Conformal boundary state for the rectangular geometry

Abstract

We discuss conformal field theories (CFTs) in rectangular geometries, and develop a formalism that involves a conformal boundary state for the 1+1d open system. We focus on the case of homogeneous boundary conditions (no insertion of a boundary condition changing operator), for which we derive an explicit expression of the associated boundary state, valid for any arbitrary CFT. We check the validity of our solution, comparing it with known results for partition functions, numerical simulations of lattice discretizations, and coherent state expressions for free theories.

12 pages, 6 figures

References in corpus (11)

• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• 2D growth processes: SLE and Loewner chains
• Associative-algebraic approach to logarithmic conformal field theories
• Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects
• Phase transition in the Rényi-Shannon entropy of Luttinger liquids
• Logarithmic terms in entanglement entropies of 2D quantum critical points and Shannon entropies of spin chains
• From boundary to bulk in logarithmic CFT
• Universal behavior of a bipartite fidelity at quantum criticality
• Corner free energies and boundary effects for Ising, Potts and fully-packed loop models on the square and triangular lattices
• D-branes as coherent states in the open string channel

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• Multipartitioning topological phases by vertex states and quantum entanglement
• Shape dependent finite-size effect of critical two-dimensional Ising model on a triangular lattice
• Logarithmic corrections to the free energy from sharp corners with angle $2\pi$
• Rectangular amplitudes, conformal blocks, and applications to loop models
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• Accurate expansions of internal energy and specific heat of critical two-dimensional Ising model with free boundaries
• Finite-size corrections for universal boundary entropy in bond percolation
• The critical phenomena of a single defect
• Exact finite-size corrections in the dimer model on a planar square lattice
• Topological and Geometric Universal Thermodynamics in Conformal Field Theory
• Efficient algortihms for the two dimensional Ising model with a surface field
• Two-point boundary correlation functions of dense loop models
• Universality and exact finite-size corrections for spanning trees on cobweb and fan networks