arXiv subjects

Corinne de Lacroix

Publications and source records attributed to Corinne de Lacroix.

8 recordsLinked to original sources

arXiv2024

Gravitational action for a massive Majorana fermion in 2d quantum gravity

We compute the gravitational action of a free massive Majorana fermion coupled to two-dimensional gravity on compact Riemann surfaces of arbitrary genus. The structure is similar to the case of the massive scalar. The small-mass expansion of the gravitational yields the Liouville action at zeroth order, and we can identify the Mabuchi action at first order. While the massive Majorana action is a conformal deformation of the massless Majorana CFT, we find an action different from the one given by the David-Distler-Kawai (DDK) ansatz.

hep-th↗

arXiv2021

Effective gravitational action for 2D massive fermions

We work out the effective gravitational action for 2D massive Euclidean fermions in a small mass expansion. Besides the leading Liouville action, the order $m^2$ gravitational action contains a piece characteristic of the Mabuchi action, much as for 2D massive scalars, but also several non-local terms involving the Green's functions and Green's functions at coinciding points on the manifold.

hep-th↗

arXiv2020

A short note on dynamics and degrees of freedom in $2d$ classical gravity

We comment on some peculiarities of matter with and without Weyl invariance coupled to classical $2d$ Einstein-Hilbert gravity for several models, in particular, related to the counting of degrees of freedom and on the dynamics. We find that theories where the matter action is Weyl invariant has generically more degrees of freedom than action without the invariance. This follows from the Weyl invariance of the metric equations of motion independently of the invariance of the action. Then, we study another set of models with scalar fields and show that solutions to the equations of motion are either trivial or inconsistent. To our knowledge, these aspects of classical $2d$ gravity have not been put forward and can be interesting to be remembered when using it as a toy model for $4d$ gravity. The goal of this note is also as a pedagogical exercise: our results follow from standard methods, but we emphasize more direct computations.

gr-qc↗

arXiv2019

Analyticity and Crossing Symmetry of Superstring Loop Amplitudes

Bros, Epstein and Glaser proved crossing symmetry of the S-matrix of a theory without massless fields by using certain analyticity properties of the off-shell momentum space Green's function in the complex momentum plane. The latter properties follow from representing the momentum space Green's function as Fourier transform of the position space Green's function, satisfying certain properties implied by the underlying local quantum field theory. We prove the same analyticity properties of the momentum space Green's functions in superstring field theory by directly working with the momentum space Feynman rules even though the corresponding properties of the position space Green's function are not known. Our result is valid to all orders in perturbation theory, but requires, as usual, explicitly subtracting / regulating the non-analyticities associated with massless particles. These results can also be used to prove other general analyticity properties of the S-matrix of superstring theory.

hep-th↗

arXiv2018

Minisuperspace computation of the Mabuchi spectrum

It was shown recently that, beside the traditional Liouville action, other functionals appear in the gravitational action of two-dimensional quantum gravity in the conformal gauge, the most important one being the Mabuchi functional. In a letter we proposed a minisuperspace action for this theory and used it to perform its canonical quantization. We found that the Hamiltonian of the Mabuchi theory is equal to the one of the Liouville theory and thus that the spectrum and correlation functions match in this approximation. In this paper we provide motivations to support our conjecture.

hep-th↗

arXiv2017

2D gravitational Mabuchi action on Riemann surfaces with boundaries

We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a Riemann surface with boundaries. A small-mass expansion gives back the Liouville action in the massless limit, while the first-order mass correction allows us to identify what should be the appropriate generalization of the Mabuchi action on a Riemann surface with boundaries. We provide a detailed study for the example of the cylinder. Contrary to the case of manifolds without boundary, we find that the gravitational Lagrangian explicitly depends on the space-point, via the geodesic distances to the boundaries, as well as on the modular parameter of the cylinder, through an elliptic theta-function.

hep-th↗

arXiv2017

Closed Superstring Field Theory and its Applications

We review recent developments in the construction of heterotic and type II string field theories and their various applications. These include systematic procedures for determining the shifts in the vacuum expectation values of fields under quantum corrections, computing renormalized masses and S-matrix of the theory around the shifted vacuum and a proof of unitarity of the S-matrix. The S-matrix computed this way is free from all divergences when there are more than 4 non-compact space-time dimensions, but suffers from the usual infrared divergences when the number of non-compact space-time dimensions is 4 or less.

hep-th↗

arXiv2016

Mabuchi spectrum from the minisuperspace

It was recently shown that other functionals contribute to the effective action for the Liouville field when considering massive matter coupled to two-dimensional gravity in the conformal gauge. The most important of these new contributions corresponds to the Mabuchi functional. We propose a minisuperspace action that reproduces the main features of the Mabuchi action in order to describe the dynamics of the zero-mode. We show that the associated Hamiltonian coincides with the (quantum mechanical) Liouville Hamiltonian. As a consequence the Liouville theory and our model of the Mabuchi theory both share the same spectrum, eigenfunctions and - in this approximation - correlation functions.

hep-th↗