| 1. |
- Caron-Huot, Simon, et al.
(författare)
-
Uniqueness of Two-Loop Master Contours
- 2012
-
Ingår i: Journal of High Energy Physics (JHEP). - 1126-6708 .- 1029-8479. ; :10, s. 026-
-
Tidskriftsartikel (refereegranskat)abstract
- Generalized-unitarity calculations of two-loop amplitudes are performed by expanding the amplitude in a basis of master integrals and then determining the coefficients by taking a number of generalized cuts. In this paper, we present a complete classification of the solutions to the maximal cut of integrals with the double-box topology. The ideas presented here are expected to be relevant for all two-loop topologies as well. We find that these maximal-cut solutions are naturally associated with Riemann surfaces whose topology is determined by the number of states at the vertices of the double-box graph. In the case of four massless external momenta we find that, once the geometry of these Riemann surfaces is properly understood, there are uniquely defined master contours producing the coefficients of the double-box integrals in the basis decomposition of the two-loop amplitude. This is in perfect analogy with the situation in one-loop generalized unitarity. In addition, we point out that the chiral integrals recently introduced by Arkani-Hamed et al. can be used as master integrals for the double-box contributions to the two-loop amplitudes in any gauge theory. The infrared finiteness of these integrals allow for their coefficients as well as their integrated expressions to be evaluated in strictly four dimensions, providing significant technical simplification. We evaluate these integrals at four points and obtain remarkably compact results.
|
|
| 2. |
- Larsen, Kasper, 1983-
(författare)
-
Global Poles of the Two-Loop Six-Point N=4 SYM integrand
- 2012
-
Ingår i: Physical Review D. - 1550-7998 .- 1550-2368. ; 86:8, s. 085032-
-
Tidskriftsartikel (refereegranskat)abstract
- Recently, a recursion relation has been developed, generating the four-dimensional integrand of the amplitudes of N=4 supersymmetric Yang-Mills theory for any number of loops and legs. In this paper, I provide a comparison of the prediction for the two-loop six-point maximally helicity violating (MHV) integrand against the result obtained by use of the leading singularity method. The comparison is performed numerically for a large number of randomly selected momenta and in all cases finds agreement between the two results to high numerical accuracy.
|
|
| 3. |
- Larsen, Kasper, 1983-, et al.
(författare)
-
MHV, CSW and BCFW : field theory structures in string theory amplitudes
- 2008
-
Ingår i: Journal of High Energy Physics (JHEP). - : Springer Science and Business Media LLC. - 1126-6708 .- 1029-8479. ; 11:015, s. 1-59
-
Tidskriftsartikel (refereegranskat)abstract
- Motivated by recent progress in calculating field theory amplitudes, we study applications of the basic ideas in these developments to the calculation of amplitudes in string theory. We consider in particular both non-Abelian and Abelian open superstring disk amplitudes in a flat space background, focusing mainly on the four-dimensional case. The basic field theory ideas under consideration split into three separate categories. In the first, we argue that the calculation of α'-corrections to MHV open string disk amplitudes reduces to the determination of certain classes of polynomials. This line of reasoning is then used to determine the α'3-correction to the MHV amplitude for all multiplicities. A second line of attack concerns the existence of an analog of CSW rules derived from the Abelian Dirac-Born-Infeld action in four dimensions. We show explicitly that the CSW-like perturbation series of this action is surprisingly trivial: only helicity conserving amplitudes are non-zero. Last but not least, we initiate the study of BCFW on-shell recursion relations in string theory. These should appear very naturally as the UV properties of the string theory are excellent. We show that all open four-point string amplitudes in a flat background at the disk level obey BCFW recursion relations. Based on the naturalness of the proof and some explicit results for the five-point gluon amplitude, it is expected that this pattern persists for all higher point amplitudes and for the closed string.
|
|
