Goldstone Tensor Modes

TL;DR

This paper presents a general method to derive and analyze Goldstone modes of various spins in supergravity brane solutions, clarifying their origin, properties, and equations, with applications to D3, M2, and M5 branes.

Contribution

It introduces a systematic approach to identify and describe collective Goldstone modes of any spin in supergravity brane backgrounds, including explicit expressions and normalisability conditions.

Findings

Derived explicit expressions for zero-modes in target space fields.

Verified normalisability of modes in transverse directions.

Clarified the origin and nature of scalar, spinor, and tensor Goldstone modes.

Abstract

In the context of brane solutions of supergravity, we discuss a general method to introduce collective modes of any spin by exploiting a particular way of breaking symmetries. The method is applied to the D3, M2 and M5 branes and we derive explicit expressions for how the zero-modes enter the target space fields, verify normalisability in the transverse directions and derive the corresponding field equations on the brane. In particular, the method provides a clear understanding of scalar, spinor, and rank r tensorial Goldstone modes, chiral as well as non-chiral, and how they arise from the gravity, Rarita-Schwinger, and rank r+1 Kalb-Ramond tensor gauge fields, respectively. Some additional observations concerning the chiral tensor modes on the M5 brane are discussed.