Dieter Lust

We study the degrees of freedom of R ² gravity in flat spacetime with two approaches. By rewriting the theory a la Stueckelberg, and implementing Lorentz-like gauges to the metric perturbations, we confirm that the pure theory propagates one scalar degree of freedom, while the full theory contains two tensor modes in addition. We then consider the degrees of freedom by directly examining the metric perturbations. We show that the degrees of freedom of the full theory match with those obtained with the manifestly covariant approach. In contrast, we find that the pure R ² gravity has no degrees of freedom. We show that a similar discrepancy between the two approaches appears also in a theory dual to the three-form, and appears due to the Lorentz-like gauges, which lead to the fictitious modes even after the residual gauge redundancy has been taken into account. At first sight, this implies a discontinuity between the full theory and the pure case. By studying the first-order corrections of the full R ² gravity beyond the linear regime, we show that at high-energies, both scalar and tensor degrees of freedom become strongly coupled. This implies that the apparent discontinuity of pure and full R ² gravity is just an artefact of the perturbation theory, and further supports the absence of degrees of freedom in the pure R ² gravity.

We derive a massive double copy construction within string theory. To this end, we use massive vectors of the open string spectrum that appear in compactifications to four dimensions and construct massive spin-2 tensors as closed string states, thereby mimicking the structure of the massless graviton. We then compute three-point amplitudes for the scattering of massless and massive spin-2 closed string states and reveal the double copy structure of the latter. With these results being finite in the string scale, we are further able to reproduce the cubic Lagrangian of ghost-free bimetric theory around flat spacetime for bulk massive spin-2 states originating in products of vectors of extended brane supersymmetry.

We derive a massive double copy construction within string theory. To this end, we use massive vectors of the open string spectrum that appear in compactifications to four dimensions and construct massive spin-2 tensors as closed string states, thereby mimicking the structure of the massless graviton. We then compute three-point amplitudes for the scattering of massless and massive spin-2 closed string states and reveal the double copy structure of the latter. With these results being finite in the string scale, we are further able to reproduce the cubic Lagrangian of ghost-free bimetric theory around flat spacetime for bulk massive spin-2 states originating in products of vectors of extended brane supersymmetry.

We study the metric perturbations around the de Sitter and Minkowski backgrounds in Conformal Gravity. We confirm the presence of ghosts in both cases. In the de Sitter case, by applying the Maldacena boundary conditions — the Neumann boundary condition and the positive-frequency mode condition — to the metric, we show that one cannot recover a general solution for the perturbations. In turn, alongside the Neumann boundary condition, we derive an additional condition with which the perturbations of conformal gravity and dS perturbations of Einstein gravity with cosmological constant coincide. We further show that the Neumann boundary condition does not lead to a general solution in Minkowski space. Conversely, we derive the alternative boundary conditions, with which we attain an agreement between the perturbations of conformal and Einstein gravity in full generality, thus removing the ghost of conformal gravity.

We derive how to incorporate topological features of Riemann surfaces in string amplitudes by insertions of bi-local operators called handle operators. The resulting formalism is exact and globally well-defined in moduli space. After a detailed and pedagogical discussion of Riemann surfaces, complex structure deformations, global vs local aspects, boundary terms, an explicit choice of gluing-compatible and global (modulo U(1)) coordinates (termed `holomorphic normal coordinates'), finite changes in normal ordering, and factorisation of the path integral measure, we construct these handle operators explicitly. Adopting an offshell local coherent vertex operator basis for the latter, and gauge fixing invariance under Weyl transformations using holomorphic normal coordinates (developed by Polchinski), is particularly efficient. All loop amplitudes are gauge-invariant (BRST-exact terms decouple up to boundary terms in moduli space), and reparametrisation invariance is manifest, for arbitrary worldsheet curvature and topology (subject to the Euler number constraint). We provide a number of complementary viewpoints and consistency checks (including one-loop modular invariance, we compute all one- and two-point sphere amplitudes, glue two three-point sphere amplitudes to reproduce the exact four-point sphere amplitude, etc.).

We revisit and extend the correspondence between black holes, domain walls and fluxes in type IIA compactifications. We argue that these three systems can be described by the same supergravity effective action, modulo proper identifications and adjustments. Then, we apply the correspondence to investigate swampland conjectures on de Sitter and anti-de Sitter vacua, as well as on the black hole entropy. We show that, in certain cases, swampland conjectures can be motivated from properties of black hole solutions, such as positiveness of the entropy. This provides a bottom-up rationale which is complementary to the usual tests in string theory. When asking for an agreement between the anti-de Sitter and the black hole entropy distance conjectures, we are led to an extension of the correspondence which includes geometric fluxes and the associated Kaluza-Klein monopoles domain walls. Finally, we point out that the anti-de Sitter distance conjecture is naturally implemented in certain asymptotically anti-de Sitter black holes as a consequence of a constraint involving black hole charges and supergravity gauge couplings.

Ricci flow is a natural gradient flow of the Einstein-Hilbert action. Here we consider the analog for the Einstein-Maxwell action, which gives Ricci flow with a stress tensor contribution coupled to a Yang-Mills flow for the Maxwell field. We argue that this flow is well-posed for static spacetimes with pure electric or magnetic potentials and show it preserves both non-extremal and extremal black hole horizons. In the latter case we find the flow of the near horizon geometry decouples from that of the exterior. The Schwarzschild black hole is an unstable fixed point of Ricci flow for static spacetimes. Here we consider flows of the Reissner-Nordström (RN) fixed point. The magnetic RN solution becomes a stable fixed point of the flow for sufficient charge. However we find that the electric RN black hole is always unstable. Numerically solving the flow starting with a spherically symmetric perturbation of a non-extremal RN solution, we find similar behaviour in the electric case to the Ricci flows of perturbed Schwarzschild, namely the horizon shrinks to a singularity in finite time or expands forever. In the magnetic case, a perturbed unstable RN solution has a similar expanding behaviour, but a perturbation that decreases the horizon size flows to a stable black hole solution rather than a singularity. For extremal RN we solve the near horizon flow for spherical symmetry exactly, and see in the electric case two unstable directions which flow to singularities in finite flow time. However, even turning these off, and fixing the near horizon geometry to be that of RN, we numerically show that the flows appear to become singular in the vicinity of its horizon.

We consider the setup of a black hole in AdS₄ coupled to an external bath, embedded in type IIB string theory. We study quantum extremal islands in these backgrounds, in relation to the existence of a massive graviton. Using explicit results of the microscopic embedding of AdS₄ massive gravity in string theory, we investigate whether it is possible to achieve backgrounds with extremal islands, in which the lowest lying graviton is only slightly massive. For certain regions of the microscopic parameters, the graviton mass can be computed explicitly, and we explain how it directly affects the existence and the properties of the islands. We also show that islands can in principle exist within the regime of validity of the massive gravity effective field theory. However we see via numerical computations that the existence of quantum extremal islands at zero temperature is highly constrained, also when the dilaton is allowed to vary, so that the mass of the graviton cannot be made arbitrarily light. At finite temperature, we also identify a critical parameter, above and below which islands still exist but exhibit a different behavior. Our work supports recent proposals that the unitary evolution of black holes in higher dimensions, and more precisely their Page curve, relies on the presence of a massive graviton in the effective theory.

The origin of the graviton from string theory is well understood: it corresponds to a massless state in closed string spectra, whose low-energy effective action, as extracted from string scattering amplitudes, is that of Einstein-Hilbert. In this talk, we will discuss our recent published work on the possibility of such a string-theoretic emergence of ghost-free bimetric theory, a recently proposed extension of general relativity that involves two dynamical metrics and which around particular backgrounds propagates the graviton and a massive spin-2 field, with the latter having been put forward as a viable dark matter candidate.