Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-03-20
Phys.Rev.D74:105006,2006
Physics
High Energy Physics
High Energy Physics - Theory
latex, 28 pages, 5 epsf figures
Scientific paper
10.1103/PhysRevD.74.105006
We use the recently developed tools for an exact bosonization of a finite number $N$ of non-relativistic fermions to discuss the classic Tomonaga problem. In the case of noninteracting fermions, the bosonized hamiltonian naturally splits into an O$(N)$ piece and an O$(1)$ piece. We show that in the large-N and low-energy limit, the O$(N)$ piece in the hamiltonian describes a massless relativistic boson, while the O$(1)$ piece gives rise to cubic self-interactions of the boson. At finite $N$ and high energies, the low-energy effective description breaks down and the exact bosonized hamiltonian must be used. We also comment on the connection between the Tomonaga problem and pure Yang-Mills theory on a cylinder. In the dual context of baby universes and multiple black holes in string theory, we point out that the O$(N)$ piece in our bosonized hamiltonian provides a simple understanding of the origin of two different kinds of nonperturbative O$(e^{-N})$ corrections to the black hole partition function.
Dhar Avinash
Mandal Gautam
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