69 research outputs found
Boundary correlation numbers in one matrix model
We introduce one matrix model coupled to multi-flavor vectors. The two-flavor
vector model is demonstrated to reproduce the two-point correlation numbers of
boundary primary fields of two dimensional (2, 2p+1) minimal Liouville gravity
on disk, generalizing the loop operator (resolvent) description. The model can
properly describe non-trivial boundary conditions for the matter Cardy state as
well as for the Liouville field. From this we propose that the n-flavor vector
model will be suited for producing the boundary correlation numbers with n
different boundary conditions on disk.Comment: 16 pages, 3 figures, add elaboration on matter Cardy state and
reference
Partial Deconfinement
We argue that the confined and deconfined phases in gauge theories are
connected by a partially deconfined phase (i.e. SU(M) in SU(N), where M<N, is
deconfined), which can be stable or unstable depending on the details of the
theory. When this phase is unstable, it is the gauge theory counterpart of the
small black hole phase in the dual string theory. Partial deconfinement is
closely related to the Gross-Witten-Wadia transition, and is likely to be
relevant to the QCD phase transition.
The mechanism of partial deconfinement is related to a generic property of a
class of systems. As an instructive example, we demonstrate the similarity
between the Yang-Mills theory/string theory and a mathematical model of the
collective behavior of ants [Beekman et al., Proceedings of the National
Academy of Sciences, 2001]. By identifying the D-brane, open string and black
hole with the ant, pheromone and ant trail, the dynamics of two systems closely
resemble with each other, and qualitatively the same phase structures are
obtained.Comment: 27 pages, many figures. v2: reference updated, minor improvements.
v3: comments added. v4: version published in JHEP. A few comments and
references added. v5: Normalization error in eq.(14) has been corrected,
descriptions in Appendix B and Sec.3 have been corrected accordingly. A few
footnotes and references have been adde
Emergent bubbling geometries in gauge theories with SU(2|4) symmetry
We study the gauge/gravity duality between bubbling geometries in type IIA
supergravity and gauge theories with SU(2|4) symmetry, which consist of N=4
super Yang-Mills on , N=8 super Yang-Mills on
and the plane wave matrix model. We show that the geometries are realized as
field configurations in the strong coupling region of the gauge theories. On
the gravity side, the bubbling geometries can be mapped to electrostatic
systems with conducting disks. We derive integral equations which determine the
charge densities on the disks. On the gauge theory side, we obtain a matrix
integral by applying the localization to a 1/4-BPS sector of the gauge
theories. The eigenvalue densities of the matrix integral turn out to satisfy
the same integral equations as the charge densities on the gravity side. Thus
we find that these two objects are equivalent.Comment: 29 pages, 3 figures; v2: typos corrected and a reference adde
Emergent bubbling geometries in the plane wave matrix model
The gravity dual geometry of the plane wave matrix model is given by the
bubbling geometry in the type IIA supergravity, which is described by an
axially symmetric electrostatic system. We study a quarter BPS sector of the
plane wave matrix model in terms of the localization method and show that this
sector can be mapped to a one-dimensional interacting Fermi gas system. We find
that the mean-field density of the Fermi gas can be identified with the charge
density in the electrostatic system in the gravity side. We also find that the
scaling limits in which the dual geometry reduces to the D2-brane or NS5-brane
geometry are given as the free limit or the strongly coupled limit of the Fermi
gas system, respectively. We reproduce the radii of 's in these geometries
by solving the Fermi gas model in the corresponding limits.Comment: 34 pages, 3 figures; typos correcte
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