Abstract
We present a simple Lie-algebraic approach to momentum-space two-point functions of two-dimensional conformal field theory at finite temperature dual to the BTZ black hole. Making use of the real-time prescription of AdS/CFT correspondence and ladder equations of the Lie algebra so(2,2) ∼= sl(2,R)<sub>L</sub>⊕sl(2,R)<sub>R</sub>, we show that the finite-temperature two-point functions in momentum space satisfy linear recurrence relations with respect to the left and right momenta. These recurrence relations are exactly solvable and completely determine the momentum-dependence of retarded and advanced two-point functions of finite-temperature conformal field theory.
Highlights
Introduction and summaryConformal symmetry is powerful enough to constrain the possible forms of correlation functions in quantum field theory
We present a simple Lie-algebraic approach to momentum-space two-point functions of twodimensional conformal field theory at finite temperature dual to the BTZ black hole
Making use of the real-time prescription of AdS/CFT correspondence and ladder equations of the Lie algebra so(2, 2) ∼= sl(2, )L ⊕sl(2, )R, we show that the finite-temperature two-point functions in momentum space satisfy linear recurrence relations with respect to the left and right momenta
Summary
Conformal symmetry is powerful enough to constrain the possible forms of correlation functions in quantum field theory. It is important to develop efficient methods to compute momentumspace correlators directly through symmetry considerations, because Fourier transforms of positionspace correlators are hard in general In this short paper we continue our investigation [1] and present a novel Lie-algebraic approach to momentum-space two-point functions of conformal field theory at finite temperature by using the AdS/CFT correspondence. In contrast to the conventional approaches to momentum-space CFT correlators (such as Fourier-transform of position-space correlators or original real-time AdS/CFT prescription [4,5,6] that requires to solve bulk field equations explicitly), our Lie-algebraic method is quite simple and clarifies the role of conformal symmetry in momentumspace correlators in a direct way: For finite-temperature two-point functions in momentum space, conformal symmetry manifests itself in a form of recurrence relations, which are exactly solvable and, up to an overall normalization factor, completely determine the momentum dependence of two-point functions. We will see that our method correctly reproduces the known results [5, 8, 9]
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