493 research outputs found
Responding to the Great Work: The Role of Earth Jurisprudence and Wild Law in the 21st Century
In this lead article, the authors build on the idea that we do not need more environmental law in response to the deteriorating health of the natural world. Rather, they argue that what is needed are different approaches to managing human relationships with the earth. They argue that the burgeoning Earth jurisprudence movement offers a deep philosophical anchor and a range of practical and multi-disciplinary approaches necessary to create law reform and societal change that will better support the natural world and human societies than our current system. The authors will outline the origins and key elements of the Earth jurisprudence movement. In addition, they explore some of the ways groups inspired by Earth laws have implemented their work. Lastly, they will provide an overview of the work being carried out by the Global Alliance for the Rights of Nature, the Earth Advocates, the Center for Earth Jurisprudence, and the Australian Earth Laws Alliance
Non-Einstein geometries in Chiral Gravity
We analyze the asymptotic solutions of Chiral Gravity (Topologically Massive
Gravity at \mu l = 1 with Brown-Henneaux boundary conditions) focusing on
non-Einstein metrics. A class of such solutions admits curvature singularities
in the interior which are reflected as singularities or infinite bulk energy of
the corresponding linear solutions. A non-linear solution is found exactly. The
back-reaction induces a repulsion of geodesics and a shielding of the
singularity by an event horizon but also introduces closed timelike curves.Comment: 11 pages, 3 figures. v2: references and comments on linear stability
(Sect.2) adde
Generalised massive gravity one-loop partition function and AdS/(L)CFT
The graviton 1-loop partition function is calculated for Euclidean
generalised massive gravity (GMG) using AdS heat kernel techniques. We find
that the results fit perfectly into the AdS/(L)CFT picture. Conformal
Chern-Simons gravity, a singular limit of GMG, leads to an additional
contribution in the 1-loop determinant from the conformal ghost. We show that
this contribution has a nice interpretation on the conformal field theory side
in terms of a semi-classical null vector at level two descending from a primary
with conformal weights (3/2,-1/2).Comment: 25 p., 2 jpg figs, v2: added 6 lines of clarifying text after Eq.
(2.38
The Heat Kernel on AdS_3 and its Applications
We derive the heat kernel for arbitrary tensor fields on S^3 and (Euclidean)
AdS_3 using a group theoretic approach. We use these results to also obtain the
heat kernel on certain quotients of these spaces. In particular, we give a
simple, explicit expression for the one loop determinant for a field of
arbitrary spin s in thermal AdS_3. We apply this to the calculation of the one
loop partition function of N=1 supergravity on AdS_3. We find that the answer
factorizes into left- and right-moving super Virasoro characters built on the
SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.Comment: 46 pages, LaTeX, v2: Reference adde
Quantum W-symmetry in AdS_3
It has recently been argued that, classically, massless higher spin theories
in AdS_3 have an enlarged W_N-symmetry as the algebra of asymptotic isometries.
In this note we provide evidence that this symmetry is realised
(perturbatively) in the quantum theory. We perform a one loop computation of
the fluctuations for a massless spin field around a thermal AdS_3
background. The resulting determinants are evaluated using the heat kernel
techniques of arXiv:0911.5085. The answer factorises holomorphically, and the
contributions from the various spin fields organise themselves into vacuum
characters of the W_N symmetry. For the case of the hs(1,1) theory consisting
of an infinite tower of massless higher spin particles, the resulting answer
can be simply expressed in terms of (two copies of) the MacMahon function.Comment: 23 pages; v2: References adde
No chiral truncation of quantum log gravity?
At the classical level, chiral gravity may be constructed as a consistent
truncation of a larger theory called log gravity by requiring that left-moving
charges vanish. In turn, log gravity is the limit of topologically massive
gravity (TMG) at a special value of the coupling (the chiral point). We study
the situation at the level of linearized quantum fields, focussing on a unitary
quantization. While the TMG Hilbert space is continuous at the chiral point,
the left-moving Virasoro generators become ill-defined and cannot be used to
define a chiral truncation. In a sense, the left-moving asymptotic symmetries
are spontaneously broken at the chiral point. In contrast, in a non-unitary
quantization of TMG, both the Hilbert space and charges are continuous at the
chiral point and define a unitary theory of chiral gravity at the linearized
level.Comment: 20 pages, no figures, references adde
Beyond Logarithmic Corrections to Cardy Formula
As shown by Cardy modular invariance of the partition function of a given
unitary non-singular 2d CFT with left and right central charges c_L and c_R,
implies that the density of states in a microcanonical ensemble, at excitations
Delta and Delta-bar and in the saddle point approximation, is
\rho_0(\Delta,\bar\Delta;c_L, c_R)=c_L c_R
\exp(2\pi\sqrt{{c_L\Delta}/{6}})\exp(2\pi\sqrt{{c_R\bar\Delta}/{6}}). In this
paper, we extend Cardy's analysis and show that in the saddle point
approximation and up to contributions which are exponentially suppressed
compared to the leading Cardy's result, the density of states takes the form
\rho(\Delta,\bar\Delta; c_L,c_R)= f(c_L\Delta)
f(c_R\bar\Delta)\rho_0(\Delta,\bar\Delta; c_L, c_R), for a function f(x) which
we specify. In particular, we show that (i) \rho (\Delta,\bar\Delta; c_L, c_R)
is the product of contributions of left and right movers and hence, to this
approximation, the partition function of any modular invariant, non-singular
unitary 2d CFT is holomorphically factorizable and (ii) \rho(\Delta,\bar\Delta;
c_L, c_R)/(c_Lc_R) is only a function of and . In
addition, treating \rho(\Delta,\bar\Delta; c_L, c_R) as the density of states
of a microcanonical ensemble, we compute the entropy of the system in the
canonical counterpart and show that the function f(x) is such that the
canonical entropy, up to exponentially suppressed contributions, is simply
given by the Cardy's result \ln\rho_0(\Delta,\bar\Delta; c_L, c_R).Comment: 30 pages, no figures; v2: minor improvements, one reference added,
v3: minor corrections to match the published versio
Short-cut to new anomalies in gravity duals to logarithmic conformal field theories
Various massive gravity theories in three dimensions are conjecturally dual
to logarithmic conformal field theories (LCFTs). We summarise the status of
these conjectures. LCFTs are characterised by the values of the central charges
and the so-called "new anomalies". We employ a short-cut to calculate these new
anomalies in generalised massive gravity and in the recently proposed
higher-derivative gravity theories with holographic c-theorem. Both cases
permit LCFTs exhibiting intriguing features, like rank three Jordan cells or
non-zero central charges. Finally, as an example we discuss in some detail the
partially massless version of new massive gravity, a theory with several
special properties that we call "partially massless gravity".Comment: 34 pages, 2 figures; v2: added references; v3: Several rewordings in
the introduction and section 2, added references. Matches published versio
Symmetries of Holographic Super-Minimal Models
We compute the asymptotic symmetry of the higher-spin supergravity theory in
AdS_3 and obtain an infinite-dimensional non-linear superalgebra, which we call
the super-W_infinity[lambda] algebra. According to the recently proposed
supersymmetric duality between higher-spin supergravity in an AdS_3 background
and the 't Hooft limit of the N=2 CP^n Kazama-Suzuki model on the boundary,
this symmetry algebra should agree with the 't Hooft limit of the chiral
algebra of the CFT, SW_n. We provide two nontrivial checks of the duality. By
comparing the algebras, we explicitly match the lowest-spin commutation
relations in the super-W_infinity[lambda] with the corresponding commutation
relations in the 't Hooft limit on the CFT side. We also consider the
degenerate representations of the two algebras and find that the spectra of the
chiral primary fields are identical.Comment: 33 pages, references added, some errors corrected, discussions about
the truncation of the shs[lambda] algebra and reobtaining the original
shs[lambda] algebra from the super-W_infinity[lambda] algebra adde
Holography For a De Sitter-Esque Geometry
Warped dS arises as a solution to topologically massive gravity (TMG)
with positive cosmological constant and Chern-Simons coefficient
in the region . It is given by a real line fibration
over two-dimensional de Sitter space and is equivalent to the rotating Nariai
geometry at fixed polar angle. We study the thermodynamic and asymptotic
structure of a family of geometries with warped dS asymptotics.
Interestingly, these solutions have both a cosmological horizon and an internal
one, and their entropy is unbounded from above unlike black holes in regular de
Sitter space. The asymptotic symmetry group resides at future infinity and is
given by a semi-direct product of a Virasoro algebra and a current algebra. The
right moving central charge vanishes when . We discuss the
possible holographic interpretation of these de Sitter-esque spacetimes.Comment: 22 pages, 1 figure; v2: typos corrected, to match with published
versio
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