Annales Henri Poincaré最新文献

A solution of the classical Yang–Baxter equation associated with the queer Lie superalgebra is constructed in terms of Hermite theta functions.

We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model corresponds to the CDT-matrix model introduced by Benedetti and Henson (Phys Lett B 678:222, 2009). We present exact as well as approximate results for the Gaussian averages of characters of a Hermitian matrix A and (A^2) for a given representation and establish the present limitations that prevent us to solve the model analytically. This sets the stage for the formulation of more sophisticated matter models coupled to two-dimensional CDT as dually weighted multi-matrix models providing a complementary view to the standard simplicial formulation of CDT-matter models.

In this paper we make a detailed analysis of conservation principles in the context of a family of fourth-order gravitational theories generated via a quadratic Lagrangian. In particular, we focus on the associated notion of energy and start a program related to its study. We also exhibit examples of solutions which provide intuitions about this notion of energy which allows us to interpret it, and introduce several study cases where its analysis seems tractable. Finally, positive energy theorems are presented in restricted situations.

While it has become widely appreciated that (higher) gauge theories need, besides their variational phase space data, to be equipped with “flux quantization laws” in generalized differential cohomology, there used to be no general prescription for how to define and construct the resulting flux-quantized phase space stacks. In this short note, we observe that all higher Maxwell-type equations have solution spaces given by flux densities on a Cauchy surface subject to a higher Gauß law and no further constraint: The metric duality-constraint is all absorbed into the evolution equation away from the Cauchy surface. Moreover, we observe that the higher Gauß law characterizes the Cauchy data as flat differential forms valued in a characteristic (L_infty )-algebra. Using the recent construction of the non-abelian Chern–Dold character map, this implies that compatible flux quantization laws on phase space have classifying spaces whose rational Whitehead (L_infty )-algebra is this characteristic one. The flux-quantized higher phase space stack of the theory is then simply the corresponding (generally non-abelian) differential cohomology moduli stack on the Cauchy surface. We show how this systematic prescription reproduces existing proposals for flux-quantized phase spaces of vacuum Maxwell theory and of the chiral boson and its higher siblings, but reveals that there are other choices of (non-abelian) flux quantization laws even in these basic cases, further discussed in a companion article (Sati and Schreiber in Quantum observables on quantized fluxes. arXiv:2312.13037). Moreover, for the case of NS/RR-fields in type II supergravity/string theory, the traditional “Hypothesis K” of flux quantization in topological K-theory is naturally implied, without the need, on phase space, of the notorious further duality constraint. Finally, as a genuinely non-abelian example we consider flux quantization of the C-field in 11d supergravity/M-theory given by unstable differential 4-Cohomotopy (“Hypothesis H”) and emphasize again that, implemented on Cauchy data, this qualifies as the full phase space without the need for a further duality constraint.

We show that for a unitary modular invariant 2D CFT with central charge (c>1) and having a nonzero twist gap in the spectrum of Virasoro primaries, for sufficiently large spin J, there always exist spin-J operators with twist falling in the interval ((frac{c-1}{12}-varepsilon ,frac{c-1}{12}+varepsilon )) with (varepsilon =O(J^{-1/2}log J)). We establish that the number of Virasoro primary operators in such a window has a Cardy-like, i.e., (exp left( 2pi sqrt{frac{(c-1)J}{6}}right) ) growth. A similar result is proven for a family of holographic CFTs with the twist gap growing linearly in c and a uniform boundedness condition, in the regime (Jgg c^3gg 1). From the perspective of near-extremal rotating BTZ black holes (without electric charge), our result is valid when the Hawking temperature is much lower than the “gap temperature.”

We consider the zero-dimensional quartic O(N) vector model and present a complete study of the partition function Z(g, N) and its logarithm, the free energy W(g, N), seen as functions of the coupling g on a Riemann surface. We are, in particular, interested in the study of the transseries expansions of these quantities. The point of this paper is to recover such results using constructive field theory techniques with the aim to use them in the future for a rigorous analysis of resurgence in genuine quantum field theoretical models in higher dimensions. Using constructive field theory techniques, we prove that both Z(g, N) and W(g, N) are Borel summable functions along all the rays in the cut complex plane (mathbb {C}_{pi } =mathbb {C}{setminus } mathbb {R}_-). We recover the transseries expansion of Z(g, N) using the intermediate field representation. We furthermore study the small-N expansions of Z(g, N) and W(g, N). For any (g=|g| e^{imath varphi }) on the sector of the Riemann surface with (|varphi |<3pi /2), the small-N expansion of Z(g, N) has infinite radius of convergence in N, while the expansion of W(g, N) has a finite radius of convergence in N for g in a subdomain of the same sector. The Taylor coefficients of these expansions, (Z_n(g)) and (W_n(g)), exhibit analytic properties similar to Z(g, N) and W(g, N) and have transseries expansions. The transseries expansion of (Z_n(g)) is readily accessible: much like Z(g, N), for any n, (Z_n(g)) has a zero- and a one-instanton contribution. The transseries of (W_n(g)) is obtained using Möbius inversion, and summing these transseries yields the transseries expansion of W(g, N). The transseries of (W_n(g)) and W(g, N) are markedly different: while W(g, N) displays contributions from arbitrarily many multi-instantons, (W_n(g)) exhibits contributions of only up to n-instanton sectors.

In this paper, we prove a polynomial central limit theorem for several integrable models and for the (beta )-ensembles at high temperature with polynomial potential. Furthermore, we connect the mean values, the variances and the correlations of the moments of the Lax matrices of these integrable systems with the ones of the (beta )-ensembles. Moreover, we show that the local functions’ space-correlations decay exponentially fast for the considered integrable systems. For these models, we also established a Berry–Esseen-type bound.

Given an extendible spacetime one may ask how much, if any, uniqueness can in general be expected of the extension. Locally, this question was considered and comprehensively answered in a recent paper of Sbierski [22], where he obtains local uniqueness results for anchored spacetime extensions of similar character to earlier work for conformal boundaries by Chruściel [2]. Globally, it is known that non-uniqueness can arise from timelike geodesics behaving pathologically in the sense that there exist points along two distinct timelike geodesics which become arbitrarily close to each other interspersed with points which do not approach each other. We show that this is in some sense the only obstruction to uniqueness of maximal future boundaries: Working with extensions that are manifolds with boundary we prove that, under suitable assumptions on the regularity of the considered extensions and excluding the existence of such “intertwined timelike geodesics”, extendible spacetimes admit a unique maximal future boundary extension. This is analogous to results of Chruściel for the conformal boundary.

Given an Axiom A attractor for a (C^{1+alpha }) flow ((alpha >0)), we construct a countable Markov extension with exponential return times in such a way that the inducing set is a smoothly embedded unstable disk. This avoids technical issues concerning irregularity of boundaries of Markov partition elements and enables an elementary approach to certain questions involving exponential decay of correlations for SRB measures.

Analogue Hamiltonian simulation is a promising near-term application of quantum computing and has recently been put on a theoretical footing alongside experiencing wide-ranging experimental success. These ideas are closely related to the notion of duality in physics, whereby two superficially different theories are mathematically equivalent in some precise sense. However, existing characterisations of Hamiltonian simulations are not sufficiently general to extend to all dualities in physics. We give a generalised duality definition encompassing dualities transforming a strongly interacting system into a weak one and vice versa. We characterise the dual map on operators and states and prove equivalence ofduality formulated in terms of observables, partition functions and entropies. A building block is a strengthening of earlier results on entropy preserving maps—extensions of Wigner’s celebrated theorem- –to maps that are entropy preserving up to an additive constant. We show such maps decompose as a direct sum of unitary and antiunitary components conjugated by a further unitary, a result that may be of independent mathematical interest.