Lorenz Eberhardt
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View article: The complex Liouville string: The gravitational path integral
The complex Liouville string: The gravitational path integral Open
We give a rigorous definition of sine dilaton gravity in terms of the worldsheet theory of the complex Liouville string [S. Collier et al., Phys. Rev. Lett. 134, 251602 (2025)]. The latter has a known exact solution that we leverage to exp…
View article: Rademacher expansion of modular integrals
Rademacher expansion of modular integrals Open
We develop a method to evaluate integrals of non-holomorphic modular functions over the fundamental domain of the torus with modular parameter \tau analytically. It proceeds in two steps: first the integral is transformed to a Lorentzian…
View article: Rademacher expansion of modular integrals
Rademacher expansion of modular integrals Open
We develop a method to evaluate integrals of non-holomorphic modular functions over the fundamental domain of the torus with modular parameter \tau analytically. It proceeds in two steps: first the integral is transformed to a Lorentzian…
View article: Regge limit of one-loop string amplitudes
Regge limit of one-loop string amplitudes Open
We study the high-energy limit of 2 \to 2 one-loop string amplitudes at fixed momentum transfer. For the closed string, the high-energy behavior of the amplitudes can be determined from Regge theory just like in field theory, as was f…
View article: Regge limit of one-loop string amplitudes
Regge limit of one-loop string amplitudes Open
We study the high-energy limit of 2 \to 2 one-loop string amplitudes at fixed momentum transfer. For the closed string, the high-energy behavior of the amplitudes can be determined from Regge theory just like in field theory, as was f…
View article: The complex Liouville string: The worldsheet
The complex Liouville string: The worldsheet Open
We introduce a new two-dimensional string theory defined by coupling two copies of Liouville CFT with complex central charge c=13± i \lambda on the worldsheet. This string theory defines a novel, consistent and controllable model o…
View article: The complex Liouville string: Worldsheet boundaries and non-perturbative effects
The complex Liouville string: Worldsheet boundaries and non-perturbative effects Open
We investigate general observables of the complex Liouville string with worldsheet boundaries. We develop a universal formalism that reduces such observables to ordinary closed string amplitudes without boundaries, applicable to any worlds…
View article: Complex Liouville String
Complex Liouville String Open
We introduce the complex Liouville string, a solvable string theory defined by coupling two Liouville theories with complex conjugate central charges c∈13+iR on the world sheet. We compute its amplitudes from first principles and establish…
View article: The complex Liouville string: The matrix integral
The complex Liouville string: The matrix integral Open
We propose a duality between the complex Liouville string and a two-matrix integral. The complex Liouville string is defined by coupling two Liouville theories with complex central charges c = 13 ± i \lambda on the worldsheet. The …
View article: A microscopic realization of dS$_3$
A microscopic realization of dS$_3$ Open
We propose a precise duality between pure de Sitter quantum gravity in 2+1 dimensions and a double-scaled matrix integral. This duality unfolds in two distinct aspects. First, by carefully quantizing the gravitational phase space, we …
View article: The complex Liouville string: the gravitational path integral
The complex Liouville string: the gravitational path integral Open
We give a rigorous definition of sine dilaton gravity in terms of the worldsheet theory of the complex Liouville string arXiv:2409.17246. The latter has a known exact solution that we leverage to explore the gravitational path integral of …
View article: A microscopic realization of dS$_3$
A microscopic realization of dS$_3$ Open
We propose a precise duality between pure de Sitter quantum gravity in 2+1 dimensions and a double-scaled matrix integral. This duality unfolds in two distinct aspects. First, by carefully quantizing the gravitational phase space, we arriv…
View article: 3d gravity from Virasoro TQFT: Holography, wormholes and knots
3d gravity from Virasoro TQFT: Holography, wormholes and knots Open
We further develop the description of three-dimensional quantum gravity with negative cosmological constant in terms of Virasoro TQFT formulated in our previous paper [SciPost Phys. 15, 151 (2023)]. We compare the partition functions compu…
View article: The complex Liouville string: worldsheet boundaries and non-perturbative effects
The complex Liouville string: worldsheet boundaries and non-perturbative effects Open
We investigate general observables of the complex Liouville string with worldsheet boundaries. We develop a universal formalism that reduces such observables to ordinary closed string amplitudes without boundaries, applicable to any worlds…
View article: The complex Liouville string: the matrix integral
The complex Liouville string: the matrix integral Open
We propose a duality between the complex Liouville string and a two-matrix integral. The complex Liouville string is defined by coupling two Liouville theories with complex central charges $c = 13 \pm i λ$ on the worldsheet. The matrix int…
View article: The complex Liouville string: the worldsheet
The complex Liouville string: the worldsheet Open
We introduce a new two-dimensional string theory defined by coupling two copies of Liouville CFT with complex central charge $c=13\pm i λ$ on the worldsheet. This string theory defines a novel, consistent and controllable model of two-dime…
View article: The complex Liouville string
The complex Liouville string Open
We introduce the complex Liouville string, a solvable string theory defined by coupling two Liouville theories with complex conjugate central charges $c \in 13+i \mathbb{R}$ on the worldsheet. We compute its amplitudes from first principle…
View article: Lorentzian contours for tree-level string amplitudes
Lorentzian contours for tree-level string amplitudes Open
We engineer compact contours on the moduli spaces of genus-zero Riemann surfaces that achieve analytic continuation from Euclidean to Lorentzian worldsheets. These generalized Pochhammer contours are based on the combinatorics of associahe…
View article: Lorentzian contours for tree-level string amplitudes
Lorentzian contours for tree-level string amplitudes Open
We engineer compact contours on the moduli spaces of genus-zero Riemann surfaces that achieve analytic continuation from Euclidean to Lorentzian worldsheets. These generalized Pochhammer contours are based on the combinatorics of associahe…
View article: The Virasoro minimal string
The Virasoro minimal string Open
We introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral. The worldsheet theory consists of Liou…
View article: 3d gravity from Virasoro TQFT: Holography, wormholes and knots
3d gravity from Virasoro TQFT: Holography, wormholes and knots Open
We further develop the description of three-dimensional quantum gravity with negative cosmological constant in terms of Virasoro TQFT formulated in our previous paper arXiv:2304.13650. We compare the partition functions computed in the Vir…
View article: Holographic Weyl anomaly in string theory
Holographic Weyl anomaly in string theory Open
We compute the worldsheet sphere partition function of string theory on global AdS _3 with pure NS-NS flux. Because of an unfixed Möbius symmetry on the worldsheet, there is a cancellation of infinities and only a part of the answer is …
View article: Report on 2307.03000v1
Report on 2307.03000v1 Open
We compute the worldsheet sphere partition function of string theory on global AdS 3 with pure NS-NS flux.Because of an unfixed Möbius symmetry on the worldsheet, there is a cancellation of infinities and only a part of the answer is unamb…
View article: Report on 2309.10846v2
Report on 2309.10846v2 Open
We introduce a critical string theory in two dimensions and demonstrate that this theory, viewed as two-dimensional quantum gravity on the worldsheet, is equivalent to a double-scaled matrix integral.The worldsheet theory consists of Liouv…
View article: Report on 2307.03000v1
Report on 2307.03000v1 Open
We compute the worldsheet sphere partition function of string theory on global AdS 3 with pure NS-NS flux.Because of an unfixed Möbius symmetry on the worldsheet, there is a cancellation of infinities and only a part of the answer is unamb…
View article: Solving 3d gravity with Virasoro TQFT
Solving 3d gravity with Virasoro TQFT Open
We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as “Virasor…
View article: Evaluating one-loop string amplitudes
Evaluating one-loop string amplitudes Open
We evaluate one-loop open-string amplitudes at finite \alpha' for the first time. Our method involves a deformation of the integration contour over the modular parameter \tau to a fractal contour introduced by Rademacher in the conte…
View article: Notes on crossing transformations of Virasoro conformal blocks
Notes on crossing transformations of Virasoro conformal blocks Open
We carefully bootstrap the crossing kernels of Virasoro conformal blocks from first principles. Our approach emphasizes the Hilbert space structure of the space of Virasoro conformal blocks which makes the consistency of crossing transform…