Solutions of coupled BPS equations for two-family Calogero and matrix models

Bardek, V.; Meljanac, Stjepan; Meljanac, Daniel

doi:10.1103/physrevd.80.085014

Cited by 1 publication

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References 18 publications

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“…All this was the consequence of the invariance of the collective-field Hamiltonian of the twofamily Calogero model under an Abelian group of strong-weak-coupling dualities [8], analogous to (1.7). In [24] and [25] it was shown that a large class of solitons in the two-family Calogero model can be obtained by reducing it to the effectively one-family Calogero model.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations around periodic BPS-density waves in the Calogero model

Bardek

Feinberg

Meljanac

2010

J. High Energ. Phys.

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Abstract:The collective field formulation of the Calogero model supports periodic density waves. An important set of such density waves is a two-parameter family of BPS solutions of the equations of motion of the collective field theory. One of these parameters is essentially the average particle density, which determines the period, while the other parameter determines the amplitude. These BPS solutions are sometimes referred to as "small amplitude waves" since they undulate around their mean density, but never vanish. We present complete analysis of quadratic fluctuations around these BPS solutions. The corresponding fluctuation hamiltonian (i.e., the stability operator) is diagonalized in terms of bosonic creation and annihilation operators which correspond to the complete orthogonal set of Bloch-Floquet eigenstates of a related periodic Schrödinger hamiltonian, which we derive explicitly. Remarkably, the fluctuation spectrum is independent of the parameter which determines the density wave's amplitude. As a consequence, the sum over zero-point energies of the field-theoretic fluctuation hamiltonian, and its ensuing normal-ordering and regularization, are the same as in the case of fluctuations around constant density background, namely, the ground state. Thus, quadratic fluctuations do not shift the energy density tied with the BPS-density waves studied here, compared to its ground state value. Finally, we also make some brief remarks concerning fluctuations around non-BPS density waves.

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Section: Introductionmentioning

confidence: 99%