The significance of conformal inversion in quantum field theory

Koller, K.

doi:10.1007/bf01614094

Cited by 42 publications

(50 citation statements)

References 9 publications

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“…One is a method called the Euclidean connection developed by Alhassid and his collaborators [17,[23][24][25], which is based on group contractions and expansions, and the other is a method developed by Kerimov [26] (see also [27,28]), which is based on intertwining operators between Weyl equivalent principal series representations of dynamical groups. Since it is already known in the context of both CFT [29] and AdS/CFT correspondence [30] that two-point functions can be regarded as kernels of intertwining operators between two representations of conformal group conjugate with each other by Weyl reflection, it is natural to expect that one can also formulate purely algebraic methods to compute momentum-space CFT two-point functions along the line of Kerimov's method. We would like to leave this issue for future studies.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Recurrence relations for finite-temperature correlators via AdS2/CFT1

Ohya

2013

J. High Energ. Phys.

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This note is aimed at presenting a new algebraic approach to momentum-space correlators in conformal field theory. As an illustration we present a new Lie-algebraic method to compute frequency-space two-point functions for charged scalar operators of CFT 1 dual to AdS 2 black hole with constant background electric field. Our method is based on the real-time prescription of AdS/CFT correspondence, Euclideanization of AdS 2 black hole and projective unitary representations of the Lie algebra sl(2, ) ⊕ sl(2, ). We derive novel recurrence relations for Euclidean CFT 1 two-point functions, which are exactly solvable and completely determine the frequencyand charge-dependences of two-point functions. Wick-rotating back to Lorentzian signature, we obtain retarded and advanced CFT 1 two-point functions that are consistent with the known results. *

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Section: Conclusion and Discussionmentioning

confidence: 99%

Recurrence relations for finite-temperature correlators via AdS2/CFT1

Ohya

2013

J. High Energ. Phys.

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“…In ordinary conformal field theory in d dimensions, a comprehensive discussion of the building blocks for the two-and three-point correlation functions of primary fields was given by Osborn and Petkou [23] who built on the earlier works by Mack [24] and others [25][26][27][28][29][30]. Their analysis was extended to superconformal field theories formulated in superspace by Osborn and Park [21,[31][32][33].…”

Section: Two-point Functionsmentioning

confidence: 99%

“…Such superfields are defined on a supersymmetric subspace of M 3|6 × CP 1 known as the analytic subspace. It is parametrised by coordinates 27) while the harmonic derivative ∂ ++ acquires additional terms…”

Section: Jhep08(2015)125mentioning

confidence: 99%

Implications of N = 4 $$ \mathcal{N}=4 $$ superconformal symmetry in three spacetime dimensions

Buchbinder

Kuzenko

Samsonov

2015

J. High Energ. Phys.

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We study implications of N = 4 superconformal symmetry in three dimensions, thus extending our earlier results in [1] devoted to the N ≤ 3 cases. We show that the three-point function of the supercurrent in N = 4 superconformal field theories contains two linearly independent forms. However, only one of these structures contributes to the three-point function of the energy-momentum tensor and the other one is present in those N = 4 superconformal theories which are not invariant under the mirror map. We point out that general N = 4 superconformal field theories admit two inequivalent flavour current multiplets and show that the three-point function of each of them is determined by one tensor structure. As an example, we compute the two-and three-point functions of the conserved currents in N = 4 superconformal models of free hypermultiplets. We also derive the universal relations between the coefficients appearing in the two-and threepoint correlators of the supercurrent and flavour current multiplets in all superconformal theories with N ≤ 4 supersymmetry. Our derivation is based on the use of Ward identities in conjunction with superspace reduction techniques.

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“…It is widely recognized that, up to a few numerical factors, two-point functions for primary operators of conformal field theory (CFT) are completely determined through the SO (2, d) conformal symmetry in any spacetime dimension d ≥ 1. However, it is less recognized-or generally unappreciated except to experts [1][2][3][4]-that two-point functions in CFT have special representation-theoretic meanings: they are the integral kernels of intertwining operators for two equivalent representations of conformal algebra so (2, d). Namely, once given a two-point function for a primary operator of scaling dimension ∆, we can construct an operator G ∆ which maps a primary state of scaling dimension d − ∆ to another primary state of scaling dimension ∆.…”

Section: Introductionmentioning

confidence: 99%

“…Namely, once given a two-point function for a primary operator of scaling dimension ∆, we can construct an operator G ∆ which maps a primary state of scaling dimension d − ∆ to another primary state of scaling dimension ∆. 1 Such operator G ∆ -the intertwining operator-satisfies the following commutative diagram and operator identities (intertwining relations):…”

Section: Introductionmentioning

confidence: 99%

Intertwining operator in thermal CFTd

Ohya

2017

Int. J. Mod. Phys. A

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It has long been known that two-point functions of conformal field theory (CFT) are nothing but the integral kernels of intertwining operators for two equivalent representations of conformal algebra. Such intertwining operators are known to fulfill some operator identities -the intertwining relations -in the representation space of conformal algebra. Meanwhile, it has been known that the S-matrix operator in scattering theory is nothing but the intertwining operator between the Hilbert spaces of in-and out-particles. Inspired by this algebraic resemblance, in this paper, we develop a simple Lie-algebraic approach to momentum-space two-point functions of thermal CFT living on the hyperbolic space-time H 1 × H d−1 by exploiting the idea of Kerimov's intertwining operator approach to exact S-matrix. We show that in thermal CFT on H 1 × H d−1 , the intertwining relations reduce to certain linear recurrence relations for two-point functions in the complex momentum space. By solving these recurrence relations, we obtain the momentum-space representations of advanced and retarded two-point functions as well as positive-and negative-frequency two-point Wightman functions for a scalar primary operator in arbitrary space-time dimension d ≥ 3.

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The significance of conformal inversion in quantum field theory

Cited by 42 publications

References 9 publications

Recurrence relations for finite-temperature correlators via AdS2/CFT1

Recurrence relations for finite-temperature correlators via AdS2/CFT1

Implications of N = 4 $$ \mathcal{N}=4 $$ superconformal symmetry in three spacetime dimensions

Intertwining operator in thermal CFTd

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