1,600 research outputs found
Pining for the periphery: German decolonisation and the negative nostalgia of Hans Grimm
The literature of Hans Grimm is an expression of the intransigence of Germany's liberals in the face of the historical change brought about by the First World War and the persistence of imperialism as a central tenet of the liberal concept of German national identity. Since the time of Friedrich List, German liberalism had expressed its vision of modernity and progress in imperialist, colonial terms. Despite the defeat of this imperialist vision in the First World War, German liberals considered themselves as imperial masters in exile, and it was not until the Untergang of 1945 that the German middle classes jettisoned their colonial nostalgia and revised their understanding of what it meant to be a liberal nation.Unley, S
Virasoro Conformal Blocks and Thermality from Classical Background Fields
We show that in 2d CFTs at large central charge, the coupling of the stress
tensor to heavy operators can be re-absorbed by placing the CFT in a
non-trivial background metric. This leads to a more precise computation of the
Virasoro conformal blocks between heavy and light operators, which are shown to
be equivalent to global conformal blocks evaluated in the new background. We
also generalize to the case where the operators carry U(1) charges. The refined
Virasoro blocks can be used as the seed for a new Virasoro block recursion
relation expanded in the heavy-light limit. We comment on the implications of
our results for the universality of black hole thermality in , or
equivalently, the eigenstate thermalization hypothesis for at large
central charge.Comment: 27+7 pages, 3 figures; typos corrected, citations adde
Universality of Long-Distance AdS Physics from the CFT Bootstrap
We begin by explicating a recent proof of the cluster decomposition principle
in AdS_{d+1} from the CFT_d bootstrap in d > 2. The CFT argument also computes
the leading interactions between distant objects in AdS, and we confirm the
universal agreement between the CFT bootstrap and AdS gravity in the
semi-classical limit. We proceed to study the generalization to 2d CFTs, which
requires knowledge of the Virasoro conformal blocks in a lightcone OPE limit.
We compute these blocks in a semiclassical, large central charge approximation,
and use them to prove a suitably modified theorem. In particular, from the 2d
bootstrap we prove the existence of large spin operators with fixed 'anomalous
dimensions' indicative of the presence of deficit angles in AdS_3. As we
approach the threshold for the BTZ black hole, interpreted as a CFT scaling
dimension, the twist spectrum of large spin operators becomes dense. Due to the
exchange of the Virasoro identity block, primary states above the BTZ threshold
mimic a thermal background for light operators. We derive the BTZ quasi-normal
modes, and we use the bootstrap equation to prove that the twist spectrum is
dense. Corrections to thermality could be obtained from a more refined
computation of the Virasoro conformal blocks.Comment: 34+31 pages, references added, typo in higher-dimensional energy
shift corrected, discussion of coefficient density bounds expande
Nonperturbative Matching Between Equal-Time and Lightcone Quantization
We investigate the nonperturbative relation between lightcone (LC) and
standard equal-time (ET) quantization in the context of theory
in . We discuss the perturbative matching between bare parameters and the
failure of its naive nonperturbative extension. We argue that they are
nevertheless the same theory nonperturbatively, and that furthermore the
nonperturbative map between bare parameters can be extracted from ET
perturbation theory via Borel resummation of the mass gap. We test this map by
using it to compare physical quantities computed using numerical Hamiltonian
truncation methods in ET and LC.Comment: 22+8 pages, 10 figure
Multi-regime models involving Markov chains
In this work, we explore the theory and applications of various multi-regime models involving Markov chains. Markov chains are an elegant way to model path-dependent data. We study a series of problems with non-homogeneous data and the various ways that Markov chains come into play. Non-homogeneous data can be modelled using multi-regime models, which apply a distinct set of parameters to distinct population sub-groups, referred to as regimes. Such models essentially allow for a practitioner to understand the nature (and in some cases the existence) of particular regimes within the data without the need to split the population into assumed sub-groups. For example, the problem of modelling business outcomes in different economic states without explicitly using economic variables. Different regimes can apply to an entire population at different times they can apply to different subsections of the population over the whole observed time. Markov chains are involved via the estimation procedure or within models for the observed data. In our first two problems, we utilise the properties of Markov chains to discover and establish efficiencies in the estimation algorithms. In our third problem, we are analysing mixtures of Markov chains. We prove that the log-likelihood ratio test statistic for the test between 1 and 2 mixture components diverges to infinity in probability. In our fourth problem, we look at a simple case, where each Markov chain component has two states, one of which is absorbing, we derive the exact limiting distribution of the log-likelihood ratio test statistic. Although this work is largely focussed on addressing the theoretical issues of each problem, the motivation behind each of the problems studied comes from real datasets, which possess levels of complexity that are insufficiently described through more standard procedures
Use of GIS and a modified habitat suitability index model to quantify Columbian sharp-tailed grouse habitats in the Upper Blackfoot Valley Montana
Eikonalization of Conformal Blocks
Classical field configurations such as the Coulomb potential and
Schwarzschild solution are built from the t-channel exchange of many light
degrees of freedom. We study the CFT analog of this phenomenon, which we term
the `eikonalization' of conformal blocks. We show that when an operator
appears in the OPE , then the large spin
Fock space states also appear in this OPE with a
computable coefficient. The sum over the exchange of these Fock space states in
an correlator
build the classical ` field' in the dual AdS description. In some limits the
sum of all Fock space exchanges can be represented as the exponential of a
single exchange in the 4-pt correlator of . Our results should
be useful for systematizing perturbation theory in general CFTs and
simplifying the computation of large spin OPE coefficients. As examples we
obtain the leading dependence of Fock space conformal block
coefficients, and we directly compute the OPE coefficients of the simplest
`triple-trace' operators.Comment: 32+17 pages, 6 figures; references added, discussion of eikonal limit
clarifie
Hawking from Catalan
The Virasoro algebra determines all `graviton' matrix elements in
AdS/CFT. We study the explicit exchange of any number of Virasoro
gravitons between heavy and light CFT operators at large central charge.
These graviton exchanges can be written in terms of new on-shell tree diagrams,
organized in a perturbative expansion in , the heavy operator dimension
divided by the central charge. The Virasoro vacuum conformal block, which is
the sum of all the tree diagrams, obeys a differential recursion relation
generalizing that of the Catalan numbers. We use this recursion relation to sum
the on-shell diagrams to all orders, computing the Virasoro vacuum block.
Extrapolating to large determines the Hawking temperature of a BTZ
black hole in dual AdS theories.Comment: 19+8 pages, 5 figure
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