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Structure of Chern-Simons scattering amplitudes from topological equivalence theorem and double-copy
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Structure of Chern-Simons scattering amplitudes from topological equivalence theorem and double-copy
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Journal Article
Structure of Chern-Simons scattering amplitudes from topological equivalence theorem and double-copy
2022
Overview
A
bstract
We study the mechanism of topological mass-generation for 3d Chern-Simons (CS) gauge theories, where the CS term can retain the gauge symmetry and make gauge boson topologically massive. Without CS term the 3d massless gauge boson has a single physical transverse polarization state, while adding the CS term converts it into a massive physical polarization state and conserves the total physical degrees of freedom. We formulate the mechanism of topological mass-generation at
S
-matrix level. For this, we propose and prove a Topological Equivalence Theorem (TET) which connects the
N
-point scattering amplitude of the gauge boson’s physical polarization states (
A
P
a
) to that of the transverse polarization states (
A
T
a
) under high energy expansion. We present a general 3d power counting method on the leading energy dependence of the scattering amplitudes in both topologically massive Yang-Mills (TMYM) and topologically massive gravity (TMG) theories. With these, we uncover
a general energy cancellation mechanism for N -gauge boson scattering amplitudes
which predicts the cancellation
E
4
→ E
4
−N
at tree level. Then, we compute the 4-gauge boson amplitudes of
A
P
a
-states and
A
T
a
-states, with which we explicitly demonstrate the TET and establish such energy cancellations for
N
= 4. We further extend the double-copy approach to reconstruct the massive 4-graviton amplitude of TMG from the massive 4-gauge boson amplitude of TMYM. With these, we uncover
striking large energy cancellations in the 4-graviton amplitude: E
12
→ E
1
, and establish
its correspondence to the leading energy cancellation E
4
→ E
0
in the 4-gauge boson amplitude of TMYM
.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
