Lorentz invariance of effective strings

TL;DR

This paper demonstrates that Lorentz invariance is preserved in effective string theories derived from a Poincaré invariant scalar field theory, through detailed analysis of the induced Lorentz transformations on low-energy excitations.

Contribution

It derives the Lorentz representation on collective coordinates of effective strings and shows invariance due to cancellations between irrelevant terms and the free scalar action.

Findings

Lorentz transformations are expressed as an infinite series in derivatives.

Lorentz invariance is maintained due to cancellations in the effective action.

Universal dimension -1 term appears in transverse Lorentz transformations.

Abstract

Starting from a Poincar\'e invariant field theory of a real scalar field with interactions governed by a double-well potential in 2+1 dimensions, the Lorentz representation induced on the collective coordinates describing low-energy excitations about an effective string background is derived. In this representation, Lorentz transformations are given in terms of an infinite series, in powers of derivatives along the worldsheet. Transformations that act on the direction transverse to the string worldsheet involve a universal dimension $-1$ term. As a consequence, Lorentz invariance holds in this theory of long effective strings due to cancellations in the action between irrelevant terms and the dimension two term that describes free massless scalar fields in two dimensions. (in plain tex, no macropackages necessary)