engleski

Induced actions for higher spin fields

The actions for free relativistic fields posses conserved currents of all spins. While lower-spin (s=<2) currents have important phenomenological and theoretical uses - spin-1 currents form the base for electromagnetic, weak and strong interactions as described by The Standard Model of elementary particle physics, spin-2 current forms the base for gravitational interactions as described by The General Relativity, and spin 1/2 and 3/2 are essential for supersymmetry and supergravity - higher-spin (s > 2) currents have no such important implications and uses. As higher-spin free fields can be easily constructed, it would be natural to expect that one can construct interactions with the "matter sector" by coupling to the higher-spin currents. However, it is known that there are serious constraints and no-go theorems, especially strong when higher-spin fields are massless and (background) spacetime is flat. As a consequence, construction of consistent interacting theories with higher-spin fields appeared to be complicated task. On the other hand, string theory has excitations of all spins even when defined on flat spacetime, and moreover in the tensionless limit higher-spin excitations become massless. We calculate, on the 1-loop level, 2-point correlators of conserved currents of spins 1 =< s =< 10 in free theories of massive scalar and Dirac fields in flat 3 =< D =< 6 spacetime dimensions. Parts of the correlators have universal form and can be written in closed form as functions of s and D. Infrared and ultraviolet limits are analysed in detail. If one couples the conserved current to higher-spin background field, the 2-point correlator is giving us linearised induced equations of motion and quadratic part of the induced action for higher- spin field. Using lower-spin cases as guidelines, we analyse infrared and ultraviolet limits, which should give us information on classical action and UV behaviour, respectively, of higher-spin theories, if such exist. We express our results in terms of generalised linearised Riemann tensor, and compare our results with the literature.

higher spins, quantum field theories, induced action

nije evidentirano