Letters in Mathematical Physics最新文献

Copositive matrices and copositive polynomials are objects from optimization. We connect these to the geometry of Feynman integrals in physics. The integral is guaranteed to converge if its kinematic parameters lie in the copositive cone. Pólya’s method makes this manifest. We study the copositive cone for the second Symanzik polynomial of any Feynman graph. Its algebraic boundary is described by Landau discriminants.

A formula for the full nonperturbative topological string free energy was recently proposed by Hattab and Palti (Non-perturbative topological string theory on compact Calabi-Yau manifolds from M-theory. arXiv:2408.09255 [hep-th]). In this work, we extend their result to the refined topological string theory. We demonstrate that the proposed formula for the full nonperturbative refined topological string free energy correctly reproduces the trans-series structure of the refined topological string and captures the Stokes automorphisms associated with its resurgent properties.

We introduce some spectral functions on the reduced Lorentz group and on its spinor group localized at an irreducible unitary representation, and we study their main analytic properties. More precisely, we consider the trace of the heat operator and the spectral zeta function of the Hodge Laplace operator on functions. We show that the localized zeta function has a regular analytic extension with simple poles, and we find a closed formula for the zeta determinant of the localized Hodge Laplace operator. We give a closed formula for the trace of the (global) heat operator and we study its expansion for small time.

Following D. Mbouna [Lett. Math. Phys. 114:54, 2024], a new method is provided to recognize and characterize a classical orthogonal polynomial sequence defined on a quadratic lattice only by the three-term recurrence relation. This characterization includes all orthogonal polynomials in the Askey scheme (including the para-Krawtchouk polynomials), covering then all those defined on linear and constant lattices. This work suggests a simple and implementable algorithm/package for some known physical problems.

For a G-crossed braided extension of a unitary modular tensor category (mathcal {C})—as in one representing a (2+1)D symmetry enriched topological order (SETO)—preservation of global on-site group symmetry after condensation by a commutative Q-system object (A in mathcal {C}) necessitates the existence of a G-equivariant structure on A. When interpreted spatially, the condensation boundary has its own internal topological symmetries. We elaborate an algebraic framework for describing the internal topological symmetries of compatible (1+1)D gapped boundaries for (2+1)D topologically ordered systems in terms of hypergroup actions. Then, we investigate the coherence of global on-site bulk symmetries and boundary symmetries. We present a categorical obstruction to the preservation of symmetry in a way which is coherent in terms of lifts of categorical actions to a certain 2-group of bulk symmetries. We give a characterization of this obstruction in the case of condensation by a Lagrangian algebra and boundary symmetries given by subalgebras of the convolution algebra associated with a Lagrangian algebra object.

In recent work, Lusztig’s positive root vectors (with respect to a distinguished choice of reduced decomposition of the longest element of the Weyl group) were shown to give a quantum tangent space for every A-series Drinfeld–Jimbo full quantum flag manifold (mathcal {O}_q(textrm{F}_n)). Moreover, the associated differential calculus (Omega ^{(0,bullet )}_q(textrm{F}_n)) was shown to have classical dimension, giving a direct q-deformation of the classical anti-holomorphic Dolbeault complex of (textrm{F}_n). Here, we examine in detail the rank two case, namely the full quantum flag manifold of (mathcal {O}_q(textrm{SU}_3)). In particular, we examine the (*)-differential calculus associated with (Omega ^{(0,bullet )}_q(textrm{F}_3)) and its noncommutative complex geometry. We find that the number of almost-complex structures reduces from 8 (that is 2 to the power of the number of positive roots of (mathfrak {sl}_3)) to 4 (that is 2 to the power of the number of simple roots of (mathfrak {sl}_3)). Moreover, we show that each of these almost-complex structures is integrable, which is to say, each of them is a complex structure. Finally, we observe that, due to non-centrality of all the non-degenerate coinvariant 2-forms, none of these complex structures admits a left (mathcal {O}_q(textrm{SU}_3))-covariant noncommutative Kähler structure.

We study and classify the emergence of protected edge modes at the junction of one-dimensional materials. Using symmetries of Lagrangian planes in boundary symplectic spaces, we present a novel proof of the periodic table of topological insulators in one dimension. We show that edge modes necessarily arise at the junction of two materials having different topological indices. Our approach provides a systematic framework for understanding symmetry-protected modes in one dimension. It does not rely on periodic nor ergodicity and covers a wide range of operators which includes both continuous and discrete models.

Spectral decomposition with respect to the wave functions of Ruijsenaars hyperbolic system defines an integral transform, which generalizes classical Fourier integral. For a certain class of analytical symmetric functions we prove inversion formula and orthogonality relations, valid for complex valued parameters of the system. Besides, we study four regimes of unitarity, when this transform defines isomorphisms of the corresponding (L_2) spaces.

We investigate relative versions of dualizability designed for relative versions of topological field theories (TFTs), also called twisted TFTs, or quiche TFTs in the context of symmetries. In even dimensions, we show an equivalence between lax and oplax fully extended framed relative topological field theories valued in an ((infty , N)text {-}) category in terms of adjunctibility. Motivated by this, we systematically investigate higher adjunctibility conditions and their implications for relative TFTs. Our analysis leads us to identify the oplax relative TFT as the notion of choice. Finally, for fun we explore a tree version of adjunctibility and compute the number of equivalence classes thereof.