PIRSA:14090072 Scientific Series Quantum Fields and Strings Condensed Matter Strong Gravity

DOI10.48660/14090072

Series: Quantum Matter

(2014). Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography. Perimeter Institute. https://pirsa.org/14090072

Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography. Perimeter Institute, Sep. 19, 2014, https://pirsa.org/14090072 

@misc{ pirsa_PIRSA:14090072,
  doi = {10.48660/14090072},
  url = {https://pirsa.org/14090072},
  author = {},
  keywords = {Quantum Fields and Strings, Condensed Matter, Strong Gravity},
  language = {en},
  title = {Conformal field theories at non-zero temperature: operator product expansions, Monte Carlo, and holography},
  publisher = {Perimeter Institute},
  year = {2014},
  month = {sep},
  note = {PIRSA:14090072 see, \url{https://pirsa.org}}
}

Abstract

We discuss properties of 2-point functions in CFTs in 2+1D at finite temperature. For concreteness, we focus on those involving conserved flavour currents, in particular on the associated conductivity. At frequencies much greater than the temperature, ω >> T, the ω dependence of the conductivity can be computed from the operator product expansion (OPE) between the currents and operators which acquire a non-zero expectation value at T > 0. Such results are found to be in excellent agreement with quantum Monte Carlo studies of the O(2) Wilson-Fisher CFT. Results for the conductivity and other observables are also obtained in vector 1/N expansions. We match these large ω results to the corresponding correlators of holographic representations of the CFT: the holographic approach then allows us to extrapolate to small ω/T. Other holographic studies implicitly only used the OPE between the currents and the energy-momentum tensor, and this yields the correct leading large ω behavior for a large class of CFTs. However, for the Wilson-Fisher CFT a relevant “thermal” operator must also be considered, and then consistency with the Monte Carlo results is obtained without a previously needed ad hoc rescaling of the T value [1]. We also use the OPE to prove sum rules obeyed by the conductivity. **In collaboration with A. Katz, S. Sachdev and E. Sørensen** [1] WWK, E. Sørensen, S. Sachdev, Nat. Phys. 10, 361 (2014)

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