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The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the…

High Energy Physics - Theory · Physics 2015-06-12 Sheer El-Showk , Miguel F. Paulos

We determine the spectrum and correlation functions of Liouville theory with a central charge less than (or equal) one. This completes the definition of Liouville theory for all complex values of the central charge. The spectrum is always…

High Energy Physics - Theory · Physics 2018-12-13 Sylvain Ribault , Raoul Santachiara

Genus two partition functions of 2d chiral conformal field theories are given by Siegel modular forms. We compute their conformal blocks and use them to perform the conformal bootstrap. The advantage of this approach is that it imposes…

High Energy Physics - Theory · Physics 2017-05-18 Christoph A. Keller , Gregoire Mathys , Ida G. Zadeh

We generalize the construction of Compactified Imaginary Liouville Theory (CILT), a non-unitary logarithmic Conformal Field Theory (CFT) defined on closed surfaces, to surfaces with boundary. Starting from a compactified Gaussian Free Field…

Mathematical Physics · Physics 2025-11-17 Yang Xiao , Yuxiao Xie

We define the two-dimensional $O(n)$ conformal field theory as a theory that includes the critical dilute and dense $O(n)$ models as special cases, and depends analytically on the central charge. For generic values of $n\in\mathbb{C}$, we…

High Energy Physics - Theory · Physics 2022-05-11 Linnea Grans-Samuelsson , Rongvoram Nivesvivat , Jesper Lykke Jacobsen , Sylvain Ribault , Hubert Saleur

Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…

Mathematical Physics · Physics 2014-11-18 I. T. Todorov

Modular invariance imposes rigid constrains on the partition functions of two-dimensional conformal field theories. Many fundamental results follow strictly from modular invariance, giving rise to the numerical modular bootstrap program.…

High Energy Physics - Theory · Physics 2021-07-06 Anatoly Dymarsky , Alfred Shapere

The presence of nearby conformal field theories (CFTs) hidden in the complex plane of the tuning parameter was recently proposed as an elegant explanation for the ubiquity of "weakly first-order" transitions in condensed matter and…

Statistical Mechanics · Physics 2023-10-04 Arijit Haldar , Omid Tavakol , Han Ma , Thomas Scaffidi

We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non--semi-simple associative algebras appearing in their lattice regularizations (as discussed in a companion…

High Energy Physics - Theory · Physics 2008-11-26 N. Read , H. Saleur

We initiate the study of the conformal bootstrap using Sturm-Liouville theory, specializing to four-point functions in one-dimensional CFTs. We do so by decomposing conformal correlators using a basis of eigenfunctions of the Casimir which…

High Energy Physics - Theory · Physics 2018-01-17 Matthijs Hogervorst , Balt C. van Rees

We apply the numerical bootstrap program to chiral operators in four-dimensional ${\mathcal N}=2$ SCFTs. In the first part of this work we study four-point functions in which all fields have the same conformal dimension. We give special…

High Energy Physics - Theory · Physics 2016-01-12 Madalena Lemos , Pedro Liendo

The Potts conformal field theory is an analytic continuation in the central charge of conformal field theory describing the critical two-dimensional $Q$-state Potts model. Four-point functions of the Potts conformal field theory are…

High Energy Physics - Theory · Physics 2023-06-14 Rongvoram Nivesvivat

We initiate a numerical conformal bootstrap study of CFTs with $S_n \ltimes (S_Q)^n$ global symmetry. These include CFTs that can be obtained as coupled replicas of two-dimensional critical Potts models. Particular attention is paid to the…

High Energy Physics - Theory · Physics 2024-05-31 Stefanos R. Kousvos , Alessandro Piazza , Alessandro Vichi

We study the symmetry resolution of the entanglement entropy of an interval in two-dimensional conformal field theories (CFTs), by relating the bipartition to the geometry of an annulus with conformal boundary conditions. In the presence of…

High Energy Physics - Theory · Physics 2025-10-21 Giuseppe Di Giulio , René Meyer , Christian Northe , Henri Scheppach , Suting Zhao

Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…

High Energy Physics - Theory · Physics 2013-11-22 A. M. Gainutdinov , J. L. Jacobsen , N. Read , H. Saleur , R. Vasseur

We present new numerical results on the space of local, unitary, parity-preserving conformal field theories (CFTs) in three dimensions from the stress tensor bootstrap. In bounds maximizing certain OPE coefficients, we find a plethora of…

High Energy Physics - Theory · Physics 2026-02-17 Rajeev S. Erramilli , Matthew S. Mitchell

We study conformal twist field four-point functions on a $\mathbb Z_N$ orbifold. We examine in detail the case $N=3$ and analyze theories obtained by replicated $N$-times a minimal model with central charge $c<1$. A fastly convergent…

High Energy Physics - Theory · Physics 2021-11-02 Filiberto Ares , Raoul Santachiara , Jacopo Viti

Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…

Category Theory · Mathematics 2008-11-26 Ingo Runkel , Jens Fjelstad , Jurgen Fuchs , Christoph Schweigert

In this paper, we attempt to explore the landscape of two-dimensional conformal field theories (2d CFTs) by efficiently searching for numerical solutions to the modular bootstrap equation using machine-learning-style optimization. The torus…

High Energy Physics - Theory · Physics 2026-05-05 Nathan Benjamin , A. Liam Fitzpatrick , Wei Li , Jesse Thaler

We study correlation functions of a conserved spin-1 current $J_\mu$ in three dimensional Conformal Field Theories (CFTs). We investigate the constraints imposed by permutation symmetry and current conservation on the form of three point…

High Energy Physics - Theory · Physics 2020-04-13 Anatoly Dymarsky , Joao Penedones , Emilio Trevisani , Alessandro Vichi