Annales Henri Poincaré
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Published By Springer-Verlag

1424-0661, 1424-0637

Author(s):  
Vicente Cortés ◽  
Iván Tulli

AbstractWe construct a quaternionic Kähler manifold from a conical special Kähler manifold with a certain type of mutually local variation of BPS structures. We give global and local explicit formulas for the quaternionic Kähler metric and specify under which conditions it is positive-definite. Locally, the metric is a deformation of the 1-loop corrected Ferrara–Sabharwal metric obtained via the supergravity c-map. The type of quaternionic Kähler metrics we obtain is related to work in the physics literature by S. Alexandrov and S. Banerjee, where they discuss the hypermultiplet moduli space metric of type IIA string theory, with mutually local D-instanton corrections.


Author(s):  
Per Moosavi

AbstractWe study the non-equilibrium dynamics of conformal field theory (CFT) in 1+1 dimensions with a smooth position-dependent velocity v(x) explicitly breaking translation invariance. Such inhomogeneous CFT is argued to effectively describe 1+1-dimensional quantum many-body systems with certain inhomogeneities varying on mesoscopic scales. Both heat and charge transport are studied, where, for concreteness, we suppose that our CFT has a conserved U(1) current. Based on projective unitary representations of diffeomorphisms and smooth maps in Minkowskian CFT, we obtain a recipe for computing the exact non-equilibrium dynamics in inhomogeneous CFT when evolving from initial states defined by smooth inverse-temperature and chemical-potential profiles $$\beta (x)$$ β ( x ) and $$\mu (x)$$ μ ( x ) . Using this recipe, the following exact analytical results are obtained: (i) the full time evolution of densities and currents for heat and charge transport, (ii) correlation functions for components of the energy–momentum tensor and the U(1) current as well as for any primary field, and (iii) the thermal and electrical conductivities. The latter are computed by direct dynamical considerations and alternatively using a Green–Kubo formula. Both give the same explicit expressions for the conductivities, which reveal how inhomogeneous dynamics opens up the possibility for diffusion as well as implies a generalization of the Wiedemann–Franz law to finite times within CFT.


Author(s):  
Rainer Mandel ◽  
Robert Schippa

AbstractWe solve time-harmonic Maxwell’s equations in anisotropic, spatially homogeneous media in intersections of $$L^p$$ L p -spaces. The material laws are time-independent. The analysis requires Fourier restriction–extension estimates for perturbations of Fresnel’s wave surface. This surface can be decomposed into finitely many components of the following three types: smooth surfaces with non-vanishing Gaussian curvature, smooth surfaces with Gaussian curvature vanishing along one-dimensional submanifolds but without flat points, and surfaces with conical singularities. Our estimates are based on new Bochner–Riesz estimates with negative index for non-elliptic surfaces.


Author(s):  
Gleb Aminov ◽  
Alba Grassi ◽  
Yasuyuki Hatsuda

AbstractWe present new analytic results on black hole perturbation theory. Our results are based on a novel relation to four-dimensional $${\mathcal {N}}=2$$ N = 2 supersymmetric gauge theories. We propose an exact version of Bohr-Sommerfeld quantization conditions on quasinormal mode frequencies in terms of the Nekrasov partition function in a particular phase of the $$\Omega $$ Ω -background. Our quantization conditions also enable us to find exact expressions of eigenvalues of spin-weighted spheroidal harmonics. We test the validity of our conjecture by comparing against known numerical results for Kerr black holes as well as for Schwarzschild black holes. Some extensions are also discussed.


Author(s):  
Tomasz Macia̧żek ◽  
Uzy Smilansky

AbstractThe spectrum of a real and symmetric $$N\times N$$ N × N matrix determines the matrix up to unitary equivalence. More spectral data is needed together with some sign indicators to remove the unitary ambiguities. In the first part of this work, we specify the spectral and sign information required for a unique reconstruction of general matrices. More specifically, the spectral information consists of the spectra of the N nested main minors of the original matrix of the sizes $$1,2,\ldots ,N$$ 1 , 2 , … , N . However, due to the complicated nature of the required sign data, improvements are needed in order to make the reconstruction procedure feasible. With this in mind, the second part is restricted to banded matrices where the amount of spectral data exceeds the number of the unknown matrix entries. It is shown that one can take advantage of this redundancy to guarantee unique reconstruction of generic matrices; in other words, this subset of matrices is open, dense and of full measure in the set of real, symmetric and banded matrices. It is shown that one can optimize the ratio between redundancy and genericity by using the freedom of choice of the spectral information input. We demonstrate our constructions in detail for pentadiagonal matrices.


Author(s):  
Marco Benini ◽  
Marco Perin ◽  
Alexander Schenkel

AbstractThis paper proposes a refinement of the usual concept of algebraic quantum field theories (AQFTs) to theories that are smooth in the sense that they assign to every smooth family of spacetimes a smooth family of observable algebras. Using stacks of categories, this proposal is realized concretely for the simplest case of 1-dimensional spacetimes, leading to a stack of smooth 1-dimensional AQFTs. Concrete examples of smooth AQFTs, of smooth families of smooth AQFTs and of equivariant smooth AQFTs are constructed. The main open problems that arise in upgrading this approach to higher dimensions and gauge theories are identified and discussed.


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