Entanglement entropies of minimal models from null-vectors

We present a new method to compute R\'enyi entropies in one-dimensional critical systems. The null-vector conditions on the twist fields in the cyclic orbifold allow us to derive a differential equation for their correlation functions. The latter are then determined by standard bootstrap techniques. We apply this method to the calculation of various R\'enyi entropies in the non-unitary Yang-Lee model.Comment: 43 pages, 7 figure

Genesis of the alpha beta T-cell receptor

The T-cell (TCR) repertoire relies on the diversity of receptors composed of two chains, called $\alpha$ and $\beta$, to recognize pathogens. Using results of high throughput sequencing and computational chain-pairing experiments of human TCR repertoires, we quantitively characterize the $\alpha\beta$ generation process. We estimate the probabilities of a rescue recombination of the $\beta$ chain on the second chromosome upon failure or success on the first chromosome. Unlike $\beta$ chains, $\alpha$ chains recombine simultaneously on both chromosomes, resulting in correlated statistics of the two genes which we predict using a mechanistic model. We find that $\sim 28 \%$ of cells express both $\alpha$ chains. We report that clones sharing the same $\beta$ chain but different $\alpha$ chains are overrepresented, suggesting that they respond to common immune challenges. Altogether, our statistical analysis gives a complete quantitative mechanistic picture that results in the observed correlations in the generative process. We learn that the probability to generate any TCR$\alpha\beta$ is lower than $10^{-12}$ and estimate the generation diversity and sharing properties of the $\alpha\beta$ TCR repertoire

Population variability in the generation and thymic selection of T-cell repertoires

The diversity of T-cell receptor (TCR) repertoires is achieved by a combination of two intrinsically stochastic steps: random receptor generation by VDJ recombination, and selection based on the recognition of random self-peptides presented on the major histocompatibility complex. These processes lead to a large receptor variability within and between individuals. However, the characterization of the variability is hampered by the limited size of the sampled repertoires. We introduce a new software tool SONIA to facilitate inference of individual-specific computational models for the generation and selection of the TCR beta chain (TRB) from sequenced repertoires of 651 individuals, separating and quantifying the variability of the two processes of generation and selection in the population. We find not only that most of the variability is driven by the VDJ generation process, but there is a large degree of consistency between individuals with the inter-individual variance of repertoires being about 2% of the intra-individual variance. Known viral-specific TCRs follow the same generation and selection statistics as all TCRs.Comment: 13 pages, 7 figure, 2 table

Immune Fingerprinting through Repertoire Similarity

Immune repertoires provide a unique fingerprint reflecting the immune history of individuals, with potential applications in precision medicine. However, the question of how personal that information is and how it can be used to identify individuals has not been explored. Here, we show that individuals can be uniquely identified from repertoires of just a few thousands lymphocytes. We present "Immprint," a classifier using an information-theoretic measure of repertoire similarity to distinguish pairs of repertoire samples coming from the same versus different individuals. Using published T-cell receptor repertoires and statistical modeling, we tested its ability to identify individuals with great accuracy, including identical twins, by computing false positive and false negative rates $< 10^{-6}$ from samples composed of 10,000 T-cells. We verified through longitudinal datasets and simulations that the method is robust to acute infections and the passage of time. These results emphasize the private and personal nature of repertoire data

Application of extended conformal theories to statistical physics problems

L'étude des phénomènes critiques en physique statistique bidimensionnelle a pour outils privilégiés la théorie conforme et les modèles intégrables. La relation entre ces deux formalismes est un domaine de recherche actif, notamment dans le cadre des théories dites non-rationnelles. Cette thèse s'intéresse à certains systèmes critiques décrits par une théorie conforme étendue, c'est-à-dire présentant des symétries supplémentaires. Le premier problème étudié est le modèle de boucles entièrement compactes (fully packed loop model, FPL). Les modèles de boucles sont des modèles de physique statistique non locaux, s'inspirant de la description des polymères. Leur limite continue est une théorie conformes non-rationnelle. Le lien entre le modèle FPL et la symétrie W3, une symétrie conforme étendue par un champ de dimension trois, est étudié en détail. La relation avec les modèles de boucles mène naturellement à l'étude du contenu non-scalaire de la théorie W3. Le second problème concerne le calcul de l'intrication dans des systèmes quantiques unidimensionnels. Dans ce cadre, l'objet d'étude privilégié est l'entropie d'intrication entre un sous-système et son complément. Pour l'état fondamental d'une chaîne de spin, le comportement de cette entropie en fonction de la taille du sous-système est un marqueur clair de la criticalité de la chaîne. Dans ce manuscrit, une nouvelle manière de calculer ces entropies dans le cadre des modèles critiques est présentée. Elle s'appuie sur des théories conformes étendues par une symétrie dite d'orbifold. Cette méthode est particulièrement applicable aux entropies d'états excités ou de sous-systèmes disjoints.The study of critical phenomena in two-dimensional statistical physics is mainly performed with the help of conformal field theory and integrable models. The relationship between these two formalisms is an active field of research, particularly in the framework of the so-called non-rational theories. This thesis is focused on certain critical systems described by an extended conformal theory : a theory that presents additional symmetries. The first problem studied is the fully packed loop model (FPL). Loop models are non-local statistical models based on the description of assembly of polymers. In particular, they represent the interfaces formed by spin models. The FPL model is integrable and its spectrum reflects an underlying symmetry Uq(sl(3)). The link between this model and the W3 symmetry, a conformal symmetry extended by a three-dimensional field, is studied in detail, numerically (by exact diagonalization) and analytically. The relationship with loop models leads to the study of the non-scalar operator content of the W3 theory. The second problem concerns the calculation of entanglement in unidimensional quantum systems. In this context, the preferred object of study is the entropy of entanglement between a subsystem and its complement. For the fundamental state of a spin chain, the behaviour of this entropy as a function of the size of the subsystem is a clear marker of the criticality of the chain. In this manuscript, a new way of calculating these entropies in critical models is presented. It is based on conformal theories extended by a symmetry called orbifold. This method is particularly applicable to entropies of excited states or disjointed subsystems