1,310 research outputs found
Emergent Phase Space Description of Unitary Matrix Model
We show that large phases of a dimensional generic unitary matrix
model (UMM) can be described in terms of topologies of two dimensional droplets
on a plane spanned by eigenvalue and number of boxes in Young diagram.
Information about different phases of UMM is encoded in the geometry of
droplets. These droplets are similar to phase space distributions of a unitary
matrix quantum mechanics (UMQM) ( dimensional) on constant time
slices. We find that for a given UMM, it is possible to construct an effective
UMQM such that its phase space distributions match with droplets of UMM on
different time slices at large . Therefore, large phase transitions in
UMM can be understood in terms of dynamics of an effective UMQM. From the
geometry of droplets it is also possible to construct Young diagrams
corresponding to representations and hence different large states of
the theory in momentum space. We explicitly consider two examples : single
plaquette model with terms and Chern-Simons theory on . We
describe phases of CS theory in terms of eigenvalue distributions of unitary
matrices and find dominant Young distributions for them.Comment: 52 pages, 15 figures, v2 Introduction and discussions extended,
References adde
(Un)attractor black holes in higher derivative AdS gravity
We investigate five-dimensional static (non-)extremal black hole solutions in
higher derivative Anti-de Sitter gravity theories with neutral scalars
non-minimally coupled to gauge fields. We explicitly identify the boundary
counterterms to regularize the gravitational action and the stress tensor. We
illustrate these results by applying the method of holographic renormalization
to computing thermodynamical properties in several concrete examples. We also
construct numerical extremal black hole solutions and discuss the attractor
mechanism by using the entropy function formalism.Comment: 30 pages, 4 figures; V2: comments on holographic renormalization
method and ack. added, misprints corrected, expanded reference
On Euclidean and Noetherian Entropies in AdS Space
We examine the Euclidean action approach, as well as that of Wald, to the
entropy of black holes in asymptotically spaces. From the point of view
of holography these two approaches are somewhat complementary in spirit and it
is not obvious why they should give the same answer in the presence of
arbitrary higher derivative gravity corrections. For the case of the
Schwarzschild black hole, we explicitly study the leading correction to the
Bekenstein-Hawking entropy in the presence of a variety of higher derivative
corrections studied in the literature, including the Type IIB term. We
find a non-trivial agreement between the two approaches in every case. Finally,
we give a general way of understanding the equivalence of these two approaches.Comment: 36 pages, 1 figure, LaTex, v2: references added as well as
clarificatory remarks in the introductio
Near-Horizon Analysis of
It is now well understood that the coefficient of shear viscosity of boundary
fluid can be obtained from the horizon values of the effective coupling of
transverse graviton in bulk spacetime. In this paper we observe that to find
the shear viscosity coefficient it is sufficient to know only the near horizon
geometry of the black hole spacetime. One does not need to know the full
analytic solution. We consider several examples including non-trivial matter
(dilaton, gauge fields) coupled to gravity in presence of higher derivative
terms and calculate shear viscosity for both extremal and non-extremal black
holes only studying the near horizon geometry. In particular, we consider
higher derivative corrections to extremal R-charged black holes and compute
in presence of three independent charges. We also consider
asymptotically Lifshitz spacetime whose dual black hole geometry can not be
found analytically. We study the near horizon behaviour of these black holes
and find for its dual plasma at Lifshitz fixed point.Comment: 17 page
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