D branes in 2d String Theory and Classical limits

TL;DR

This paper explores the classical limits of D0 branes in 2D string theory, revealing that quantum dispersions persist and complicate the classical description in bosonic terms, contrasting with the fermionic open string perspective.

Contribution

It demonstrates that quantum fluctuations of bosonic fields remain in the classical limit, highlighting differences between open and closed string descriptions of D-branes in 2D string theory.

Findings

Quantum dispersions of bosonic quantities survive in the classical limit.

Open string (fermionic) description has a smooth classical limit.

Closed string (bosonic) description exhibits nontrivial classical behavior.

Abstract

In the matrix model formulation of two dimensional noncritical string theory, a D0 brane is identified with a single eigenvalue excitation. In terms of open string quantities (i.e fermionic eigenvalues) the classical limit of a macroscopically large number of D0 branes has a smooth classical limit : they are described by a filled region of phase space whose size is O(1) and disconnected from the Fermi sea. We show that while this has a proper description in terms of a {\em single} bosonic field at the quantum level, the classical limit is rather nontrivial. The quantum dispersions of bosonic quantities {\em survive in the classical limit} and appear as additional fields in a semiclassical description. This reinforces the fact that while the open string field theory description of these D-branes (i.e. in terms of fermions) has a smooth classical limit, a closed string field theory description (in terms of a single boson) does not.