Diagonal form factors and hexagon form factors II. Non-BPS light operator

2019

2017 MATRIX Annals

Section: Resultsmentioning

confidence: 86%

Diagonal Form Factors from Non-diagonal Ones

2019

2017 MATRIX Annals

“…In the case of heavy-heavy-light operators the string worldsheet degenerates into a cylinder and the SFT vertex is nothing but a diagonal finite volume form factor, see [14][15][16]. Another approach through cutting the string worldsheet corresponding to a 3-point correlation function into two hexagons was introduced in [17], see also [18][19][20][21][22][23] for further developments.…”

Section: Jhep06(2017)058mentioning

confidence: 99%

From the octagon to the SFT vertex — gluing and multiple wrapping

Janik

2017

J. High Energ. Phys.

Abstract:We compare various ways of decomposing and decompactifying the string field theory vertex and analyze the relations between them. We formulate axioms for the octagon and show how it can be glued to reproduce the decompactified pp-wave SFT vertex which in turn can be glued to recover the exact finite volume pp-wave Neumann coefficients. The gluing is performed by resumming multiple wrapping corrections. We observe important nontrivial contributions at the multiple wrapping level which are crucial for obtaining the exact results.

“…Their non-local counterparts can be used in the AdS/CFT correspondence to describe three-point functions in the gauge theory and the string field theory vertex in string theory [3,4,5,6,7]. Diagonal matrix elements play a special role there, as they describe the HHL type correlation functions [8,9,10,11,12].…”

Section: Introductionmentioning

confidence: 99%

Diagonal finite volume matrix elements in the sinh-Gordon model

Смирнов

2019

Nuclear Physics B

Using the fermionic basis we conjecture exact expressions for diagonal finite volume matrix elements of exponential operators and their descendants in the sinh-Gordon theory. Our expressions sum up the LeClair-Mussardo type infinite series generalized by Pozsgay for excited state expectation values. We checked our formulae against the Liouville three-point functions for small, while against Pozsgay's expansion for large volumes and found complete agreement. * Membre du CNRS the ground-state TBA densities with the excited state ones and contains additional factors, which can be interpreted as partial density of states [20,21].Alternatively, there is an other approach which focuses on specific theories and exploits their hidden (Grassmann) structure to provide compact expressions for finite volume matrix elements [22]. These specific continuum models arise as limits of integrable lattice models and the most studied examples are the sinh-Gordon and sine-Gordon models. There have been active work and relevant progress in deriving finite volume one-point functions for the exponential operators and their descendants in these theories [23,24]. These results were then extended for diagonal matrix elements in the sine-Gordon theory [25,26,27] and the aim of our paper is to provide similar expressions in the sinh-Gordon theory.The paper is organized as follows: Section 2 reviews the description of the finite size energy spectrum of the sinh-Gordon theory. A multi-particle state for large volumes can be labelled by momentum quantum numbers, which we relate at small volume to the spectrum of the Liouville conformal field theory by matching the eigenvalues of the conserved charges. In Section 3 we formulate our main conjecture for the finite volume exceptions values in the fermionic basis. The novelty compared to the vacuum expectation values is the discrete part of the convolutions, which carries information on the particles' rapidities. We check this conjecture for large volumes in Section 4. The discrete part of the convolution contains the polynomial, while the continuous part the exponentially small corrections in the volume. In Section 5 we compare our conjecture with Liouville three-point functions for low lying states including non-degenerate and degenerate L 0 subspaces. All the checks performed confirm our conjecture, thus we close the paper with conclusions in Section 6.