https://neckpinch.com/authors/georgios-papadopoulos/New arXiv papers by Georgios Papadopoulos, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2605.31181arxiv:2605.31181Fri, 29 May 2026 00:00:00 GMTGeorgios Papadopoulos, Kostas Skenderis — Based on effective D-brane actions, we present a generalisation of the Ricci flow that includes the flow of a theory with a n-form field strength for n≥ 0. This is a generalisation of both the Ricci flows and the generalised Ricci flows. Following Perelman, we show that flows that keep a suitable field-dependent volume fixed are monotonic. We also show that all steady brane flow solitons are gradient solitons and use this to demonstrate that on some occasions this implies the existence of a Killing vector field that leaves all the other fields invariant. Particular cases of gradient solitons are NS5 and D5 branes, and the volume which is kept fixed in these cases is the T-duality invariant volume (NS5 brane) or its S-dual (D5 brane). We also generalise the above analysis to gravitational actions coupled to form gauge potentials that also exhibit a Chern-Simons type term. We find an alteration is required in the adaptation of Perelman's modification to this case, which yields a new functional that also exhibits a Chern-Simons term. Under suitable assumptions, we proceed to prove the monotonicity of the flow and that all steady flow solitons are gradient solitons. We also explore the consequences of the last statement on the geometry of solitons.Ricci flowGeneralized & G₂ flowsRicci solitons https://arxiv.org/abs/2509.13092arxiv:2509.13092Tue, 16 Sep 2025 00:00:00 GMTGeorgios Papadopoulos — We investigate the properties of the renormalisation group (RG) flow of two-dimensional sigma models with a generic metric coupling by utilising known results for the Ricci flow. We point out that on many occasions the RG flow develops singularities, due to strong coupling behaviour, before it reaches a UV or an IR fixed point. We illustrate our analysis with several examples. We give particular emphasis to type I singularities, where the length of the curvature of the sigma model target space grows at most as |t-T|⁻¹ as the flow parameter t approaches the singularity at T. For these, the geometry near the singularity is described in terms of a shrinking Ricci soliton that exhibits a cosmological constant even though the original RG flow does not. Assuming that the spacetime satisfies an RG flow equation, we use the Ricci solitons to introduce a cosmological constant in a string theory setting. This can allow for different cosmological constants at different regions of spacetime. In particular, we point out how the de-Sitter space is a solution of the theory. We also raise the question on whether the techniques used to prove the geometrisation conjecture can be applied to prove the homogeneity and isotropy of the universe at large scales.Ricci flowRicci solitonsSingularitiesGeometrizationSurfacesPhysics https://arxiv.org/abs/2404.19526arxiv:2404.19526Tue, 30 Apr 2024 00:00:00 GMTGeorgios Papadopoulos, Edward Witten — By adapting previously known arguments concerning Ricci flow and the c-theorem, we give a direct proof that in a two-dimensional sigma-model with compact target space, scale invariance implies conformal invariance in perturbation theory. This argument, which applies to a general sigma-model constructed with a target space metric and B-field, is in accord with a more general proof in the literature that applies to arbitrary two-dimensional quantum field theories. Models with extended supersymmetry and a B-field are known to provide interesting test cases for the relation between scale invariance and conformal invariance in sigma-model perturbation theory. We give examples showing that in such models, the obstructions to conformal invariance suggested by general arguments can actually occur in models with target spaces that are not compact or complete. Thus compactness of the target space, or at least a suitable condition of completeness, is necessary as well as sufficient to ensure that scale invariance implies conformal invariance in models of this type.Ricci flowSurfacesLimit spaces & RCDPhysics