12 research outputs found
2D fuzzy Anti-de Sitter space from matrix models
We study the fuzzy hyperboloids AdS^2 and dS^2 as brane solutions in matrix
models. The unitary representations of SO(2,1) required for quantum field
theory are identified, and explicit formulae for their realization in terms of
fuzzy wavefunctions are given. In a second part, we study the (A)dS^2 brane
geometry and its dynamics, as governed by a suitable matrix model. In
particular, we show that trace of the energy-momentum tensor of matter induces
transversal perturbations of the brane and of the Ricci scalar. This leads to a
linearized form of Henneaux-Teitelboim-type gravity, illustrating the mechanism
of emergent gravity in matrix models.Comment: 25 page
Dynamical and Quenched Random Matrices and Homolumo Gap
We consider a rather general type of matrix model, where the matrix M
represents a Hamiltonian of the interaction of a bosonic system with a single
fermion. The fluctuations of the matrix are partly given by some fundamental
randomness and partly dynamically, even quantum mechanically. We then study the
homolumo-gap effect, which means that we study how the level density for the
single-fermion Hamiltonian matrix M gets attenuated near the Fermi surface. In
the case of the quenched randomness (the fundamental one) dominating the
quantum mechanical one we show that in the first approximation the homolumo gap
is characterized by the absence of single-fermion levels between two steep gap
boundaries. The filled and empty level densities are in this first
approximation just pushed, each to its side. In the next approximation these
steep drops in the spectral density are smeared out to have an error-function
shape. The studied model could be considered as a first step towards the more
general case of considering a whole field of matrices - defined say on some
phase space - rather than a single matrix.Comment: 15 pages, 2 figures; v2. substantial improvements, published in IJMP
Solitons and excitations in the duality-based matrix model
We analyse a specific, duality-based generalization of the hermitean matrix
model. The existence of two collective fields enables us to describe specific
excitations of the hermitean matrix model. By using these two fields, we
construct topologically non-trivial solutions (BPS solitons) of the model. We
find the low-energy spectrum of quantum fluctuations around the uniform
solution. Furthermore, we construct the wave functional of the ground state and
obtain the corresponding Green function.Comment: 13 pages,v2: new solutions constructed, title changed accordingl
2D Calogero Model in the Collective-Field Approach
We consider the large-N Calogero-Marchioro model in two dimensions in the
Hamiltonian collective field approach based on the 1/N expansion. The
Bogomol'nyi limit appears in the presence of the harmonic confinement. We
investigate density fluctuations around the semiclassical uniform solution. The
excitation spectrum splits into two branches depending on the value of the
coupling constant. The ground state exhibits long-range order
Solitons and giants in matrix models
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 -soliton solution. The singular limit of this
solution is examined and a realization of open-closed string duality is
proposed.Comment: 17 pages, JHEP cls; v2: final version to appear in JHEP, 2 references
added, physical motivation and interpretation clarifie