Asymptotic four point functions

Basso, Benjamin; Coronado, Frank; Komatsu, Shota; Lam, Ho Tat; Vieira, Pedro; Zhong, De-liang

doi:10.1007/jhep07(2019)082

Cited by 60 publications

(101 citation statements)

References 94 publications

(320 reference statements)

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“…The quantum numbers (L, M, N ± ) that characterize a states correspond to the length (L), total number of excitations (M ) and the number of excitations of a specific type (N ± ). The explicit form of the eigenstates is again of nested type can be found for instance in [44]. Just as for SU(2) and SU (3), we find that all roots must come in pairs…”

Section: Full Scalar Sectorsupporting

confidence: 62%

One-point functions in AdS/dCFT

Leeuw

2020

J. Phys. A: Math. Theor.

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In this review we discuss recent advances in the computation of onepoint functions in defect conformal field theories with holographic duals. We briefly review the appearance of integrable spin chains in N = 4 super Yang-Mills theory and reformulate the problem of computing one-point functions to determining overlaps between Bethe states and a Matrix Product State. We will then demonstrate how these overlaps can be computed by determinant formulas. This work is based on lectures given at the Young Researchers Integrability School and Workshop 2018. To appear in a special issue of J. Phys. A.

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Section: Full Scalar Sectorsupporting

confidence: 62%

One-point functions in AdS/dCFT

Leeuw

2020

J. Phys. A: Math. Theor.

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“…1 The fact that the sum over virtual particles can be written as a Fredholm pfaffian has been noticed before in [14].…”

Section: Arxiv:190511467v1 [Hep-th] 27 May 2019mentioning

confidence: 88%

The octagon as a determinant

Kostov

Petkova

Serban

2019

J. High Energ. Phys.

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The computation of a certain class of four-point functions of heavily charged BPS operators boils down to the computation of a special form factor -the octagon. In this paper, which is an extended version of the short note [1], we derive a non-perturbative formula for the square of the octagon as the determinant of a semi-infinite skew-symmetric matrix. We show that perturbatively in the weak coupling limit the octagon is given by a determinant constructed from the polylogarithms evaluating ladder Feynman graphs. We also give a simple operator representation of the octagon in terms of a vacuum expectation value of massless free bosons or fermions living in the rapidity plane. arXiv:1905.11467v1 [hep-th] 27 May 20191 The fact that the sum over virtual particles can be written as a Fredholm pfaffian has been noticed before in [14].(1.7) 2 The integrability of the fishnet Feynman graphs has been first established by A. Zamolodchikov [21]. 3 By Zhukovsky plane we mean the rapidity plane with two simple branch points at u = ±2g. A similar operator representation has been proposed in [22] for the three-point function of non-BPS operators.

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“…In order to verify intermediate steps in the procedure as well as the final formula we also calculated the desired overlaps numerically. The Bethe states were constructed either by using the appendix E.5 of [39] or by explicitly diagonalizing the Hamiltonian. The corresponding Bethe roots have been obtained with the "Fast Bethe Solver" program [40][41][42].…”

Section: Strategy Of Derivationmentioning

confidence: 99%

Spin chain overlaps and the twisted Yangian

Leeuw

Gombor

Kristjansen³

et al. 2020

J. High Energ. Phys.

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Using considerations based on the thermodynamical Bethe ansatz as well representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the SO(6) spin chain and matrix product states built from matrices whose commutators generate an irreducible representation of so(5). The latter play the role of boundary states in a domain wall version of N = 4 SYM theory which has nonvanishing, SO(5) symmetric vacuum expectation values on one side of a co-dimension one wall. This theory, which constitutes a defect CFT, is known to be dual to a D3-D7 probe brane system. We likewise show that the same methodology makes it possible to prove an overlap formula, earlier presented without proof, which is of relevance for the similar D3-D5 probe brane system.

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Asymptotic four point functions

Cited by 60 publications

References 94 publications

One-point functions in AdS/dCFT

One-point functions in AdS/dCFT

The octagon as a determinant

Spin chain overlaps and the twisted Yangian

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