Hidden symmetries of the Nambu-Goto action

TL;DR

This paper reveals hidden discrete symmetries in the Nambu-Goto string action by expressing it through a hyperdeterminant, uncovering a triality symmetry in a (2,2) signature spacetime.

Contribution

The paper introduces a novel hypermatrix formulation of the Nambu-Goto action, exposing hidden symmetries and triality not previously recognized.

Findings

Nambu-Goto Lagrangian expressed as a hyperdeterminant

Discovery of triality symmetry in the string action

Invariance under interchange of hypermatrix indices

Abstract

We organize the eight variables of the four-dimensional bosonic string ({\dot X}^{\mu}, X'^{\mu}) into a 2 x 2 x 2 hypermatrix a_{AA'A''} and show that in signature (2,2) the Nambu-Goto Lagrangian is given by \sqrt{Det a} where Det is Cayley's hyperdeterminant. This is invariant not only under [SL(2,R)]^{3} but also under interchange of the indices A, A' and A''. This triality reveals hitherto hidden discrete symmetries of the Nambu-Goto action.