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Carrollian Conformal Theories in Momentum Space

Raffaele Marotta, Arvind Shekar, Mritunjay Verma

Abstract

We consider the Carrollian conformal field theories involving scalar operators in the momentum representation. The momentum space Ward identities are explicitly solved to obtain the different branches of 2 and 3 point Carrollian conformal correlators in the momentum space. The different branches are characterized by different analytic structures in the Carrollian energies. For specific values of the conformal dimensions, the three-point functions in momentum space exhibit logarithmic behaviour. This has no analogue in position space and instead originates from singularities in the Fourier transform relating position and momentum space correlators. We also analyze the Carrollian limit of CFT 2 and 3 point functions of scalar operators in momentum space. By taking different scalings of CFT correlators with respect to the speed of light, we obtain different branches of the Carrollian conformal correlators in the momentum space.

Carrollian Conformal Theories in Momentum Space

Abstract

We consider the Carrollian conformal field theories involving scalar operators in the momentum representation. The momentum space Ward identities are explicitly solved to obtain the different branches of 2 and 3 point Carrollian conformal correlators in the momentum space. The different branches are characterized by different analytic structures in the Carrollian energies. For specific values of the conformal dimensions, the three-point functions in momentum space exhibit logarithmic behaviour. This has no analogue in position space and instead originates from singularities in the Fourier transform relating position and momentum space correlators. We also analyze the Carrollian limit of CFT 2 and 3 point functions of scalar operators in momentum space. By taking different scalings of CFT correlators with respect to the speed of light, we obtain different branches of the Carrollian conformal correlators in the momentum space.

Paper Structure

This paper contains 30 sections, 260 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Review of the Carrollian conformal group and representations
  3. Position space Carrollian correlators
  4. Two point function
  5. Three point function
  6. Carrollian correlators from momentum space Ward identities
  7. Momentum space Ward identities
  8. Ward identity constraints
  9. 2-point function
  10. 3-point function
  11. Solutions of Ward identities
  12. 2-point function
  13. 3-point function
  14. Carrollian limit of CFT correlators
  15. 2-point function
  16. ...and 15 more sections

Figures (3)

  • Figure 1: The branch cut in the $s \equiv p^2c^2$ plane for the time ordered 2-point function in equation \ref{['5.116to']}.
  • Figure 2: The contour choice (shown in blue) for performing the $\omega$ integration in equation \ref{['5123ert']}. The red wiggly lines represent the two branch cuts due to the factors in denominator.
  • Figure 3: The contour choice for performing the $k^0$ integral in equation \ref{['4.82']}. There are a total of four branch points described in equation \ref{['5.130ty']}.