Constantinos Papageorgakis

We review a framework for the conformal bootstrap that does not rely on positivity and treats the infinite tower of high-dimension OPE contributions to conformal correlators through dispersion relations and neural networks. We apply it to scalar thermal two-point functions on [Formula: see text]. We discuss the stability properties of the relevant nonconvex optimization scheme and potential relations to recent discussions of smoothness properties in CFT correlators. We illustrate the numerical application of the method to Generalized Free Fields and 4d holographic CFTs. This is a proceedings contribution to the “Athens Workshop in Theoretical Physics: 10th Anniversary”, held at the National and Kapodistrian University of Athens on December 17–19 2025.

Conformal blocks in odd spacetime dimensions are not known in closed analytic form. To facilitate efficient computations in the conformal bootstrap, we introduce : a novel conformal-block generator implemented in the Go programming language, designed for rapid, on-the-fly, parallel evaluation in general spacetime dimensions using recursive relations. The package supports both multipoint and derivative-based bootstrap approaches and allows flexible control over accuracy and performance. We benchmark against the _ package, finding significant speed improvements in applications where computational speed and moderate accuracy are critical, but ultrahigh precision is not essential. As an illustration, we apply to the mixed-correlator bootstrap of the three-dimensional Ising model, formulated as a nonconvex optimization problem in a suitable truncation scheme. We simultaneously optimize over external scaling dimensions and OPE CFT data. In addition, we discuss how the approach scales as we increase the number of mixed correlators in more general O ( N ) vector models.

We present specialized large language models (LLMs) for theoretical high-energy physics, obtained as 20 fine-tuned variants of the 8 billion parameter Llama-3.1 model. Each variant was trained on arXiv abstracts (through August 2024) from different combinations of hep-th, hep-ph and gr-qc. For a comparative study, we also trained models on datasets that contained abstracts from disparate fields such as the q-bio and cs categories. All models were fine-tuned using two distinct low-rank adaptation fine-tuning approaches and varying dataset sizes, and outperformed the base model on hep-th abstract completion tasks. We compare performance against leading commercial LLMs (ChatGPT, Claude, Gemini, DeepSeek) and derive insights for further developing specialized language models for high-energy theoretical physics.

We introduce a novel method to bootstrap crossing equations in conformal field theory (CFT) and apply it to finite temperature theories on S 1 × R d − 1 . The proposed approach does not rely on positivity constraints and does not employ uncontrolled truncation schemes. Instead, we capture the contribution of an infinite number of operators in conformal block expansions using suitable functions, which are bootstrapped (numerically) together with a finite number of exposed CFT data. Our approach at finite temperature employs three key ingredients: (1) the Kubo-Martin-Schwinger (KMS) condition, (2) thermal dispersion relations, and (3) neural networks that model spin-dependent tail functions within the conformal block expansions. We test the efficiency of the new method in the case of generalized free fields and use it to perform a preliminary bootstrap analysis of double-twist thermal data in holographic CFTs.

Operators with integer scaling dimensions in even-dimensional conformal field theories exhibit well-known type-B Weyl anomalies. In general, these anomalies depend nontrivially on exactly marginal couplings. We study the corresponding fully covariantized anomaly functional on conformal manifolds in several examples. We show that a natural consequence of the Wess-Zumino consistency condition is that the anomalies are covariantly constant with respect to the exactly marginal couplings. The argument is general and applies even when the conformal symmetry is spontaneously broken on moduli spaces of vacua.

Operators with integer scaling dimensions in even-dimensional conformal field theories exhibit well-known type-B Weyl anomalies. In general, these anomalies depend non-trivially on exactly marginal couplings. We study the corresponding fully covariantised anomaly functional on conformal manifolds in several examples. We show that a natural consequence of the Wess-Zumino consistency condition is that the anomalies are covariantly constant with respect to the exactly marginal couplings. The argument is general and applies even when the conformal symmetry is spontaneously broken on moduli spaces of vacua.