Conformal perturbation theory and higher spin entanglement entropy on the torus

Abstract

We study the free fermion theory in 1+1 dimensions deformed by chemical potentials for holomorphic, conserved currents at finite temperature and on a spatial circle. For a spin-three chemical potential µ, the deformation is related at high temperatures to a higher spin black hole in hs[0] theory on AdS 3 spacetime. We calculate the order µ 2 corrections to the single interval Rényi and entanglement entropies on the torus using the bosonized formulation. A consistent result, satisfying all checks, emerges upon carefully accounting for both perturbative and winding mode contributions in the bosonized language. The order µ 2 corrections involve integrals that are finite but potentially sensitive to contact term singularities. We propose and apply a prescription for defining such integrals which matches the Hamiltonian picture and passes several non-trivial checks for both thermal corrections and the Rényi entropies at this order. The thermal corrections are given by a weight six quasi-modular form, whilst the Rényi entropies are controlled by quasi-elliptic functions of the interval length with modular weight six. We also point out the well known connection between the perturbative expansion of the partition function in powers of the spin-three chemical potential and the Gross-Taylor genus expansion of large-N Yang-Mills theory on the torus. We note the absence of winding mode contributions in this connection, which suggests qualitatively different entanglement entropies for the two systems.

Universal corrections to entanglement entropy of local quantum quenches

“…The resulting (holomorphic) conformal perturbation theory is analytically tractable, but requires a careful definition of the prescription for integrating holomorphic functions with singularities over the complex plane. Such a prescription was made explicit in [42,43], yielding results consistent with the canonical or Hamiltonian approach, and satisfying various other consistency checks including holographic ones.…”

Rényi divergences from Euclidean quenches

“…(C.13) 10 There are some differences of signs in contrast to the CFT cases y −a+a− a ± y a+a− = a ± y ∓1 , y −L0 L ±1 y L0 = L ±1 y ±1 . This is because of the commutation relation [a − , a + ] = 1 and [L 0 , L ±1 ] = ∓L ±1 , [a + a − , a ±1 ] = ±a ±1 .…”

“…Such a deformation was studied in [8][9][10] to evaluate higher spin corrections to entanglement entropy. In [8], the corrections to the partition function to O(µ 2 ) was also evaluated.…”

Entanglement entropy for descendent local operators in 2D CFTs

“…Though there are divergences in the global contribution [31], such divergences can be regulated appropriately. Actually there are various definite extensive examples [34][35][36][37][38] to show that global contribution is finite. Actually, we can get a more general conformal transformation for the operators, which is an expansion for the previous result Open Access.…”