Long, partial-short, and special conformal fields

TL;DR

This paper classifies conformal bosonic fields in flat space-time into categories like long, partial-short, short, and special, and develops an ordinary-derivative Lagrangian formulation with gauge fixing and BRST symmetry, enabling partition function computation.

Contribution

It introduces a comprehensive classification of conformal fields and constructs an explicit second-derivative Lagrangian formulation with gauge and BRST invariance.

Findings

Derived gauge-fixed BRST invariant Lagrangian

Computed partition functions for all conformal fields

Determined the number of propagating degrees of freedom

Abstract

In the framework of metric-like approach, totally symmetric arbitrary spin bosonic conformal fields propagating in flat space-time are studied. Depending on the values of conformal dimension, spin, and dimension of space-time, we classify all conformal field as long, partial-short, short, and special conformal fields. An ordinary-derivative (second-derivative) Lagrangian formulation for such conformal fields is obtained. The ordinary-derivative Lagrangian formulation is realized by using double-traceless gauge fields, Stueckelberg fields, and auxiliary fields. Gauge-fixed Lagrangian invariant under global BRST transformations is obtained. The gauge-fixed BRST Lagrangian is used for the computation of partition functions for all conformal fields. Using the result for the partition functions, numbers of propagating D.o.F for the conformal fields are also found.