27 research outputs found
String correlation functions of the spin-1/2 Heisenberg XXZ chain
We calculate certain string correlation functions, originally introduced as
order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain
at zero temperature and in the thermodynamic limit. For small distances, we
obtain exact results from Bethe Ansatz and exact diagonalization, whereas in
the large-distance limit, field-theoretical arguments yield an asymptotic
algebraic decay. We also make contact with two-point spin-correlation functions
in the asymptotic limit.Comment: 23 pages, 4 figures. An incomplete discussion on the limit to the
spin-spin correlation function is corrected on page 1
A Gauge-Gravity Relation in the One-loop Effective Action
We identify an unusual new gauge-gravity relation: the one-loop effective
action for a massive spinor in 2n dimensional AdS space is expressed in terms
of precisely the same function [a certain multiple gamma function] as the
one-loop effective action for a massive charged scalar in 4n dimensions in a
maximally symmetric background electromagnetic field [one for which the
eigenvalues of F_{\mu\nu} are maximally degenerate, corresponding in 4
dimensions to a self-dual field, equivalently to a field of definite helicity],
subject to the identification F^2 \Lambda, where \Lambda is the
gravitational curvature. Since these effective actions generate the low energy
limit of all one-loop multi-leg graviton or gauge amplitudes, this implies a
nontrivial gauge-gravity relation at the non-perturbative level and at the
amplitude level.Comment: 6 page
Large-order Perturbation Theory and de Sitter/Anti de Sitter Effective Actions
We analyze the large-order behavior of the perturbative weak-field expansion
of the effective Lagrangian density of a massive scalar in de Sitter and anti
de Sitter space, and show that this perturbative information is not sufficient
to describe the non-perturbative behavior of these theories, in contrast to the
analogous situation for the Euler-Heisenberg effective Lagrangian density for
charged scalars in constant electric and magnetic background fields. For
example, in even dimensional de Sitter space there is particle production, but
the effective Lagrangian density is nevertheless real, even though its
weak-field expansion is a divergent non-alternating series whose formal
imaginary part corresponds to the correct particle production rate. This
apparent puzzle is resolved by considering the full non-perturbative structure
of the relevant Feynman propagators, and cannot be resolved solely from the
perturbative expansion.Comment: 18 page