One-loop gluon amplitudes in AdS

Abstract

We initiate the study of one-loop gluon amplitudes in AdS space. These amplitudes were recently computed at tree level for a variety of backgrounds of the form AdSd+1× S3. For concreteness, we compute the one-loop correction to the massless gluon amplitude on AdS5×S3, which corresponds to the four-point correlator of the flavor current multiplet in the dual 4d $$ \mathcal{N} $$ N = 2 SCFT. This requires solving a mixing problem that involves tree-level amplitudes of arbitrarily massive Kaluza-Klein modes. The final answer has the same color structure as in flat space but the dependence on Mandelstam variables is more complicated, with logarithms replaced by polygamma functions.

Holographic S-fold theories at one loop

“…This shows that the ambiguity is simply a constant or a Mack polynomial of spin zero. 27 As further confirmation, the Mellin amplitude found in [44] is a formal expression which does not converge until one chooses a regularization scheme which leaves the same contact term unfixed. Finally, the double discontinuity in (2.31) also appears in a newer dispersion relation [96] which directly reconstructs a four-point function (either in position or Mellin space) instead of the spectral density.…”

“…one can employ the "triangle method" of [10] which becomes trivial when there is only one R-symmetry cross ratio. As in [44],…”

“…where α is a cross ratio for the SU(2) R-symmetry and f IJ K are the structure constants of the flavour group. The one-loop correction to (1.3) was recently computed in [44] yielding an expression from which double-trace operator dimensions are easy to extract. Our results will regard these anomalous dimensions as fundamental and show how they differ between three types of S-folds.…”

“…To deal with this mixing problem, [61][62][63] proposed a general algorithm and used it to analyze N = 4 SYM. After further loop-level studies of N = 4 SYM [64][65][66][67][68], the AdS unitarity method was first applied to other fullfledged theories in [44,69,70]. 5 Before extending this list, it is important to mention [73] which represents the current state of the art for N = 4 SYM with gauge groups other than SU(N).…”

On the Differential Representation and Color-Kinematics Duality of AdS Boundary Correlators

“…The difficulty of such calculations in position space [6][7][8][9][10] is similar in spirit (although less severe because of the large symmetry of AdS space) with difficulties with tree-level calculations in general smooth curved spaces: even the simplest diagrams are given by nontrivial bulk integrals which lead to transcendental functions. This led to the development of several alternative methods: the AdS momentum space [11][12][13][14][15][16][17][18][19][20], position-Mellin space [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and momentum-Mellin space [36,37]. While simplifying various aspects of calculations, these representations do not completely eliminate the problem of nontrivial integrals which still appear at tree-level in the momentum space formulation of AdS Witten diagrams and in the inverse Mellin-transform to position or momentum space.…”