A Lorentzian inversion formula for defect CFT

Self Cite

101

For a single free scalar field in d ≥ 2 dimensions, almost all the unitary conformal defects must be ‘trivial’ in the sense that they cannot hold interesting dynamics. The only possible exceptions are monodromy defects in d ≥ 4 and co-dimension three defects in d ≥ 5. As an intermediate result we show that the n-point correlation functions of a conformal theory with a generalized free spectrum must be those of the generalized free theory.

Section: Jhep01(2021)060mentioning

confidence: 99%

Line and surface defects for the free scalar field

Lauria

Liendo

Rees

et al. 2021

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101

“…correlation functions that involve one or more non-local operators like line or surface defects etc. Once again, the Calogero-Sutherland models for the relevant wave functions ψ are known from [30], at least in the scalar case. From this work on may also infer the analogue of the factorΩ.…”

Section: Jhep10(2020)004 6 Conclusion and Outlookmentioning

confidence: 99%

Conformal group theory of tensor structures

Burić

Schomerus

Isachenkov

2020

Self Cite

The decomposition of correlation functions into conformal blocks is an indispensable tool in conformal field theory. For spinning correlators, non-trivial tensor structures are needed to mediate between the conformal blocks, which are functions of cross ratios only, and the correlation functions that depend on insertion points in the d-dimensional Euclidean space. Here we develop an entirely group theoretic approach to tensor structures, based on the Cartan decomposition of the conformal group. It provides us with a new universal formula for tensor structures and thereby a systematic derivation of crossing equations. Our approach applies to a ‘gauge’ in which the conformal blocks are wave functions of Calogero-Sutherland models rather than solutions of the more standard Casimir equations. Through this ab initio construction of tensor structures we complete the Calogero-Sutherland approach to conformal correlators, at least for four-point functions of local operators in non-supersymmetric models. An extension to defects and superconformal symmetry is possible.

“…In the spinning case, one must additionally account for the Jacobian matrix ∂y a /∂x m . 5 Next we use conformal symmetry to express the correlator in terms of two vectors. This is similar to expressing the correlator in terms of two scalar cross-ratios, with the difference that here we fix two, instead of the customary three, positions using translations and special conformal transformations to express the correlator in terms of the remaining two position vectors.…”

Section: Regge Limitmentioning

confidence: 99%

“…In recent years it has been shown that powerful analytical results for scattering amplitudes in quantum field theory, namely the Froissart-Gribov formula and dispersion relations, have equally powerful CFT analogues in the Lorentzian inversion formula [1][2][3][4][5] and the two-variable CFT dispersion relation [6,7]. Dispersion relations reconstruct a scattering amplitude from the discontinuity of the amplitude, while the Froissart-Gribov formula extracts the partial wave coefficients from the discontinuity and makes their analyticity in spin manifest.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Antunes

Costa

Hansen

et al. 2021

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.