Scattering amplitudes of massive spin-2 Kaluza-Klein states grow only as O ( s )

We study the perturbative unitarity of scattering amplitudes in general dimensional reductions of Yang-Mills theories and general relativity on closed internal manifolds. For the tree amplitudes of the dimensionally reduced theory to have the expected high-energy behavior of the higherdimensional theory, the masses and cubic couplings of the Kaluza-Klein states must satisfy certain sum rules that ensure there are nontrivial cancellations between Feynman diagrams. These sum rules give constraints on the spectra and triple integrals of eigenfunctions of Laplacian operators on the internal manifold and can be proven directly using Hodge and eigenfunction decompositions. One consequence of these constraints is that there is an upper bound on the ratio of consecutive eigenvalues of the scalar Laplacian on closed Ricci-flat manifolds with special holonomy. This gives a sharp bound on the allowed gaps between Kaluza-Klein excitations of the graviton that also applies to Calabi-Yau compactifications of string theory.

Section: Strong Coupling Scalementioning

confidence: 99%

“…The unitarity of four-dimensional amplitudes coming from a five-dimensional compactification has been studied in Refs. [9,13,14].…”

Section: General Relativitymentioning

confidence: 99%

Section: Strong Coupling Scalementioning

confidence: 99%

Section: Interactionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Structure of Chern-Simons scattering amplitudes from topological equivalence theorem and double-copy

Hang

Shen

2022

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 ($$ {A}_{\mathrm{P}}^a $$ A P a ) to that of the transverse polarization states ($$ {A}_{\mathrm{T}}^a $$ 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 E4→ E4−N at tree level. Then, we compute the 4-gauge boson amplitudes of $$ {A}_{\mathrm{P}}^a $$ A P a -states and $$ {A}_{\mathrm{T}}^a $$ 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: E12→ E1, and establish its correspondence to the leading energy cancellation E4→ E0in the 4-gauge boson amplitude of TMYM.