Operator product expansions in non-relativistic CFTs

by Zuhair Khandker (Boston U.)

Friday 13 Feb 2015, 16:00 → 17:00 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

[this is a seminar by vydio link, the speaker being physically in the US] Recent interest in non-relativistic conformal field theories (NRCFTs) stems from novel experiments involving cold, atomic gases with tunable S-wave scattering length, a. Adjusting the scattering length interpolates these gases between regimes of BCS (1/a ∼ −∞) and BEC (1/a ∼ +∞) superfluidity. At the midpoint (1/a ∼ 0) of this BCS-BEC crossover, the system is in a strongly-coupled regime called unitarity and is an NRCFT. After reviewing these facts, I will discuss recent work aimed at developing an important tool in the study of NRCFTs and the unitarity regime: the operator product expansion (OPE). I will discuss applications of the OPE and then turn to its mathematical structure. I will demonstrate that in the charged (non-zero particle number) sector of NRCFTs, the OPE exhibits powerful properties just as in relativistic CFTs. Specifically, (i) OPE coefficients of descendant operators are determined by the underlying primary, (ii) the OPE converges, and (iii) convergence is exponentially fast in operator dimensions. Given the similarities with CFTs, I will conclude by posing an intriguing question for future study, namely, is there an NRCFT analog of the conformal bootstrap?