Loop amplitudes in the Coulomb branch of $$ \mathcal{N} $$ = 4 super-Yang-Mills theory
Md. Abhishek (Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400085, India, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, 211019, India); Subramanya Hegde (Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400085, India, The Institute of Mathematical Sciences, IV Cross Road, CIT Campus, Taramani, Chennai, 600113, India); Dileep Jatkar (Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400085, India, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad, 211019, India); Arnab Saha (Centre for High Energy Physics, Indian Institute of Science, C.V. Raman Avenue, Bangalore, 560012, India, Indian Institute of Science Education and Research Bhopal, Bhopal Bypass Road, Bhauri, Bhopal, 462066, India); Amit Suthar (Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400085, India, The Institute of Mathematical Sciences, IV Cross Road, CIT Campus, Taramani, Chennai, 600113, India)
We study four point planar loop amplitudes at an arbitrary point in the Coulomb branch of $$ \mathcal{N} $$ = 4 super-Yang-Mills theory. We study two particle unitary cuts up to four loop order. We explicitly verify that bubble and triangle graphs do not contribute at one loop level and show that the results hold at higher loop level as well. We also write down an all loop recursion relation for two particle reducible graphs for four point amplitudes.