Authors: V. Niarchos, C. Papageorgakis, P. Richmond, A. G. Stapleton, M. Woolley

Paper available on the arXiv at 2306.15730. Included as reference [1]

Abstract

We study the conformal bootstrap of 1D CFTs on the straight Maldacena–Wilson line in 4D \({\cal N}=4\) super-Yang–Mills theory. We introduce an improved truncation scheme with an ‘OPE tail’ approximation and use it to reproduce the ‘bootstrability’ results of Cavaglià et al. for the OPE-coefficients squared of the first three unprotected operators. For example, for the lowest-dimension OPE-coefficient squared at ‘t Hooft coupling \((4\pi)^2\), linear-functional methods with two sum rules from integrated correlators give the rigorous result \(0.294014873 \pm 4.88 \cdot 10^{-8}\), whereas our methods give with machine-precision computations \(0.294014228 \pm 6.77 \cdot 10^{-7}\). For our numerical searches, we benchmark the Reinforcement Learning Soft Actor-Critic algorithm against an Interior Point Method algorithm (IPOPT) and comment on the merits of each algorithm.

How our results compare:

Unconstrained Soft-Actor-Critic and IPOPT

Results for the OPE-coefficients squared of the first three long operators with no integral constraints. The solid lines indicate the rigorous bounds presented in Figure 6 of [2], reprinted here with permission from the authors. Same-coloured circles and squares indicate our results from the SAC and IPOPT runs respectively. The corresponding statistical errors are too small to display on this plot but can be found in Table 7 of [1].

Constrained Interior Point Optimiser (IPOPT)

Results for the OPE-coefficients squared of the first three long operators after the incorporation of two integral constraints. The solid lines indicate the rigorous bounds presented in Figure 10 of [3], reprinted here with permission from the authors. Same-colored squares indicate our results from the IPOPT runs. The corresponding statistical errors are too small to display on this plot but can be found in Table 7 of [1]

References

• [1] V. Niarchos, C. Papageorgakis, P. Richmond, A. G. Stapleton and M. Wooley, Bootstrability in Line-Defect CFT with Improved Truncation Methods, arXiv:2306.15730
• [2] A. Cavaglià, N. Gromov, J. Julius & M. Preti Integrability and conformal bootstrap: One dimensional defect conformal field theory, Phys. Rev. D 105, L021902 (2022), arXiv:2107.08510
• [3] A. Cavaglià, N. Gromov, J. Julius & M. Preti Bootstrability in defect CFT: integrated correlators and sharper bounds, JHEP 2205, 164 (2022, L021902 (2022), arXiv:2203.09556

Authors: G. Kantor, V. Niarchos, C. Papageorgakis, P. Richmond

Paper available on the arXiv at 2209.02801. Included as reference [1]

Abstract

We study numerically the 6D (2,0) superconformal bootstrap using the Soft-Actor-Critic (SAC) algorithm as a stochastic optimizer. We focus on the four-point functions of scalar superconformal primaries in the energy-momentum multiplet. Starting from the supergravity limit, we perform searches for adiabatically varied central charges and derive two curves for a collection of 80 conformal field theory (CFT) data (70 of these data correspond to unprotected long multiplets and 10 to protected short multiplets). We conjecture that the two curves capture the A- and D-series (2,0) theories. Our results are competitive when compared to the existing bounds coming from standard numerical bootstrap methods, and data obtained using the OPE inversion formula. With this paper we are also releasing our Python implementation of the SAC algorithm, BootSTOP. The paper discusses the main functionality features of this package.

References

• [1] G. Kantor, V. Niarchos, C. Papageorgakis, P. Richmond 6D (2,0) Bootstrap with soft-Actor-Critic, Phys.Rev.D 107 (2023) 2, 025005, arXiv:2209.02801

Authors: G. Kantor, V. Niarchos, C. Papageorgakis

Paper available on the arXiv at 2108.09330. Included as reference [1]

Abstract

We introduce the use of reinforcement-learning (RL) techniques to the conformal-bootstrap program. We demonstrate that suitable soft Actor-Critic RL algorithms can perform efficient, relatively cheap high-dimensional searches in the space of scaling dimensions and OPE-squared coefficients that produce sensible results for tens of CFT data from a single crossing equation. In this paper we test this approach in well-known 2D CFTs, with particular focus on the Ising and tricritical Ising models and the free compactified boson CFT. We present results of as high as 36-dimensional searches, whose sole input is the expected number of operators per spin in a truncation of the conformal-block decomposition of the crossing equations. Our study of 2D CFTs uses only the global \(so(2,2)\) part of the conformal algebra, and our methods are equally applicable to higher-dimensional CFTs. When combined with other, already available, numerical and analytical methods, we expect our approach to yield an exciting new window into the nonperturbative structure of arbitrary (unitary or nonunitary) CFTs.

References

• [1] G. Kantor, V. Niarchos, C. Papageorgakis Conformal Bootstrap with Reinforcement Learning, Phys.Rev.D 105 (2022) 2, 025018, arXiv:2108.09330

Authors: G. Kantor, V. Niarchos, C. Papageorgakis

Paper available on the arXiv at 2108.08859. Included as reference [1]

Abstract

In this Letter, we deploy for the first time reinforcement-learning algorithms in the context of the conformal-bootstrap program to obtain numerical solutions of conformal field theories (CFTs). As an illustration, we use a soft actor-critic algorithm and find approximate solutions to the truncated crossing equations of two-dimensional CFTs, successfully identifying well-known theories like the 2D Ising model and the 2D CFT of a compactified scalar. Our methods can perform efficient high-dimensional searches that can be used to study arbitrary (unitary or nonunitary) CFTs in any spacetime dimension.

References

• [1] G. Kantor, V. Niarchos, C. Papageorgakis Solving Conformal Field Theories with Artificial Intelligence, Phys.Rev.Lett. 128 (2022) 4, 041601, arXiv:2108.08859