A matrix CFT at multiple large charges

We investigate matrix models in three dimensions where the global $\text{SU}(N)$ symmetry acts via the adjoint map. Analyzing their ground state which is homogeneous in space and can carry either a unique or multiple fixed charges, we show the existence of at least two distinct fixed points of the renormalization group (RG) flow. In particular, the one type of those fixed points manifests itself via tractable deviations in the large-charge expansion from the known predictions in the literature. We demonstrate most of the novel features using mainly the example of the $\text{SU}(4)$ matrix theory to compute the anomalous dimension of the lowest scalar operator with large global charge(s).Comment: 1+36 pages, 2 figures, minor clarifications added, version to be published in JHE

Matrix models at large charge

We show that the large-charge formalism can be successfully applied to models that go beyond the vector models discussed so far in the literature. We study the explicit example of a conformal $SU(3)$ matrix model in 2+1 space-time dimensions at fixed charge and calculate the anomalous dimension and fusion coefficients at leading order in the $U(1)$ charge.Comment: 31 pages, 1 figur

An AdS/EFT correspondence at large charge

Considering theories in sectors of large global charge $Q$ results in a semiclassical effective field theory (EFT) description for some strongly-coupled conformal field theories (CFTs) with continuous global symmetries. Hence, when studying dualities at large charge, we can have control over the strongly coupled side of the duality and gain perturbative access to both dual pairs. In this work we discuss the AdS/CFT correspondence in the regime $Q \gg C_T \gg 1$ where both the EFT and gravity descriptions are valid and stable ($C_T$ being the central charge). We present the observation that the ground state energy as a function of the Abelian charge $Q$ for a simple EFT in some three-dimensional CFT coincides with the expression for the mass of an anti-de Sitter-Reissner-Nordstr\"om black hole as a function of its charge. This observation allows us to introduce a dictionary relating CFT, EFT and holographic descriptions. We also find agreement for the higher-derivative corrections on both sides, suggesting a large-$C_T$ expansion on the EFT side.Comment: 23 pages. Matches published version in Nucl.Phys.

Calabi-Yau compactifications of non-supersymmetric heterotic string theory

Phenomenological explorations of heterotic strings have conventionally focused primarily on the E8xE8 theory. We consider smooth compactifications of all three ten-dimensional heterotic theories to exhibit the many similarities between the non-supersymmetric SO(16)xSO(16) theory and the related supersymmetric E8xE8 and SO(32) theories. In particular, we exploit these similarities to determine the bosonic and fermionic spectra of Calabi-Yau compactifications with line bundles of the non-supersymmetric string. We use elements of four-dimensional supersymmetric effective field theory to characterize the non-supersymmetric action at leading order and determine the Green-Schwarz induced axion-couplings. Using these methods we construct a non-supersymmetric Standard Model(SM)-like theory. In addition, we show that it is possible to obtain SM-like models from the standard embedding using at least an order four Wilson line. Finally, we make a proposal of the states that live on five branes in the SO(16)xSO(16) theory and find under certain assumptions the surprising result that anomaly factorization only admits at most a single brane solution.Comment: 1+40 pages LaTeX, 3 figures, 8 tables. v2: Flux quantization condition for the non-supersymmetric theory correcte

Compensating strong coupling with large charge

We study some (conformal) field theories with global symmetries in the sector where the value of the global charge $Q$ is large. We find (as expected) that the low energy excitations of this sector are described by the general form of Goldstone's theorem in the non-relativistic regime. We also derive the unexpected result, first presented in [Hellerman et al. 2015], that the effective field theory describing such sector of fixed $Q$ contains effective couplings $\lambda_{\text{eff}}\sim \lambda^b /Q^{a}$, where $\lambda$ is the original coupling. Hence, large charge leads to weak coupling. In the last section of the paper we present an outline of how to compute anomalous dimensions of the $O(n)$ model in this limit.Comment: 20 pages, 2 figures. Version accepted by JHE

On the estimation and interpretation of effect size metrics

Effect size estimates are thought to capture the collective, two-way response to an intervention or exposure in a three-way problem among the intervention/exposure, various confounders and the outcome. For meaningful causal inference from the estimated effect size, the joint distribution of observed confounders must be identical across all intervention/exposure groups. However, real-world observational studies and even randomized clinical trials often lack such structural symmetry. To address this issue, various methods have been proposed and widely utilized. Recently, elementary combinatorics and information theory have motivated a consistent way to completely eliminate observed confounding in any given study. In this work, we leverage these new techniques to evaluate conventional methods based on their ability to (a) consistently differentiate between collective and individual responses to intervention/exposure and (b) establish the desired structural parity for sensible effect size estimation. Our findings reveal that a straightforward application of logistic regression homogenizes the three-way stratified analysis, but fails to restore structural symmetry leaving in particular the two-way effect size estimate unadjusted. Conversely, the Mantel-Haenszel estimator struggles to separate three-way effects from the two-way effect of intervention/exposure, leading to inconsistencies in interpreting pooled estimates as two-way risk metrics.Comment: 10 pages, 1 Figure, 3 diagrams, 2 table

Total Empiricism: Learning from Data

Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems in the analysis and interpretation of the results. Instead of trying to fix the model or "correct" the data, we here describe a totally empirical statistical approach that does not rely on ad hoc distributional assumptions in order to overcome many problems in contemporary statistics. Starting from elementary combinatorics, we motivate an information-guided formalism to quantify knowledge extracted from the given data. Subsequently, we derive model-agnostic methods to identify patterns that are solely evidenced by the data based on our prior knowledge. The data-centric character of empiricism allows for its universal applicability, particularly as sample size grows larger. In this comprehensive framework, we re-interpret and extend model distributions, scores and statistical tests used in different schools of statistics.Comment: Keywords: effective description, large-N, operator formalism, statistical testing, inference, information divergenc

Eliminating confounder-induced bias in the statistics of intervention

Experimental and observational studies often lead to spurious association between the outcome and independent variables describing the intervention, because of confounding to third-party factors. Even in randomized clinical trials, confounding might be unavoidable due to small sample sizes. Practically, this poses a problem, because it is either expensive to re-design and conduct a new study or even impossible to alleviate the contribution of some confounders due to e.g. ethical concerns. Here, we propose a method to consistently derive hypothetical studies that retain as many of the dependencies in the original study as mathematically possible, while removing any association of observed confounders to the independent variables. Using historic studies, we illustrate how the confounding-free scenario re-estimates the effect size of the intervention. The new effect size estimate represents a concise prediction in the hypothetical scenario which paves a way from the original data towards the design of future studies.Comment: 16 pages, 5 figures, 3 table

Infinite number of MSSMs from heterotic line bundles?

We consider heterotic E8xE8 supergravity compactified on smooth Calabi-Yau manifolds with line bundle gauge backgrounds. Infinite sets of models that satisfy the Bianchi identities and flux quantization conditions can be constructed by letting their background flux quanta grow without bound. Even though we do not have a general proof, we find that all examples are at the boundary of the theory's validity: the Donaldson-Uhlenbeck-Yau equations, which can be thought of as vanishing D-term conditions, cannot be satisfied inside the Kaehler cone unless a growing number of scalar Vacuum Expectation Values (VEVs) is switched on. As they are charged under various line bundles simultaneously, the gauge background gets deformed by these VEVs to a non-Abelian bundle. In general, our physical expectation is that such infinite sets of models should be impossible, since they never seem to occur in exact CFT constructions.Comment: LaTeX, 8 pages, 4 tables, some references and comments adde