Year: 2024
Type: article
Abstract: A bstract The mutual information, I 2 , of general spacetime regions is expected to capture the full data of any conformal field theory (CFT). For spherical regions, this data can be accessed from long-distance expansions of the mutual information of pairs of regions as well as of suitably chosen linear combinations of mutual informations involving more than two regions and their unions — namely, the N -partite information, I N . In particular, the leading term in the I 2 long-distance expansion is fully determined by the spin and conformal dimension of the lowest-dimensional primary of the theory. When the operator is a scalar, an analogous formula for the tripartite information I 3 contains information about the OPE coefficient controlling the fusion of such operator into its conformal family. When it is a fermionic field, the coefficient of the leading term in I 3 vanishes instead. In this paper we present an explicit general formula for the long-distance four-partite information I 4 of general CFTs whose lowest-dimensional operator is a fermion ψ . The result involves a combination of four-point and two-point functions of ψ and $$ \overline{\psi} $$ ψ ¯ evaluated at the locations of the regions. We perform explicit checks of the formula for a (2 + 1)-dimensional free fermion in the lattice finding perfect agreement. The generalization of our result to the N -partite information (for arbitrary N ) is also discussed. Similarly to I 3 , we argue that I 5 vanishes identically at leading order for general fermionic theories, while the I N with N = 7 , 9 , … only vanish when the theory is free.
Source: Journal of High Energy Physics
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Awards: G1105844351, G1175115578, G1455481585, G1855990336, G2262748287, G2309174360, G2525577871, G2585926585, G279363373, G300979063, G34346518, G3480869486, G377623426, G425668148, G430777504, G4691964718, G491712853, G5080475149, G5421974903, G586857820, G624877701, G7391727506, G7525315620, G7805626310, G7863371703, A theory of waves for an ocean of quarks, G8497050386, G8920660035, G99296377
OpenAlex ID: W4405979999