Gravity amplitudes from n-space
Abstract
We identify a hidden GL( n, {C} ) symmetry of the tree level n-point MHV gravity amplitude. Representations of this symmetry reside in an auxiliary n-space whose indices are external particle labels. Spinor helicity variables transform non-linearly under GL( n, {C} ), but linearly under its notable subgroups, the little group and the permutation group S n . Using GL( n, {C} ) covariant variables, we present a new and simple formula for the MHV amplitude which can be derived solely from geometric constraints. This expression carries a huge intrinsic redundancy which can be parameterized by a pair of reference 3-planes in n-space. Fixing this redundancy in a particular way, we reproduce the S n-3 symmetric form of the MHV amplitude of [1], which is in turn equivalent to the S n-2 symmetric form of [2] as a consequence of the matrix tree theorem. The redundancy of the amplitude can also be fixed in a way that fully preserves S n , yielding new and manifestly S n symmetric forms of the MHV amplitude. Remarkably, these expressions need not be manifestly homogenous in spinorial weight or mass dimension. We comment on possible extensions to N k-2MHV amplitudes and speculate on the deeper origins of GL( n, {C} ).
- Publication:
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Journal of High Energy Physics
- Pub Date:
- December 2012
- DOI:
- 10.1007/JHEP12(2012)057
- arXiv:
- arXiv:1207.4458
- Bibcode:
- 2012JHEP...12..057C
- Keywords:
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- Scattering Amplitudes;
- Classical Theories of Gravity;
- High Energy Physics - Theory
- E-Print:
- 11 pages