S-matrix bootstrap for resonances

Doroud, Nima; Miró, Joan Elias

doi:10.1007/jhep09(2018)052

Cited by 37 publications

(51 citation statements)

References 26 publications

(52 reference statements)

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“…The symmetry-breaking vacua and the symmetry-preserving vacuum coexist in the 11) and the two solutions coincide at m 2 = λ 2π . 9 The symmetry-breaking vacuum is always energetically favored in this range. A similar situation happens in flat space when there is a first-order phase transition.…”

Section: Adsmentioning

confidence: 99%

“…Rather recently the approach was also successfully applied to conformal field theories in higher dimensions [4], most notably to the three-dimensional Ising model [5], with the help of numerical implementation and has been a subject of active research since then. Motivated by this success, the original idea of the S-matrix bootstrap was also revisited, resulting in several interesting outcomes [6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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A study of quantum field theories in AdS at finite coupling

Carmi

Pietro

Komatsu

2019

J. High Energ. Phys.

191

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We study the O(N ) and Gross-Neveu models at large N on AdS d+1 background.Thanks to the isometries of AdS, the observables in these theories are constrained by the SO(d, 2) conformal group even in the presence of mass deformations, as was discussed by Callan and Wilczek [1], and provide an interesting two-parameter family of quantities which interpolate between the S-matrices in flat space and the correlators in CFT with a boundary. For the actual computation, we judiciously use the spectral representation to resum loop diagrams in the bulk. After the resummation, the AdS 4-particle scattering amplitude is given in terms of a single unknown function of the spectral parameter. We then "bootstrap" the unknown function by requiring the absence of double-trace operators in the boundary OPE. Our results are at leading nontrivial order in 1 N , and include the full dependence on the quartic coupling, the mass parameters, and the AdS radius. In the bosonic O(N ) model we study both the massive phase and the symmetry-breaking phase, which exists even in AdS 2 evading Coleman's theorem, and identify the AdS analogue of a resonance in flat space. We then propose that symmetry breaking in AdS implies the existence of a conformal manifold in the boundary conformal theory. We also provide evidence for the existence of a critical point with bulk conformal symmetry, matching existing results and finding new ones for the conformal boundary conditions of the critical theories. For the Gross-Neveu model we find a bound state, which interpolates between the familiar bound state in flat space and the displacement operator at the critical point.

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Section: Adsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A study of quantum field theories in AdS at finite coupling

Carmi

Pietro

Komatsu

2019

J. High Energ. Phys.

191

View full text Add to dashboard Cite

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“…In the dispersion relations (11) we have trivialized crossing taking into account the O(N ) symmetry of the problem and possible large energy behaviour. The remaining ingredient 12 Note that the subtraction constants S(2) satisfy the crossing condition S(2) = d · S(2) which fixes one of the constants in terms of the other two (e.g. we can eliminate S sing (2) by writing S sing (2) = 1 2 [(N + 2)S sym (2) − N S anti (2)]).…”

Section: Numerical Setupmentioning

confidence: 99%

“…We could maximize bound state couplings g 2 n as originally proposed in [2] or the value of the S-matrix at a symmetric point s = t = 2 as in the pion toy models in [3] or we could impose a zero at a given value for some component (i.e. add a resonance) and maximize its slope as in [12]. In the next section we will start with a few such maximization questions (some of which are mixed versions of the ones just mentioned) which lead to the integrable S-matrices discussed previously.…”

Section: Numerical Setupmentioning

confidence: 99%

Adding flavour to the S-matrix bootstrap

Córdova

Vieira

2018

J. High Energ. Phys.

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We explore the S-matrices of gapped, unitary, Lorentz invariant quantum field theories with a global O(N ) symmetry in 1+1 dimensions. We extremize various cubic and quartic couplings in the two-to-two scattering amplitudes of vector particles. Saturating these bounds, we encounter known integrable models with O(N ) symmetry such as the O(N ) Gross-Neveu and non-linear sigma models and the scattering of kinks in the sine-Gordon model. We also considered more general mass spectra for which we move away from the integrable realm. In this regime we find (numerically, through a large N analysis and sometimes even analytically) that the S-matrices saturating the various coupling bounds have an extremely rich structure exhibiting infinite resonances and virtual states in the various kinematical sheets. They are rather exotic in that they admit no particle production yet they do not obey Yang-Baxter equations. We discuss their physical (ir)relevance and speculate, based on some preliminary numerics, that they might be close to more realistic realistic theories with particle production.1 The higher dimensional counterpart is currently being investigated in [5] 2 In two dimensions the initial and final rapidities are the same because of energy-momentum conservation.

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“…2. Very similar dispersion relations appear in the derivation of the superluminality bound [31], in the proof of the a-theorem [32] and in the recent work on the S-matrix bootstrap [33,34]. The integral in (5) receives contributions from the pole at s = 0 where…”

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confidence: 62%

QCD β -function on the string worldsheet

Dubovsky

2018

Phys. Rev. D

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We consider confining strings in pure gluodynamics and its extensions with adjoint (s)quarks. We argue that there is a direct map between the set of bulk fields and the worldsheet degrees of freedom. This suggests a close link between the worldsheet S-matrix and parton scattering amplitudes. We report an amusing relation between the Polchinski-Strominger amplitude responsible for the breakdown of integrability on the string worldsheet and the Yang-Mills β-function b0 = Dcr − D ph 6 .Here b0 = 11/3 is the one-loop β-function coefficient in the pure Yang-Mills theory, Dcr = 26 is the critical dimension of bosonic strings and D ph = 4 is the dimensionality of the physical space-time we live in. A natural extension of this relation continues to hold in the presence of adjoint (s)quarks, connecting two of the most celebrated anomalies-the scale anomaly in quantum chromodynamics (QCD) and the Weyl anomaly in string theory.Our description of strong interactions is embarrassingly incomplete without understanding of strings (flux tubes) responsible for quark confinement. The stringy nature of the real world QCD manifests itself through the existence of Regge trajectories-families of hadrons following a quadratic relation between the spin J and the mass M ,s is the string tension. Critical string theory was born exactly 50 years ago [1] as an effort to explain this behavior. Theoretical and lattice studies of confining strings are natural to perform in a more pristine environment obtained by eliminating dynamical quarks in the fundamental representation of the gauge group SU (N c ). As a result, strings do not break and one may study dynamics of an isolated infinitely long flux tube. In lattice simulations a long string state is created by the Polyakov loop operator [2]wrapped around one of the spatial directions.In the planar limit [3], N c → ∞, the worldsheet excitations decouple from bulk degrees of freedom and define a microscopic two-dimensional theory. Importantly, the worldsheet theory itself remains interacting even in the strict planar limit. Furthermore, there is mounting evidence that the worldsheet dynamics is not described by a conventional local quantum field theory, but rather exhibits characteristic features of a gravitational theory [4].Much of the recent progress is triggered by identification of the worldsheet S-matrix as a primary fundamental observable [5]. This S-matrix is a natural theoretical target and at the same time has proven itself as an indispensable tool for the analysis of lattice data [6,7].Current lattice results [8][9][10][11][12][13] (see [14,15] for reviews) for both D = 4 and D = 3 gluodynamics can be summa-rized by the Axionic String Ansatz (ASA) [16,17]. According to the ASA the only stable asymptotic degrees of freedom on the confining string are massless Goldstone excitations X i (i = 1, . . . , D − 2) associated with spontaneous breaking of translations in the presence of a long string. In addition, worldsheet scattering at D = 4 exhibits a metastable resonance-the worldsheet ax...

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S-matrix bootstrap for resonances

Cited by 37 publications

References 26 publications

A study of quantum field theories in AdS at finite coupling

A study of quantum field theories in AdS at finite coupling

Adding flavour to the S-matrix bootstrap

QCD β -function on the string worldsheet

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