Research: Fractonic Folds and Tears in Paper

What paper airplanes have to do with modern field theory

Although not consciously appreciated, making paper planes as kids exposes us to a simple fact -- one can fold a flat sheet of paper smoothly only along a straight line. Even the most careful attempt to fold along a curve feels harder and ends up producing additional creases and/or tears! This work reveals an intriguing connection between this seemingly mundane phenomenon of paper folding/tearing and one of the current and actively researched notions in theoretical physics.

This is the area of fractonic gauge field theories which could have potential applications in broad areas ranging from quantum computation to entangled phases of matter.  These theories are original generalizations of the celebrated theory of Maxwell electromagnetism describing the charges of the electrons and the propagation of light familiar from everyday life. A collaboration of scientists from the Max Planck Institute for the Physics of Complex Systems in Dresden (Germany) and the Indian Institute of Science in Bangalore (India) have demonstrated that the point where the fold ends in a partially folded paper, the fold-tip, is analogous to an electric charge, but one which has a vector character: the fold-tip is not just a positive or negative charge, but a charge with a direction.

This directional character of the charge comes with restrictions -- called fractonic constraints -- on how it can move: the fold-tip can move only along the direction of its charge! This is what happens in the process of folding the paper along a straight line, as the fold-tip motion respects the fractonic constraint. On the other hand, trying to violate the constraint ends up tearing the paper. Luckily for our little paper airplane engineers, the unwanted operation of tearing is the harder one, while the required folding is easy. 

Nandagopal Manoj, an undergraduate student at IISc Bangalore and lead author of this work,  wonders "Who would have thought exotic fractons hide in plain sight on a piece of paper?’’

N. Manoj, R. Moessner, V. B. Shenoy,
Fractonic View of Folding and Tearing Paper: Elasticity of Plates Is Dual to a Gauge Theory with Vector Charges,
Phys. Rev. Lett. 127, 067601 (2021)