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This paper advances the theoretical framework for quantum Hall interfaces by introducing an open-worldsheet junction model that rigorously defines endpoint conditions and topological boundary data. It provides a systematic basis for understanding dynamical QH networks, specifically addressing why certain excitations like chiral Majoranas cannot terminate on finite-dimensional endpoints without additional channels. The work establishes a precise operational definition of quantum Hall branes within the context of strongly correlated electron systems.
An Effective String Theory Toolbox for Quantum Hall Interfaces III: Open Worldsheets, Endpoint Conditions, and Branes
arXiv:2608.06100v1 Announce Type: cross Abstract: A freely moving quantum Hall (QH) interface may end on a physical edge or topological boundary, but fixed-edge theory cannot determine what endpoint data make such a termination consistent. Here we formulate an open-worldsheet junction framework in which the embedding, material charge, anomaly flow, and topological boundary condition are organized together. The endpoint is specified by a geometric support and variational boundary data, together with condensable topological sectors and any outgoing channels required to absorb or continue the worldsheet flux. This construction extends the charge--shape relation to an interval and shows why a lone chiral Majorana cannot terminate on a finite-dimensional endpoint degree of freedom. It gives an operational definition of a QH brane and a systematic basis for endpoint and network theories of dynamical QH interfaces.
Abstract:A freely moving quantum Hall (QH) interface may end on a physical edge or topological boundary, but fixed-edge theory cannot determine what endpoint data make such a termination consistent. Here we formulate an open-worldsheet junction framework in which the embedding, material charge, anomaly flow, and topological boundary condition are organized together. The endpoint is specified by a geometric support and variational boundary data, together with condensable topological sectors and any outgoing channels required to absorb or continue the worldsheet flux. This construction extends the charge--shape relation to an interval and shows why a lone chiral Majorana cannot terminate on a finite-dimensional endpoint degree of freedom. It gives an operational definition of a QH brane and a systematic basis for endpoint and network theories of dynamical QH interfaces.
Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
arXiv:2608.06100 [cond-mat.mes-hall]
(or arXiv:2608.06100v1 [cond-mat.mes-hall] for this version)
https://doi.org/10.48550/arXiv.2608.06100 arXiv-issued DOI via DataCite (pending registration)
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