Leading exponential finite size corrections for non-diagonal form factors

Abstract

We derive the leading exponential finite volume corrections in two dimensional integrable models for non-diagonal form factors in diagonally scattering theories. These formulas are expressed in terms of the infinite volume form factors and scattering matrices. If the particles are bound states then the leading exponential finite-size corrections ($\mu$-terms) are related to virtual processes in which the particles disintegrate into their constituents. For non-bound state particles the leading exponential finite-size corrections (F-terms) come from virtual particles traveling around the finite world. In these F-terms a specifically regulated infinite volume form factor is integrated for the momenta of the virtual particles. The F-term is also present for bound states and the $\mu$-term can be obtained by taking an appropriate residue of the F-term integral. We check our results numerically in the Lee-Yang and sinh-Gordon models based on newly developed Hamiltonian truncations.

arXiv comment34 pages, 16 figures

References in corpus (34)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Exact expectation values of local fields in quantum sine-Gordon model
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Excited states by analytic continuation of TBA equations
• Finite Temperature Correlation Functions in Integrable QFT
• Form factors in finite volume II:disconnected terms and finite temperature correlators
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• A Cheap Alternative to the Lattice?
• Form factors in finite volume I: form factor bootstrap and truncated conformal space
• Wrapping interactions at strong coupling -- the giant magnon
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality
• A comment on finite temperature correlations in integrable QFT
• Towards the Construction of Wightman Functions of Integrable Quantum Field Theories
• On the spectrum of the Sinh-Gordon model in finite volume
• Mean values of local operators in highly excited Bethe states
• Structure constants at wrapping order
• TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
• On the Thermodynamic Bethe Ansatz Equation in Sinh-Gordon Model
• String field theory vertex from integrability
• Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories
• Truncated Hilbert space approach to the 2d ${\varphi }^4$ theory
• Review of AdS/CFT Integrability, Chapter III.6: Thermodynamic Bethe Ansatz
• Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density
• Luscher's mu-term and finite volume bootstrap principle for scattering states and form factors
• From the octagon to the SFT vertex - gluing and multiple wrapping
• LeClair-Mussardo series for two-point functions in Integrable QFT
• A next-to-leading Luescher formula
• Form factor approach to diagonal finite volume matrix elements in Integrable QFT
• Diagonal finite volume matrix elements in the sinh-Gordon model
• Exact finite volume expectation values of local operators in excited states
• Finite-Volume Spectra of the Lee-Yang Model
• Field theoretical derivation of Lüscher's formula and calculation of finite volume form factors
• Diagonal form factors from non-diagonal ones

Cited by in corpus (9)

• Generalized hydrodynamics regime from the thermodynamic bootstrap program
• Approaching the Self-Dual Point of the Sinh-Gordon model
• Diagonal finite volume matrix elements in the sinh-Gordon model
• Chirally Factorised Truncated Conformal Space Approach
• Duality and Form Factors in the Thermally Deformed Two-Dimensional Tricritical Ising Model
• Three-point functions at strong coupling in the BMN limit
• TCSA and the finite volume boundary state
• Finite volume form factors in integrable theories
• Finite volume corrections of non-diagonal form factors