Dual EFT bootstrap: QCD flux tubes

We explore the correspondence between geometric function theory (GFT) and quantum field theory (QFT). The crossing symmetric dispersion relation provides the necessary tool to examine the connection between GFT, QFT, and effective field theories (EFTs), enabling us to connect with the crossing-symmetric EFT-hedron. Several existing mathematical bounds on the Taylor coefficients of Typically Real functions are summarized and shown to be of enormous use in bounding Wilson coefficients in the context of 2-2 scattering. We prove that two-sided bounds on Wilson coefficients are guaranteed to exist quite generally for the fully crossing symmetric situation. Numerical implementation of the GFT constraints (Bieberbach-Rogosinski inequalities) is straightforward and allows a systematic exploration. A comparison of our findings obtained using GFT techniques and other results in the literature is made. We study both the three-channel as well as the two-channel crossing-symmetric cases, the latter having some crucial differences. We also consider bound state poles as well as massless poles in EFTs. Finally, we consider nonlinear constraints arising from the positivity of certain Toeplitz determinants, which occur in the trigonometric moment problem.

Section: Jhep12(2021)203mentioning

confidence: 96%

“…If so, how do we go about showing this? This question has been investigated by several groups starting with the seminal works [1][2][3][4] followed more JHEP12(2021)203 recently by [5][6][7][8][9][10][11][12][13]. The typical starting point is to use a fixed-t dispersion relation and examine the constraints imposed by crossing symmetry.…”

Section: Introductionmentioning

confidence: 99%

QFT, EFT and GFT

Raman

Sinha

2021

“…The generalization of the unitarity constraint (5.1) was worked out in [24]. 20 So although generalizing our work to 3d would involve significant work, at least all the pieces have already been assembled and are waiting to be used.…”

Section: Jhep02(2022)146mentioning

confidence: 99%

“…In this paper we will refer to it as the numerical S-matrix bootstrap. The S-matrix bootstrap gained further attention in recent years, see [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The recent work [23,24] made a concrete proposal for how to extended the S-matrix bootstrap to accommodate form factors and spectral densities.…”

Section: Jhep02(2022)146 1 Introductionmentioning

confidence: 99%

Bootstrapping 2d ϕ4 theory with Hamiltonian truncation data

Chen

Fitzpatrick

Karateev

2022

We combine the methods of Hamiltonian Truncation and the recently proposed generalisation of the S-matrix bootstrap that includes local operators to determine the two-particle scattering amplitude and the two-particle form factor of the stress tensor at s > 0 in the 2d ϕ4 theory. We use the form factor of the stress tensor at s ≤ 0 and its spectral density computed using Lightcone Conformal Truncation (LCT), and inject them into the generalized S-matrix bootstrap set-up. The obtained results for the scattering amplitude and the form factor are fully reliable only in the elastic regime. We independently construct the “pure” S-matrix bootstrap bounds (bootstrap without including matrix elements of local operators), and find that the sinh-Gordon model and its analytic continuation the “staircase model” saturate these bounds. Surprisingly, the ϕ4 two-particle scattering amplitude also very nearly saturates these bounds, and moreover is extremely close to that of the sinh-Gordon/staircase model.

“…• It will be appealing to see the implications of our bounds and sum rules (2.21) to S-matrix bootstrap for pion amplitudes [36,37,54] and to the dual the S-matrix bootstrap [55][56][57][58]. n,r,m (µ, δ), χ (1) n,r,m (µ, δ), χ (2) n,r,m (µ, δ) First, we take the combinations…”

Section: Summary and Future Directionsmentioning

confidence: 99%

Positivity and geometric function theory constraints on pion scattering

Zahed

2021

This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with O(N) global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the z-variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for O(N) model in z-variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the O(N) model arising from the fully crossing symmetric dispersion relations. We have derived three sets of positivity conditions. We have obtained two-sided bounds on Taylor coefficients of physical Pion amplitudes around the crossing symmetric point (for example, π+π−→ π0π0) applying the positivity conditions and the Bieberbach-Rogosinski inequalities from geometric function theory.