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Bootstrap and collider physics of parity violating conformal field theories in d = 3

  • Subham Dutta ChowdhuryEmail author
  • Justin R. David
  • Shiroman Prakash
Open Access
Regular Article - Theoretical Physics
  • 44 Downloads

Abstract

We study the crossing equations in d = 3 for the four point function of two U(1) currents and two scalars including the presence of a parity violating term for the s-channel stress tensor exchange. We show the existence of a new tower of double trace operators in the t-channel whose presence is necessary for the crossing equation to be satisfied and determine the corresponding large spin parity violating OPE coefficients. Contrary to the parity even situation, we find that the parity odd s-channel light cone stress tensor block do not have logarithmic singularities. This implies that the parity odd term does not contribute to anomalous dimensions in the crossed channel at this order light cone expansion. We then study the constraints imposed by reflection positivity and crossing symmetry on such a four point function. We reproduce the previously known parity odd collider bounds through this analysis. The contribution of the parity violating term in the collider bound results from a square root branch cut present in the light cone block as opposed to a logarithmic cut in the parity even case, together with the application of the Cauchy-Schwarz inequality.

Keywords

Conformal Field Theory Field Theories in Lower Dimensions Space-Time Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Centre for High Energy PhysicsIndian Institute of ScienceBangaloreIndia
  2. 2.Department of Physics and Computer ScienceDayalbagh Educational InstituteAgraIndia
  3. 3.Tata Institute of Fundamental ResearchMumbaiIndia

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