Related papers: Compactified Imaginary Liouville Theory

Causal Dynamical Triangulations (CDT) is a methodology to define and compute the gravitational path integral, whose aim is a fully fledged nonperturbative quantum field theory of gravity and spacetime. Analogous to lattice formulations of…

Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…

Within the framework of the path-integral formalism we reinvestigate the different methods of removing the unphysical degrees of freedom from spontanously broken gauge theories. These are: construction of the unitary gauge by gauge fixing;…

We conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of N=2 SCFTs recently defined by one of…

Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…

The partition function of a quantum statistical system in flat space can always be written as an integral over a classical Boltzmann factor $\exp[ -\beta V^{\rm eff cl({\bf x}_0)]$, where $V^{\rm eff cl({\bf x}_0)$ is the so-called…

We try to develop a coherent picture on Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of path-integral approach, bootstrap, canonical quantization and operator approach. To do this, we…

We derive the conformal Ward identities for the correlation functions of the Stress--Energy tensor in probabilistic Liouville Conformal Field Theory on compact Riemann surfaces by varying the correlation functions with respect to the…

Recently, a new path integral formulation of Loop Quantum Gravity (LQG) has been derived in arXiv:1910.03763 from the reduced phase space formulation of the canonical LQG. This paper focuses on the semiclassical analysis of this path…

We consider those two-dimensional rational conformal field theories (RCFTs) whose chiral algebras, when maximally extended, are isomorphic to the current algebra formed from some affine non-twisted Kac--Moody algebra at fixed level. In this…

We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property,…

Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin, Polyakov, and Zamolodchikov [BPZ84a]. Both exhibit exactly solvable structures in two dimensions. A…

There is a substantial literature concerning Liouville quantum gravity (LQG) in two dimensions with conformal matter field of central charge ${\mathbf{c}}_{\mathrm M}\in(-\infty,1]$. Via the DDK ansatz, LQG can equivalently be described as…

Imaginary time is often used in quantum tunnelling calculations. This article advocates a conceptually sounder alternative: complex lapse. In the ``3+1'' action for the Einstein gravitational field minimally coupled to a Klein-Gordon field,…

Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the…

We derive the path-integral representation of the fractional Ornstein-Uhlenbeck process driven by Riemann-Liouville fractional Gaussian noise, for both the subdiffusive and superdiffusive regimes. We express the corresponding action, which…

If the diffeomorphism symmetry of general relativity is fully implemented into a path integral quantum theory, the path integral leads to a partition function which is an invariant of smooth manifolds. We comment on the physical…

We discuss scalar conformal field theories (CFTs) that can be realized in structural phase transitions. The Landau condition and Lifshitz condition are reviewed, which are necessary conditions for a structural phase transition to be second…

We introduce a framework for two-dimensional conformal field theory (CFT) in the language of analytic number theory. Attached to the torus partition function of every two-dimensional CFT is a self-dual, degree-4 $L$-function of root number…

We describe Stochastic Loewner Evolution on arbitrary Riemann surfaces with boundary using Conformal Field Theory methods. We propose in particular a CFT construction for a probability measure on (clouded) paths, and check it against known…