On dynamics of 5D superconformal theories

TL;DR

This paper investigates the classical and quantum dynamics of 5D superconformal theories, revealing nonperturbative features, ghost states, and the structure of physical supermultiplets, with implications for higher-derivative supersymmetric theories.

Contribution

It provides a detailed analysis of the classical trajectories, quantum spectrum, and ghost states in 5D superconformal theories, proposing a mechanism to eliminate ghosts in such models.

Findings

Classical trajectories fall on the scalar moduli space singularity.

Quantum spectrum contains ghost states with negative energies.

Physical states form positive-energy supermultiplets.

Abstract

5D superconformal theories involve vacuum valleys characterized in the simplest case by the vacuum expectation value of a real scalar field. If it is nonzero, conformal invariance is spontaneously broken and the theory is not renormalizable. In the conformally invariant sector with zero scalar v.e.v., the theory is intrinsically nonperturbative. We study classical and quantum dynamics of this theory in the limit when field dependence of the spatial coordinates is disregarded. The classical trajectories ``fall'' on the singularity at the origin of scalar moduli space. The quantum spectrum involves ghost states with unbounded from below negative energies, but such states fail to form complete 16-plets as is dictated by the presence of four complex supercharges and should be rejected by that reason. Physical excited states come in supermultiplets and have all positive energies. We conjecture that the spectrum of the complete field theory hamiltonian is nontrivial and has a similar nontrivial ghost-free structure and also speculate that the ghosts in higher-derivative supersymmetric field theories are exterminated by a similar mechanism.