its soft behaviour manifest. Finally, we explore the connection between the two Graßmannian formulations, using the global residue theorem, and find that it is much more intricate compared to scattering amplitudes
Higgs Amplitudes from N=4 Supersymmetric Yang-Mills Theory
The work of A. B. and G. T. was supported by the Science and Technology Facilities Council (STFC) Consolidated Grant No. ST/L000415/1 “String theory, gauge theory, and duality.” The work of M. K. is supported by a STFC quota studentship. B. P. is funded by the ERC Starting Grant No. 637019 “MathAm.” A. B. and G. T. thank the KITP at the University of California, Santa Barbara, where their research was supported by the National Science Foundation under Grant No. NSF PHY-1125915. G. T. is grateful to the Alexander von Humboldt Foundation for support through a Friedrich Wilhelm Bessel Research Awar