Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · hep-th/0312327

Three Dimensional Gravity and M-Theory

Michael McGuigan
View original source ↗Read source document ↗Export metadata ↓

Abstract

It is well known that string theory can be formulated as two dimensional gravity coupled to matter. In the 2d gravity formulation the central charge of the matter together with a hidden dimension from the conformal factor or Liouville mode determines the Target space dimension. Also the vacuum amplitude of the 2d gravity formulation implies important constraints on the Target space theory associated with modular invariance. In this paper we study a three dimensional gravity approach to M-theory. We find that there are three hidden Liouville type fields coming from the 3d gravity sector and that these together with the number of zero modes of the matter fields determine an eleven dimensional Target space of M theory. We investigate the perturbative vacuum amplitude for the 3d gravity approach to M theory and constraints imposed from SL(3,Z) modular invariance using a method of Dolan and Nappi together with a sum over spin structures which generalizes the SL(2,Z) invariance found in string theory. To introduce gauge fields in M-theory we study the vacuum amplitude on a three annulus and introduce interactions with two dimensional matter on a boundary in analogy with the introduction of gauge fields for open string theory. We study a three dimensional version of M-theory from the 3d gravity perspective and show how it relates to two dimensional type 0A string theory described by a 2d superLiouville theory with c=1 matter and, on manifolds with boundary, to a E8xSO(8) 2d heterotic string. We discuss a nonperturbative 3d gravity approach to M-theory and the expansion about e=0 in the Chern-Simons gauge formulation of the theory. Finally we study the interaction of fermionic matter with 3d gravity to investigate the origins of conformal dimension and Liouville effective action from a 3d gravity approach.

Explore related subjects

hep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Michael McGuigan. 2004-01-02. Three Dimensional Gravity and M-Theory. https://arxiv.org/abs/hep-th/0312327

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

KEEP EXPLORING

Related papers

arXiv2026

Timelike Entanglement from Spacetime Density Matrices: A Lattice Realization

We investigate timelike entanglement in quantum field theory using spacetime density matrices and provide a microscopic lattice realization. For a two-dimensional free real scalar field, we extend Gaussian diagonalization methods to the generally non-Hermitian reduced spacetime density matrix and determine its complete nonzero spectrum in the generic regular case, together with all integer R\'enyi moments. The real-time replica construction identifies these moments with Lorentzian branch-point twist-operator correlation functions. We test this identification against the full four-point function on a circle, boundary two-point functions with Dirichlet and Neumann boundary conditions, and massive form-factor predictions, finding quantitative agreement in both magnitude and phase across distinct causal regimes. The boundary setup exhibits a finite causally connected window in which every integer R\'enyi entropy is real, showing that reality is not equivalent to causal disconnection. These results provide a microscopic lattice foundation for timelike entanglement and for Lorentzian twist-operator methods beyond equal-time regions.

hep-th↗
arXiv2026

Landau-Ginzburg description of an exceptional ${\mathcal N}=1$ minimal model

The $\mathcal N=1$ superconformal minimal model with $m=12$ and the exceptional modular invariant $(E_6,D_8)$ is the unitary minimal model of the super-$W_3$ algebra. We propose its Landau-Ginzburg description using two real scalar superfields with the cubic superpotential ${\cal W}=g_1 XY^2/2 + g_2X^3/6$. For $g_1=g_2$, this superpotential is known to describe a product of two $m=3$ $\mathcal N=1$ superconformal minimal models, which is the $m=10$ model with the $(D_6,E_6)$ modular invariant. The exceptional $m=12$ superconformal minimal model is realized at a different fixed point of the same theory. Testing this Landau-Ginzburg description requires the fusion ring of the minimal model, which we obtain from the modular data of the extended algebra. The fusion ring has a $\mathbb Z_2$ grading by chiral fermion parity that the ordinary fusion coefficients do not determine. This grading, composed with conjugation, gives the generator of the R-parity $\mathbb Z_2^{R}$ of the Landau-Ginzburg theory. We then treat the theory with superpotential $\cal W$ as a Gross-Neveu-Yukawa model in $d=4-\epsilon$ and find a weakly coupled infrared fixed point with $g_1/g_2=3/2+\mathcal O(\epsilon)$, at which supersymmetry emerges. We also describe the renormalization group flow from this fixed point to the decoupled fixed point with $g_1=g_2$. The operator dimensions at the coupled fixed point, continued to $d=2$, agree approximately with their values in the $m=12$ superconformal minimal model. Finally, we estimate the scaling dimensions in the new interacting $d=3$ $\mathcal N=1$ superconformal field theory.

hep-th↗
arXiv2026

Detecting one-dimensional bosonic SPT phases via twisted entropic order parameter

Entanglement asymmetry, introduced by F. Ares, S. Murciano and P. Calabrese, provides a density-matrix diagnostic of symmetry breaking and successfully captures the Landau data associated with a broken symmetry pattern. However, it is by now well established that gapped quantum many-body systems can exhibit phases which are not characterized solely by Landau symmetry breaking. A fundamental example is a symmetry-protected topological (SPT) phase, and the ordinary definition of entanglement asymmetry is insensitive to this topological information. In this work we introduce a refined quantity, which we call the twisted entropic order parameter, designed to detect SPT phases from reduced density matrices, particularly focusing on one-dimensional bosonic systems. The key ingredient in our construction is an ancilla degrees of freedom that coherently records the untwisted state and the twisted state associated to a one-ended topological defect of unbroken symmetry, so that the enlarged density matrix retains the charge carried by the defect endpoint. We demonstrate our proposal in concrete lattice models and further generalize it beyond ordinary group symmetries, establishing its ability to diagnose SPT phases. This provides a first step toward a unified entanglement-asymmetry framework for diagnosing quantum phases of matter.

hep-th↗