Abstract
Starting with the general stress-tensor commutation relations consistent with the Poincar\'e algebra in local quantum field theory, we impose the tracelessness condition and focus on the dominating contributions in the lightcone limit. It is shown that, under a certain assumption on the Schwinger term, a Virasoro-algebra-like structure emerges near the lightcone in $d>2$ conformal field theories.
Highlights
As the universal central extension of the Witt algebra, the existence of the Virasoro algebra [1] plays a crucial role in mathematics and theoretical physics, of deep importance in conformal field theory (CFT)
In higher dimensions, where the conformal group is finite dimensional, Virasoro-algebra related techniques employed in understanding d 1⁄4 2 CFT become generally invalid
As the form of two commuting copies, the Virasoro algebra can be expressed as the stress-tensor commutation relation
Summary
As the universal central extension of the Witt algebra, the existence of the Virasoro algebra [1] plays a crucial role in mathematics and theoretical physics, of deep importance in conformal field theory (CFT) It is, a special luxury one has in two-dimensional spacetime. We make an initial attempt, starting from the most general stress-tensor commutation relations in Lorentz invariant, local quantum field theory (QFT) [2,3,4], to search for a possible Virasoro-like structure in higher-dimensional CFTs. In particular, while the tracelessness constraint must be imposed, we would like to see under what additional conditions an effective Virasoro-like algebra may emerge. Some subtleties of the Schwinger term will be discussed
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