Related papers: Consistent truncations from the geometry of sphere…
Quantum simulations of bosonic field theories require a truncation in field space to map the theory onto finite quantum registers. Ideally, the truncated theory preserves the symmetries of the original model and has a critical point in the…
The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…
We review the basic features of some recently found consistent Kaluza-Klein truncations including massive modes. We emphasize the general ideas underlying the reduction procedure, then we focus on type IIB supergravity on 5-dimensional…
We establish a supersymmetric consistent truncation of type IIB supergravity on the T^{1,1} coset space, based on extending the Papadopoulos-Tseytlin ansatz to the full set of SU(2)xSU(2) invariant Kaluza-Klein modes. The five-dimensional…
In a previous paper [BTF21] the authors employed the fiber join construction of Yamazaki [Yam99] together with the admissible construction of Apostolov, Calderbank, Gauduchon, and T{\o}nnesen-Friedman [ACGTF08a] to construct new extremal…
We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold $M$, preserving minimal $\mathcal{N}=2$ supersymmetry in five dimensions. These are based on $G_S \subseteq USp(6)$ structures for the…
In this paper, we prove some convergence theorems for the mean curvature flow of closed submanifolds in the unit sphere $\mathbb{S}^{n+d}$ under integral curvature conditions. As a consequence, we obtain several differentiable sphere…
The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points…
Several recent papers have made considerable progress in proving the existence of remarkable consistent Kaluza-Klein sphere reductions of D=10 and D=11 supergravities, to give gauged supergravities in lower dimensions. A proof of the…
We study the existence problem for complete contact forms with constant Tanaka--Webster scalar curvature on non-compact strictly pseudoconvex CR manifolds. We prove that, under mild assumptions, the universal cover of a compact strictly…
We construct a consistent four-scalar truncation of ten-dimensional IIA supergravity on nearly K\"ahler spaces in the presence of dilatino condensates. The truncation is universal, i.e. it does not depend on any detailed features of the…
In seven dimensions any spin manifold admits an SU(2) structure and therefore very general M-theory compactifications have the potential to allow for a reduction to N=4 gauged supergravity. We perform this general SU(2) reduction and give…
We present a systematic framework for constructing consistent truncations of supergravity based on exceptional generalized cosets of the form $\GS \backslash G/H$. This approach generalizes the well-established generalized Scherk-Schwarz…
We consider generalized Scherk-Schwarz reductions of E$_9$ exceptional field theory to D=2 space-time dimensions and in particular construct the resulting scalar potential of all gauged supergravities that can be obtained in this way. This…
We study continuous symmetry reduction of dynamical systems by the method of slices (method of moving frames) and show that a `slice' defined by minimizing the distance to a single generic `template' intersects the group orbit of every…
We start by taking the analytical approach to discuss how the minimizer of Yamabe functional provides constant scalar curvature and its relationship with the Sobolev Space $W^{1,2}.$ Then, after demonstrating the importance of the sphere…
The purpose of this paper is to study the Sasakian geometry on odd dimensional sphere bundles over a smooth projective algebraic variety $N$ with the ultimate, but probably unachievable goal of understanding the existence and non-existence…
Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in…
We address some issues related to the construction of general Kaluza-Klein (KK) ans\"atze for the compactification of a supergravity (sugra) theory on a sphere $S_m$. We first reproduce various ans\"atze for compactification to 7d from the…
In this paper, we give a definition of coherent tangent bundles of space form type, which is a generalized notion of space forms. Then, we classify their realizations in the sphere as a wave front, which is a generalization of a theorem of…