Dualities for loop amplitudes of N = 6 Chern-Simons matter theory

Abstract

In this paper we study the one-and two-loop corrections to the four-point amplitude of N = 6 Chern-Simons matter theory. Using generalized unitarity methods we express the one-and two-loop amplitudes in terms of dual-conformal integrals. Explicit integration by using dimensional reduction gives vanishing one-loop result as expected, while the twoloop result is non-vanishing and matches with the Wilson loop computation. Furthermore, the two-loop correction takes the same form as the one-loop correction to the four-point amplitude of N = 4 super Yang-Mills. We discuss possible higher loop extensions of this correspondence between the two theories. As a side result, we extend the method of dimensional reduction for three dimensions to five dimensions where dual conformal symmetry is most manifest, demonstrating significant simplification to the computation of integrals. *

ABJM flux-tube and scattering amplitudes

“…9 They are thus rational functions. The two-loop amplitudes are functions of transcendentality two [49,50,59]. This is consistent with would-be dual conformal anomaly equations which would predict the presence of the BDS function accompanied by the cusp anomalous dimension in addition to a remainder function of the conformal cross ratios.…”

“…The explicit result for the four-point ABJM planar amplitude up to two loops confirms this expectation. In particular, the cut-based construction of the amplitude [49] from a set of dual conformal invariant integrals coincides with a direct Feynman diagram computation [50] which does not assume this property from the onset. Moreover, the final result, in a fashion analogous to SYM, can be interpreted as a solution to the anomalous dual conformal Ward identities, which fix it up uniquely.…”

From U(1) to E8: soft theorems in supergravity amplitudes

“…In previous section, we have derived the result of double-soft limits for tree-level amplitudes in N = 16 supergravity, in this section we will consider the double-soft limits at one-loop using generalized unitary cuts in three dimensions [14][15][16][17][18]. The integral representation of the three-dimensional theory can be deduced from its four-dimensional parent which is known to be expressible as linear combinations of scalar box integrals.…”

1/2BPS Wilson loop inN=6superconformal Chern-Simons theory at two loops

“…The precise statement of the duality is that type IIA string theory on AdS 4 Â CP 3 is dual to the N ¼ 6 CS theory coupled to bifundamental matter, with gauge group UðNÞ Â UðMÞ, in the limit of large N, M and large CS level k, with ¼ N=k and ¼ M=k fixed. 1 In the last four years, this particular realization of the AdS/CFT correspondence has been extensively investigated, and different observables of the theory, such as scattering amplitudes [3][4][5][6][7][8][9][10][11][12][13] and Wilson loops (WLs) [14][15][16][17][18][19] were studied. In this paper, we will be concerned with the computation of the expectation value of WL operators in ABJM theory.…”