Solitons in the Calogero model for distinguishable particles

We study the collective field formulation of a restricted form of the multispecies Calogero model, in which the three-body interactions are set to zero. We show that the resulting collective field theory is invariant under certain duality transformations, which interchange, among other things, particles and antiparticles, and thus generalize the well-known strong-weak coupling duality symmetry of the ordinary Calogero model. We identify all these dualities, which form an Abelian group, and study their consequences. We also study the ground state and small fluctuations around it in detail, starting with the two-species model, and then generalizing to an arbitrary number of species.

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“…It is worth mentioning here that (28) and (29) possess also nonuniform static soliton solutions, which were studied extensively in [47,54].…”

Section: Ground State and Small Fluctuationsmentioning

confidence: 99%

“…Not surprisingly, this construction can be generalized to the F -family case, as we now show. 15 See the discussions following (47) and (51).…”

Section: Special F -Family Calogero Models Which Resemble Single-famimentioning

confidence: 99%

Collective field formulation of the multi-species Calogero model and its duality symmetries

2007

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“…As we are aware that solving nonlinear coupled equations is sensitive to the regularization used, the application of the symbolic manipulation is not suitable and does not give a unique answer because the product of distributions is not uniquely defined. The authors also claim that their paper [35] gives convicing arguments that a singular form of the solution does not exist, but they simply have not checked the limit c → 0 in that paper.…”

Section: Semiclassical Solutions In the Singular Limitmentioning

confidence: 99%

Solitons and giants in matrix models

Andrić¹,

Jonke²,

Jurman³

2006

J. High Energy Phys.

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We present a method for solving BPS equations obtained in the collective-field approach to matrix models. The method enables us to find BPS solutions and quantum excitations around these solutions in the one-matrix model, and in general for the Calogero model. These semiclassical solutions correspond to giant gravitons described by matrix models obtained in the framework of AdS/CFT correspondence. The two-field model, associated with two types of giant gravitons, is investigated. In this duality-based matrix model we find the finite form of the n-soliton solution. The singular limit of this solution is examined and a realization of open-closed string duality is proposed.

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“…The multispecies Calogero model has been extensively studied in the quantum mechanical [1][2][3][4] and in the collective-field theory context [5][6][7][8][9]. It represents the generalization of the ordinary Calogero model with identical particles to the Calogero model with nonidentical particles.…”

Section: Introductionmentioning

confidence: 99%