Communications in Mathematical Physics最新文献

We show the strong graded locality of all unitary minimal W-algebras, so that they give rise to irreducible graded-local conformal nets. Among these unitary vertex superalgebras, up to taking tensor products with free fermion vertex superalgebras, there are the unitary Virasoro vertex algebras ((N=0)) and the unitary (N=1,2,3,4) super-Virasoro vertex superalgebras. Accordingly, we have a uniform construction that gives, besides the already known (N=0,1,2) super-Virasoro nets, also the new (N=3,4) super-Virasoro nets. All strongly rational unitary minimal W-algebras give rise to previously known completely rational graded-local conformal nets and we conjecture that the converse is also true. We prove this conjecture for all unitary W-algebras corresponding to the (N=0,1,2,3,4) super-Virasoro vertex superalgebras.

We give a classification of the regular soliton solutions of the KP hierarchy, referred to as the KP solitons, under the Gel’fand-Dickey (ell )-reductions in terms of the permutation of the symmetric group. As an example, we show that the regular soliton solutions of the (good) Boussinesq equation as the 3-reduction can have at most one resonant soliton in addition to two sets of solitons propagating in opposite directions. We also give a systematic construction of these soliton solutions for the (ell )-reductions using the vertex operators. In particular, we show that the non-crossing permutation gives the regularity condition for the soliton solutions.

The von Neumann entropy of an n-partite system (A_1^n) given a system B can be written as the sum of the von Neumann entropies of the individual subsystems (A_k) given (A_1^{k-1}) and B. While it is known that such a chain rule does not hold for the smooth min-entropy, we prove a counterpart of this for a variant of the smooth min-entropy, which is equal to the conventional smooth min-entropy up to a constant. This enables us to lower bound the smooth min-entropy of an n-partite system in terms of, roughly speaking, equally strong entropies of the individual subsystems. We call this a universal chain rule for the smooth min-entropy, since it is applicable for all values of n. Using duality, we also derive a similar relation for the smooth max-entropy. Our proof utilises the entropic triangle inequality based technique developed in Marwah and Dupuis (Commun Math Phys 405(9):211, 2024. https://doi.org/10.1007/s00220-024-05074-8) for analysing approximation chains. Additionally, we also prove an approximate version of the entropy accumulation theorem, which significantly relaxes the conditions required on the state to bound its smooth min-entropy. In particular, it does not require the state to be produced through a sequential process like previous entropy accumulation type bounds. In our companion paper Marwah and Dupuis (Security proof for parallel DIQKD, 2025. https://arxiv.org/abs/2507.03991), we use it to prove the security of parallel device independent quantum key distribution.

In Special Relativity, the vanishing of mass indicates either the absence of energy (vacuum) or the presence of massless radiation moving at the speed of light. In General Relativity, the same principle governs the interpretation of zero total mass: asymptotically flat initial data sets (IDS) ((M^n, g, k)) with vanishing mass correspond either to slices of Minkowski spacetime or to slices of (pp)-wave spacetimes that model radiation. In contrast, we demonstrate that asymptotically hyperboloidal spin IDS with zero mass must embed isometrically into Minkowski space, with no possible IDS configurations that model radiation in this setting. Our result holds under general decay assumptions where the total mass is well-defined. The proof relies on precise decay estimates for spinors on level sets of spacetime harmonic functions and works in all dimensions.

Let (M, g) be a compact, boundaryless, Riemannian manifold whose geodesic flow on its unit sphere bundle is Anosov. Consider the (semiclassical) Laplace-Beltrami operator on M. Let (varepsilon >0). We study the semiclassical measures (mu _{sc}) of quasimodes of width (varepsilon frac{hbar }{|log hbar |}), a critical-type regime when considering “delocalization". We derive a lower bound for the Kolmogorov-Sinai entropy of (mu _{sc}) that depends explicitly on (varepsilon ), in the spirit of that given by Anantharaman-Koch-Nonnenmacher.

The thermodynamics of Dirac fields under the influence of external electromagnetic fields is studied. For perturbations which act only for finite time, the influence of the perturbation can be described by an automorphism which can be unitarily implemented in the GNS representations of KMS states, a result long known for the Fock representation. For time-independent perturbations, however, the time evolution cannot be implemented in typical cases, so the standard methods of quantum statistical mechanics do not apply. Instead we show that a smooth switching on of the external potential allows a comparison of the free and the perturbed time evolution, and approach to equilibrium, a possible existence of non-equilibrium stationary states and Araki’s relative entropy can be investigated. As a byproduct, we find an explicit formula for the relative entropy of gauge invariant quasi-free states.

In this paper, we first establish a connection between Yangians and the unique formal solution of the quantum confluent hypergeometric system at irregular singularities. We then realize the Stokes matrices of the hypergeometric system as infinite matrix products of representations of Yangians, with the help of the theory of difference systems. Along the way, we also investigate the algebroid structure associated with the Stokes matrices.

We study webs of 5-branes with 7-branes in Type IIB string theory from a geometric perspective. Mathematically, a web of 5-branes with 7-branes is a tropical curve in (mathbb {R}^2) with focus-focus singularities introduced. To any such a web W, we attach a log Calabi–Yau surface (Y, D) with a line bundle L. We then describe supersymmetric webs, which are webs defining 5d superconformal field theories (SCFTs), in terms of the geometry of (Y, D, L). We also introduce particular supersymmetric webs called “consistent webs", and show that any 5d SCFT defined by a supersymmetric web can be obtained from a consistent web by adding free hypermultiplets. Using birational geometry of degenerations of log Calabi–Yau surfaces, we provide an algorithm to test the consistency of a web in terms of its dual polygon. Moreover, for a consistent web W, we provide an algebro-geometric construction of the mirror (mathcal {X}^{textrm{can}}) to (Y, D, L), as a non-toric canonical 3-fold singularity, and show that M-theory on (mathcal {X}^{textrm{can}}) engineers the same 5d SCFT as W. We also explain how to derive explicit equations for (mathcal {X}^{textrm{can}}) using scattering diagrams, encoding disk worldsheet instantons in the A-model, or equivalently the BPS states of an auxiliary rank one 4d (mathcal {N}=2) theory.

To compare two Gaussian states of the Weyl-CCR algebra of a free scalar QFT we study three closely related perspectives: (i) quasi-equivalence of the GNS-representations, (ii) differences of the total energy (on some Cauchy surface), and (iii) differences between functions of the modular Hamiltonians. (For perspective (ii) we will only consider real linear free scalar quantum fields on ultrastatic spacetimes.) These three perspectives are known to be related qualitatively, due to work of Araki and Yamagami, Verch and Longo. Our aim is to investigate quantitative relations, including in particular estimates of differences between functions of modular Hamiltonians in terms of energy differences. E.g., for a suitable class of perturbations of the Minkowski vacuum state of a massive free scalar field, which have a positive energy density and a finite total energy E on some inertial time slice, the modular Hamiltonian K satisfies (Big Vert frac{1}{cosh left( frac{K}{2}right) }Big Vert _{text {HS}}^2le 8frac{E}{m}).

We propose a new approach to studying hyperbolic Kac–Moody algebras, focussing on the rank-3 algebra ({mathfrak {F}}) first investigated by Feingold and Frenkel. Our approach is based on the concrete realization of this Lie algebra in terms of a Hilbert space of transverse and longitudinal physical string states, which are expressed in a basis using DDF operators. When decomposed under its affine subalgebra ({A_1^{(1)}}), the algebra ({mathfrak {F}}) decomposes into an infinite sum of affine representation spaces of ({A_1^{(1)}}) for all levels (ell in mathbb {Z}). For (|ell | >1) there appear in addition coset Virasoro representations for all minimal models of central charge (c<1), but the different level-(ell ) sectors of ({mathfrak {F}}) do not form proper representations of these because they are incompletely realized in ({mathfrak {F}}). To get around this problem we propose to nevertheless exploit the coset Virasoro algebra for each level by identifying for each level a (for (|ell |ge 3) infinite) set of ‘Virasoro ground states’ that are not necessarily elements of ({mathfrak {F}}) (in which case we refer to them as ‘virtual’), but from which the level-(ell ) sectors of ({mathfrak {F}}) can be fully generated by the joint action of affine and coset Virasoro raising operators. We conjecture (and present partial evidence) that the Virasoro ground states for (|ell |ge 3) in turn can be generated from a finite set of ‘maximal ground states’ by the additional action of the ‘spectator’ coset Virasoro raising operators present for all levels (|ell | > 2). Our results hint at an intriguing but so far elusive secret behind Einstein’s theory of gravity, with possibly important implications for quantum cosmology.