A next-to-leading Lüscher formula

Bombardelli, Diego

doi:10.1007/jhep01(2014)037

Cited by 18 publications

(32 citation statements)

References 69 publications

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“…Analyzing the analytic structure of the candidate solution will allow us to consistently define these contours in such a way that the TBA equations are satisfied, and by taking the integration contours back to the real line we can explicitly pick up the corresponding driving terms. Coming back to our simple example, it would be as if internal 50 Interestingly, it appears to be possible to obtain the same terms by viewing an excited state as a momentum dependent generalized defect operator [88]. 51 As we will see in chapter 7, there are very specific circumstances in which the situation is a little more subtle.…”

Section: Analytic Continuation Of Tba Equationsmentioning

confidence: 81%

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Integrability of the ${\rm Ad}{{{\rm S}}_{5}}\times {{{\rm S}}^{5}}$ superstring and its deformations

Tongeren

Stijn²

2014

J. Phys. A: Math. Theor.

103

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This article reviews the application of integrability to the spectral problem of strings on AdS 5 × S 5 and its deformations. We begin with a pedagogical introduction to integrable field theories culminating in the description of their finite-volume spectra through the thermodynamic Bethe ansatz. Next, we apply these ideas to the AdS 5 × S 5 string and in later chapters discuss how to account for particular integrable deformations. Through the AdS/CFT correspondence this gives an exact description of anomalous scaling dimensions of single trace operators in planar N = 4 supersymmetry Yang-Mills theory, its 'orbifolds', and β and γ-deformed supersymmetric Yang-Mills theory. We also touch upon some subtleties arising in these deformed theories. Furthermore, we consider complex excited states (bound states) in the su(2) sector and give their thermodynamic Bethe ansatz description. Finally we discuss the thermodynamic Bethe ansatz for a quantum deformation of the AdS 5 × S 5 superstring S-matrix, with close relations to among others Pohlmeyer reduced string theory, and briefly indicate more recent developments in this area.

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Section: Analytic Continuation Of Tba Equationsmentioning

confidence: 81%

“…In other words, denoting the number of bound states of length Q occurring in a given configuration by N Q we have 88) under the constraint…”

Section: The Bethe-yang Equations For Stringsmentioning

confidence: 99%

Integrability of the ${\rm Ad}{{{\rm S}}_{5}}\times {{{\rm S}}^{5}}$ superstring and its deformations

Tongeren

Stijn²

2014

J. Phys. A: Math. Theor.

103

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“…The total energy contains not only the particles' energies, but also the contribution of the sea of virtual particles. The next exponential correction contains two virtual particle pairs and a single pair which wraps twice around the cylinder [10]. For an exact description all of these virtual processes have to be summed up, which is provided by the Thermodynamic Bethe Ansatz (TBA) equations [11].…”

Section: Contentsmentioning

confidence: 99%

“…u|O|β 1 , β 2 R = F 3 (u + iπ, β 1 , β 2 ) ρ 1 (u)ρ 2 (β 1 , β 2 ) + O(e −mR ) (D.6) 10 In order to be comparable to the calculations of [17,18] we use their normalization for form factors, which is related to the normalization θ|θ = 2πδ(θ − θ).…”

Section: D1 Finite Volume Regularizationmentioning

confidence: 99%

Field theoretical derivation of Lüscher’s formula and calculation of finite volume form factors

Bajnok

Balog

Lajer

et al. 2018

J. High Energ. Phys.

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We initiate a systematic method to calculate both the finite volume energy levels and form factors from the momentum space finite volume two-point function. By expanding the two point function in the volume we extracted the leading exponential volume correction both to the energy of a moving particle state and to the simplest non-diagonal form factor. The form factor corrections are given in terms of a regularized infinite volume 3-particle form factor and terms related to the Lüsher correction of the momentum quantization. We tested these results against second order Lagrangian and Hamiltonian perturbation theory in the sinh-Gordon theory and we obtained perfect agreement.ArXiv ePrint: 1802.04021 1

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“…The key example here are the Lüscher corrections for the mass of a single particle [31] and their multiparticle generalization [32]. Once one wants to incorporate multiple wrapping corrections, the situation becomes much more complicated however in some cases this can be done [33].…”

Section: Jhep06(2017)058mentioning

confidence: 99%

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

Bajnok

Janik

2017

J. High Energ. Phys.

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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.

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A next-to-leading Lüscher formula

Cited by 18 publications

References 69 publications

Integrability of the ${\rm Ad}{{{\rm S}}_{5}}\times {{{\rm S}}^{5}}$ superstring and its deformations

Integrability of the ${\rm Ad}{{{\rm S}}_{5}}\times {{{\rm S}}^{5}}$ superstring and its deformations

Field theoretical derivation of Lüscher’s formula and calculation of finite volume form factors

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

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