Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · hep-th/9411014

Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules

K. Hamada
View original source ↗Read source document ↗Export metadata ↓

Abstract

The recursion relations of 2D quantum gravity coupled to the Ising model discussed by the author previously are reexamined. We study the case in which the matter sector satisfies the fusion rules and only the primary operators inside the Kac table contribute. The theory involves unregularized divergences in some of correlators. We obtain the recursion relations which form a closed set among well-defined correlators on sphere, but they do not have a beautiful structure that the bosonized theory has and also give an inconsistent result when they include an ill-defined correlator with the divergence. We solve them and compute the several normalization independent ratios of the well-defined correlators, which agree with the matrix model results.

Explore related subjects

hep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

K. Hamada. 1994-11-02. Recursion Relations in Liouville Gravity coupled to Ising Model satisfying Fusion Rules. https://doi.org/10.1103/physrevd.51.6959

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Euler-Heisenberg actions in higher dimensions

Using Schwinger's proper-time formalism, we compute the one-loop effective action in both spinor and scalar quantum electrodynamics in $d=2n>4$ dimensions using algebraic techniques. We derive the closed form expression for the corresponding Euler-Heisenberg Lagrangian, and extract its weak-field approximation in 6, 8 and 10 dimensions in terms of invariants of the electromagnetic field. A subsequent analysis of pair production in $d$ dimensions is given. We also elaborate on conformal actions for the electromagnetic field in $d=2n>4$ dimensions. In the $d=6$ and 8 cases, such actions are generated by DeWitt's coefficients $a_3$ and $a_4$ which, for completeness, are re-computed in this work for spinor QED and scalar QED, respectively.

hep-th↗
arXiv2026

Finite-time memory detectors and fully constraining Faddeev-Kulish dressings in QED and gravity

We show that for both QED and perturbative quantum gravity, time dependent Faddeev-Kulish dressings can be fully constrained either by symmetry, or by demanding that they reproduce the correct outgoing classical memory contribution. For gravity, we show that using this dressing to construct finite-time Fock spaces allows us to recover both the first order gravitational memory, as well as higher order Christodoulou contributions from the gravitational field. We explain how these higher order perturbative corrections arise in inclusive in-in calculations.

hep-th↗
arXiv2026

Effect of $ξRϕ^2$ non-minimal coupling on gravitational light bending

We investigate the bending of massless fields by a massive object in the presence of a curvature-scalar $\sqrt{-g}ξR ϕ^2$ non-minimal coupling up to one loop, using the perturbative quantum gravity computations. It is well known that without such coupling a self interacting scalar field theory cannot be renormalised in the presence of gravity. The massive object is modelled by a massive scalar $ϕ$, and it is assumed to be non-relativistic, e.g., a star. We compute the 2-2 scattering of massless scalar and photons off this object via graviton exchanges. Assuming both $ξ$ and the bending angle to be small, we use the eikonal approximation to compute the angle up to ${\cal O}(ξG^2)$. At tree level $({\cal O}(ξG))$ we find no bending, and hence the ${\cal O}(ξG^2)$ result happens to be leading in this case. The non-minimal vertices are qualitatively different from that of the standard minimal ones, e.g. $ \sqrt{G} h_{μν} T^{μν}$, as the former contains explicit momenta of the gravitons instead of the scalar, complementing the second. The bending angle is found to behave like $\sim b^{-7}$, where $b$ is the impact parameter. We have emphasised the qualitative differences of our results from that of the well studied minimal case.

hep-th↗