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Amplitudes for Multiple M5 Branes

Bartlomiej Czech, Yu-tin Huang, Moshe Rozali

Abstract

We study N=(m,0) super-Poincare invariant six-dimensional massless and five-dimensional massive on-shell amplitudes. We demonstrate that in six dimensions, all possible three-point amplitudes involving tensor multiplets are necessarily embedded in gravitational theories. For non-gravitational amplitudes we consider instead five-dimensional massive amplitudes with N=(2,0) supersymmetry, aiming at describing the world volume theory of multiple M5 branes compactified on M^{4,1}x S^1. We find non-gravitational amplitudes whose on-shell degrees of freedom are shown to match those of the massive particle states that arise from self-dual strings wrapping a circle. Along the way we find interesting hints of a fermionic symmetry in the (2,0) theory, which accompanies the self-dual tensor gauge symmetry. We also discuss novel theories with (3,0) and (4,0) supersymmetry.

Amplitudes for Multiple M5 Branes

Abstract

We study N=(m,0) super-Poincare invariant six-dimensional massless and five-dimensional massive on-shell amplitudes. We demonstrate that in six dimensions, all possible three-point amplitudes involving tensor multiplets are necessarily embedded in gravitational theories. For non-gravitational amplitudes we consider instead five-dimensional massive amplitudes with N=(2,0) supersymmetry, aiming at describing the world volume theory of multiple M5 branes compactified on M^{4,1}x S^1. We find non-gravitational amplitudes whose on-shell degrees of freedom are shown to match those of the massive particle states that arise from self-dual strings wrapping a circle. Along the way we find interesting hints of a fermionic symmetry in the (2,0) theory, which accompanies the self-dual tensor gauge symmetry. We also discuss novel theories with (3,0) and (4,0) supersymmetry.

Paper Structure

This paper contains 34 sections, 162 equations, 4 figures.

Table of Contents

  1. Introduction and Discussion
  2. Preliminaries
  3. On-shell $\mathcal{N}=(N,0)$ multiplets
  4. Superconformal generators and on-shell variables
  5. Three-point kinematics
  6. Dimensional reduction to $D=4$
  7. General six-dimensional $\mathcal{N}=(1,0)$ three-point amplitudes
  8. Supersymmetry in three-point kinematics
  9. $\mathcal{N}=(1,0)$ three-point amplitudes
  10. The $\mathcal{N}=(1,0)$ vector-scalar-scalar interaction
  11. The $\mathcal{N}=(1,0)$ vector-vector-tensor interaction
  12. The lack of a vector-tensor-tensor interaction
  13. $\mathcal{N}=(2,0)$ Amplitudes with higher spins
  14. $\mathcal{N}=(2,0)$ Self-dual tensor-spin-3/2 multiplet coupling
  15. General features of tensor coupling
  16. ...and 19 more sections

Figures (4)

  • Figure 1:
  • Figure 2:
  • Figure 3: Interactions in eq. (\ref{['BfieldBfield']}) and eq. (\ref{['Spin3/2']}) describe uncharged KK mode interaction as well as two-charged KK mode, one-uncharged interaction. They correspond to coincident and a few separated M5 branes, respectively.
  • Figure 4: