1,509 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
From Phase Space to Integrable Representations and Level-Rank Duality
We explicitly find representations for different large phases of
Chern-Simons matter theory on . These representations are
characterised by Young diagrams. We show that no-gap and lower-gap phase of
Chern-Simons-matter theory correspond to integrable representations of
affine Lie algebra, where as upper-cap phase corresponds to
integrable representations of affine Lie algebra. We use phase
space description of arXiv:0711.0133 to obtain these representations and argue
how putting a cap on eigenvalue distribution forces corresponding
representations to be integrable. We also prove that the Young diagrams
corresponding to lower-gap and upper-cap representations are related to each
other by transposition under level-rank duality. Finally we draw phase space
droplets for these phases and show how information about eigenvalue and Young
diagram descriptions can be captured in topologies of these droplets in a
unified way.Comment: 37 pages, 10 figures, v2 Introduction extended, References adde
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
Light-Cone Reduction vs. TsT transformations : A Fluid Dynamics Perspective
We compute constitutive relations for a charged dimensional
Schr\"odinger fluid up to first order in derivative expansion, using
holographic techniques. Starting with a locally boosted, asymptotically ,
dimensional charged black brane geometry, we uplift that to ten
dimensions and perform transformations to obtain an effective five
dimensional local black brane solution with asymptotically Schr\"odinger
isometries. By suitably implementing the holographic techniques, we compute the
constitutive relations for the effective fluid living on the boundary of this
space-time and extract first order transport coefficients from these relations.
Schr\"odinger fluid can also be obtained by reducing a charged relativistic
conformal fluid over light-cone. It turns out that both the approaches result
the same system at the end. Fluid obtained by light-cone reduction satisfies a
restricted class of thermodynamics. Here, we see that the charged fluid
obtained holographically also belongs to the same restricted class.Comment: 0+22 pages, 1 figur
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