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#### Classical and Quantum Branes in c=1 String Theory and Quantum Hall Effect

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##### Fulltext (public)

60196.pdf

(Preprint), 447KB

##### Supplementary Material (public)

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##### Citation

Boyarsky, A., Kulik, B., & Ruchayskiy, O. (2003). *Classical
and Quantum Branes in c=1 String Theory and Quantum Hall Effect*.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5349-5

##### Abstract

Interpretation of D1 and D0-branes in 1+1 string theory as classical and quantum eigen-values in dual c=1 Matrix Quantum Mechanics (MQM) was recently suggested. MQM is known to be equivalent to a system of N free fermions (eigen-values). By considering quantum mechanics of fermions in the presence of classical eigen-value we are able to calculate explicitly the perturbation of the shape of Fermi-sea due to the interaction with the brane. We see that the shape of the Fermi-sea depending on the position of the classical eigen-value can exhibit critical behavior, such as development of cusp. On quantum level we build explicitly the operator describing quantum eigen-value. This is a vertex operator in bosonic CFT. Its expectation value between vacuum and Dirichlet boundary state is equal to the correct wave-function of the fermion. This supports the conjecture that quantum eigen-value corresponds to D0-brane. We also show that c=1 MQM can be obtained as analytical continuation of the system of 2d electrons in magnetic field which is studied in Quantum Hall Effect.