Conformal Regge theory at finite boost

Caron-Huot, Simon; Sandor, Joshua

doi:10.1007/jhep05(2021)059

Cited by 13 publications

(18 citation statements)

References 26 publications

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“…The extra phase comes from the additional Wick rotations. The final result matches the definition of the discontinuity in [42]. Note that z is continued an extra half circle in opposite directions for the first two lines in (4.4), so that with these definitions the relation to the dDisc in (2.14) remains valid.…”

Section: Ads Impact Parameter Spacesupporting

confidence: 66%

“…Next we have to analyze the discontinuities on the right hand side of the optical theorem (4.5). The discontinuity of the scalar s-channel block was recently computed in general without taking the Regge limit in [42] and we will review it here. The generalization to external spinning operators is done in section 4.4, after taking the Regge limit.…”

Section: S-channel Discontinuities In the Regge Limitmentioning

confidence: 99%

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The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop

Antunes,

Costa,

Hansen

et al. 2020

Preprint

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We derive an optical theorem for perturbative CFTs which computes the double discontinuity of conformal correlators from the single discontinuities of lower order correlators, in analogy with the optical theorem for flat space scattering amplitudes. The theorem takes a purely multiplicative form in the CFT impact parameter representation used to describe high-energy scattering in the dual AdS theory. We use this result to study four-point correlation functions that are dominated in the Regge limit by the exchange of the graviton Regge trajectory (Pomeron) in the dual theory. At one-loop the scattering is dominated by double Pomeron exchange and receives contributions from tidal excitations of the scattering states which are efficiently described by an AdS vertex function, in close analogy with the known Regge limit result for one-loop string scattering in flat space at finite string tension. We compare the flat space limit of the conformal correlator to the flat space results and thus derive constraints on the one-loop vertex function for type IIB strings in AdS and also on general spinning tree level type IIB amplitudes in AdS.

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Section: Ads Impact Parameter Spacesupporting

confidence: 66%

Section: S-channel Discontinuities In the Regge Limitmentioning

confidence: 99%

The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop

Antunes,

Costa,

Hansen

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…88 Another approach could be via alternative representations of the 4-point function having an extended region of analyticity, e.g. [92].…”

Section: Discussionmentioning

confidence: 99%

“…For this it might not be necessary to understand the Reggeon or more general light-ray operators, since the resummation procedure can be stopped at a point where the correlator is expressed as an integral of C(∆, ) over a region where LIF converges. See[92] for progress on these questions. Papers by this group of authors are characterized by the systematic use of momentum space in Lorentzian CFT.…”

mentioning

confidence: 99%

Distributions in CFT. Part II. Minkowski space

Kravchuk

Qiao

Rychkov

2021

J. High Energ. Phys.

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CFTs in Euclidean signature satisfy well-accepted rules, such as the convergent Euclidean OPE. It is nowadays common to assume that CFT correlators exist and have various properties also in Lorentzian signature. Some of these properties may represent extra assumptions, and it is an open question if they hold for familiar statistical-physics CFTs such as the critical 3d Ising model. Here we consider Wightman 4-point functions of scalar primaries in Lorentzian signature. We derive a minimal set of their properties solely from the Euclidean unitary CFT axioms, without using extra assumptions. We establish all Wightman axioms (temperedness, spectral property, local commutativity, clustering), Lorentzian conformal invariance, and distributional convergence of the s-channel Lorentzian OPE. This is done constructively, by analytically continuing the 4-point functions using the s-channel OPE expansion in the radial cross-ratios ρ, $$ \overline{\rho} $$ ρ ¯ . We prove a key fact that |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ < 1 inside the forward tube, and set bounds on how fast |ρ|, $$ \left|\overline{\rho}\right| $$ ρ ¯ may tend to 1 when approaching the Minkowski space.We also provide a guide to the axiomatic QFT literature for the modern CFT audience. We review the Wightman and Osterwalder-Schrader (OS) axioms for Lorentzian and Euclidean QFTs, and the celebrated OS theorem connecting them. We also review a classic result of Mack about the distributional OPE convergence. Some of the classic arguments turn out useful in our setup. Others fall short of our needs due to Lorentzian assumptions (Mack) or unverifiable Euclidean assumptions (OS theorem).

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“…(1.1) With this assumption, all the operators in a given sector are lifted together. The main motivation to this analysis comes from recent works on conformal Regge theory and lightcone bootstrap [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], which showed that CFT operators organize in families, or Regge trajectories. Hence, a twist gap corresponds to imposing that the leading Regge trajectory lies above a certain line.…”

Section: Jhep05(2021)111mentioning

confidence: 99%

Bootstrapping mixed correlators in $$ \mathcal{N} $$ = 4 super Yang-Mills

Bissi

Manenti

Vichi

2021

J. High Energ. Phys.

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We perform a numerical bootstrap study of the mixed correlator system containing the half-BPS operators of dimension two and three in $$ \mathcal{N} $$ N = 4 Super Yang-Mills. This setup improves on previous works in the literature that only considered single correlators of one or the other operator. We obtain upper bounds on the leading twist in a given representation of the R-symmetry by imposing gaps on the twist of all operators rather than the dimension of a single one. As a result we find a tension between the large N supergravity predictions and the numerical finite N results already at N∼ 100. A few possible solutions are discussed: the extremal spectrum suggests that at large but finite N, in addition to the double trace operators, there exists a second tower of states with smaller dimension. We also obtain new bounds on the dimension of operators which were not accessible with a single correlator setup. Finally we consider bounds on the OPE coefficients of various operators. The results obtained for the OPE coefficient of the lightest scalar singlet show evidences of a two dimensional conformal manifold.

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Conformal Regge theory at finite boost

Cited by 13 publications

References 26 publications

The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop

The perturbative CFT optical theorem and high-energy string scattering in AdS at one loop

Distributions in CFT. Part II. Minkowski space

Bootstrapping mixed correlators in $$ \mathcal{N} $$ = 4 super Yang-Mills

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