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Scattering Amplitudes and BCFW in $\mathcal{N}=2^*$ Theory

by Md. Abhishek, Subramanya Hegde, Dileep P. Jatkar, and Arnab Priya Saha

This Submission thread is now published as

Submission summary

As Contributors: Md Abhishek · Subramanya Hegde · Arnab Saha
Preprint link: scipost_202203_00042v2
Date accepted: 2022-06-08
Date submitted: 2022-05-23 13:19
Submitted by: Abhishek, Md
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


We use massive spinor helicity formalism to study scattering amplitudes in $\mathcal{N}=2^*$ super-Yang-Mills theory in four dimensions. We compute the amplitudes at an arbitrary point in the Coulomb branch of this theory. We compute amplitudes using projection from $\mathcal{N}=4$ theory and write three point amplitudes in a convenient form using special kinematics. We then compute four point amplitudes by carrying out massive BCFW shifts of the amplitudes. We find some of the shifted amplitudes have a pole at $z=\infty$. Taking the residue at $z=\infty$ into account ensures little group covariance of the final result.

Published as SciPost Phys. 13, 008 (2022)

Author comments upon resubmission

We thank the referees for their comments which helped improve the manuscript. We have incorporated all the suggestions of referees and the changes in the manuscript are in red color for the ease of perusal for the referee. Nevertheless we will briefly summarize changes in the manuscript below.

  1. We have made four changes in the introduction.

  2. We have added text in subsections 3.2, 3.3, and 3.4.

  3. In section 4 we have emphasized that the amplitudes under consideration are color ordered.

  4. Finally we have added a speculation in the conclusion section.

List of changes

Changes in the introduction are as follows.

1A. We have expanded on our motivation in taking up the N=2* problem, which has intermediate level of complexity compared to N=4 and N=2. We have also added a couple of references in this amendment.

1B. We reiterate this point again in the context of the BCFW relations.

1C. We have rephrased the sentence about the long multiplet.

1D. We have elaborated a bit on the u-spinor and pointed the reader to section 3 for more details.

2A. In subsection 3.2, we explicitly mention that we are looking at the color ordered amplitudes.

2B. In subsection 3.3, we elaborate on the massive fields by using the example of excursion in the Coulomb branch.

2C. In subsection 3.4, we add a preamble to the section by mentioning about the band structure in the N=4 SYM theory.

3. We added a parenthetical remark on color ordering in the first line of section 4.

4. In the Conclusion section, we speculate about the BCFW shift for higher point functions for massive fields.

Reports on this Submission

Anonymous Report 2 on 2022-5-24 (Invited Report)


I am happy with the changes made by the authors in the introduction.

  • validity: -
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Anonymous Report 1 on 2022-5-24 (Invited Report)


We thank the authors for incorporating changes in the draft. We recommend publication of the draft in its current form.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
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