scholarly journals blocks_3d: software for general 3d conformal blocks

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Rajeev S. Erramilli ◽  
Luca V. Iliesiu ◽  
Petr Kravchuk ◽  
Walter Landry ◽  
David Poland ◽  
...  
Keyword(s):  
Primary Effect ◽  
Conformal Blocks ◽  
Recursion Relations ◽  
Symmetric Configuration ◽  
Stress Tensors ◽  
Dead End ◽  
Performance Benchmarks ◽  
Derivatives Of

Abstract We introduce the software blocks_3d for computing four-point conformal blocks of operators with arbitrary Lorentz representations in 3d CFTs. It uses Zamolodchikov-like recursion relations to numerically compute derivatives of blocks around a crossing-symmetric configuration. It is implemented as a heavily optimized, multi-threaded, C++ application. We give performance benchmarks for correlators containing scalars, fermions, and stress tensors. As an example application, we recompute bootstrap bounds on four-point functions of fermions and study whether a previously observed sharp jump can be explained using the “fake primary” effect. We conclude that the fake primary effect cannot fully explain the jump and the possible existence of a “dead-end” CFT near the jump merits further study.

scholarly journals On the classic geometrodynamics of a spherically-symmetric configuration of gravitational and electromagnetic fields

2019 ◽  
Vol 27 (1) ◽  
pp. 3-8
Author(s):  
V. D. Gladush
Keyword(s):  
Hamiltonian Constraint ◽  
Spherically Symmetric ◽  
Action Functional ◽  
Hamiltonian Action ◽  
Gravitational Fields ◽  
Motion Trajectories ◽  
Symmetric Configuration ◽  
Functional Derivatives ◽  
Derivatives Of ◽  
Hamilton Jacobi Equation

Analytical aspects of the classical geometrodynamics for the spherically-symmetric configuration of the electromagnetic and gravitational fields in GR are considered. The feature of such configurations is that they admit two motion integrals – the total mass and charge. The Einstein-Hilbert action for the configuration, after dimensional reduction, by means of the Legendre transformation is reduced to the Hamiltonian action. Using the conservation laws for the mass and charge, as well as the Hamiltonian constraint, the momenta are found as functions of configuration variables. The set of equations, which associate momenta and functional derivatives of the action in the configuration space (CS) is integrable. This allows us to obtain the action functional as a solution of the Einstein-Hamilton-Jacobi equation in functional derivatives. Variations of the action functional with respect to mass M and charge Q of the configuration lead to the motion trajectories in the CS. We note that the minisuperspace metric, which is induced by the kinetic part of the Lagrangian, does not coincide with the CS metric that arises when the function of lapse N is excluded from the action. The space-time metric for which the indicated metrics coincide in the T-region up to a coefficient are considered. The metric of CS is constructed and its geometry is studied. Under the trivial embedding of hypersurfaces of the foliation into a dynamical T-region, the CS is flat. It allows introducing pseudo-Cartesian coordinates in which the CS metric takes the Lorentz form.

scholarly journals Recursion relations for conformal blocks

2016 ◽  
Vol 2016 (9) ◽  
Author(s):  
João Penedones ◽  
Emilio Trevisani ◽  
Masahito Yamazaki
Keyword(s):  
Conformal Blocks ◽  
Recursion Relations

scholarly journals Logarithmic CFT at generic central charge: from Liouville theory to the $Q$-state Potts model

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Rongvoram Nivesvivat ◽  
Sylvain Ribault
Keyword(s):  
Potts Model ◽  
Free Parameter ◽  
Central Charge ◽  
Liouville Theory ◽  
Conformal Dimension ◽  
Conformal Blocks ◽  
Potts Models ◽  
Dimension 2 ◽  
Arbitrary Precision ◽  
Derivatives Of

Using derivatives of primary fields (null or not) with respect to the conformal dimension, we build infinite families of non-trivial logarithmic representations of the conformal algebra at generic central charge, with Jordan blocks of dimension 2 or 3. Each representation comes with one free parameter, which takes fixed values under assumptions on the existence of degenerate fields. This parameter can be viewed as a simpler, normalization-independent redefinition of the logarithmic coupling. We compute the corresponding non-chiral conformal blocks, and show that they appear in limits of Liouville theory four-point functions.As an application, we describe the logarithmic structures of the critical two-dimensional O(n) and Q-state Potts models at generic central charge. The validity of our description is demonstrated by semi-analytically bootstrapping four-point connectivities in the Q-state Potts model to arbitrary precision. Moreover, we provide numerical evidence for the Delfino-Viti conjecture for the three-point connectivity. Our results hold for generic values of Q in the complex plane and beyond.

scholarly journals Recursion relations for 5-point conformal blocks

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
David Poland ◽  
Valentina Prilepina
Keyword(s):  
Linear Combination ◽  
Energy Operator ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Point Function ◽  
Conformal Blocks ◽  
Recursion Relations ◽  
Expectation Value ◽  
Conformal Field ◽  
Weight Shifting

Abstract We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.

scholarly journals How to succeed at Witten diagram recursions without really trying

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Xinan Zhou
Keyword(s):  
Dimensional Reduction ◽  
Recursion Relation ◽  
Conformal Block ◽  
Analytic Functional ◽  
Conformal Blocks ◽  
Recursion Relations ◽  
Similar Formula

Abstract Witten diagrams are basic objects for studying dynamics in AdS space, and also play key roles in the analytic functional bootstrap. However, these diagrams are notoriously hard to evaluate, making it extremely difficult to search for recursion relations among them. In this note, we present simple methods to obtain recursion relations for exchange Witten diagrams from conformal block recursion relations. We discover a variety of new relations, including the dimensional reduction formulae for exchange Witten diagrams. In particular, we find a five-term recursion relation relating exchange Witten diagrams in d and d − 2 dimensions. This gives the holographic analogue of a similar formula for conformal blocks due to Parisi-Sourlas supersymmetry. We also extend the analysis to two-point functions in CFTs with conformal boundaries, and obtain similar results.

Physical Properties of TCNQ Salts with N-Methyl Derivatives of Pyridine

1982 ◽  
Vol 85 (1) ◽  
pp. 257-263 ◽  
Author(s):  
A. Graja ◽  
M. Przybylski ◽  
B. Butka ◽  
R. Swietlik
Keyword(s):  
Physical Properties ◽  
Methyl Derivatives ◽  
Derivatives Of
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