Short-distance expansion for products of current-like operators

Thorsten Emig A, Giuseppe Bimonte

Carlo Pagani, Hidenori Sonoda

We discuss a general method of constructing the products of composite operators using the exact renormalization group formalism. Considering mainly the Wilson action at a generic fixed point of the renormalization group, we give an argument for the validity of short-distance expansions of operator products. We show how to compute the expansion coefficients by solving differential equations, and test our method with some simple examples.

Yihao Wang, Jiaju Zhang

We develop a systematic method to compute the subsystem fidelity and Rényi fidelity in two-dimensional conformal field theories (CFTs) from the operator product expansion of twist operators, and apply it to the subsystem quantum Bhattacharyya distance (BD) and Rényi-Bhattacharyya distance (RBD). We validate the method against exact results in the free massless fermion and boson theories, and then use it to compute the BD and RBD in holographic CFTs between two heavy primary states, between two thermal states, and between a heavy primary state and a thermal state. When the two states differ in their classical, order-$c$ data, the distances are of order $c$, and the states are distinguishable already at the level of classical gravity; when the leading data coincide, the distances are of order $1/c$ at every order of the short interval expansion, so that the distinguishability becomes a perturbative quantum gravity effect. For a heavy primary state and its thermal counterpart, the leading contribution to the BD appears at order $\ell^8$ and is of order $c^0$, whereas the RBD is generically of order $c$, in line with the earlier finding that a heavy primary state and a thermal state share the same order-$c$ entanglement entropy but have different order-$c$ Rényi entropies in the short interval expansion.

T. D. Lee

S. Boffi, F. Capuzzi, Paraskevi Demetriou +1 more

Dam Thanh Son, Ethan G. Thompson

We consider the operator product expansions for unitarity fermions. We compute the dynamic structure factor $S(\mathbf{q},\ensuremath{\omega})$ at large frequency and wave number away from the one-particle peak. The overall normalization of $S(\mathbf{q},\ensuremath{\omega})$ is determined by Tan's contact parameter, and the dependence on $\mathbf{q}$ and $\ensuremath{\omega}$ is obtained in closed analytic form. We also find energy deposited into the system by small, rapid variations of the inverse scattering length.