Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBorel Summation and Analytic Continuation of the Heat Kernel on Hyperbolic Space
87
0
0.0
(
0
)
Authors
Gerald V. Dunne
Ask ChatGPT about the research
No Arabic abstract
The heat kernel expansion on even-dimensional hyperbolic spaces is asymptotic at both short and long times, with interestingly different Borel properties for these short and long time expansions. Resummations in terms of incomplete gamma functions provide accurate extrapolations and analytic continuations, relating the heat kernel to the Schrodinger kernel, and the heat kernel on hyperbolic space to the heat kernel on spheres. For the diagonal heat kernel there is also a duality between short and long times which mixes the scalar and spinor heat kernels.
rate research
Read More
In this paper we give a streamlined derivation of the exact quantization condition (EQC) on the quantum periods of the Schrodinger problem in one dimension with a general polynomial potential, based on Wronskian relations. We further generalize the EQC to potentials with a regular singularity, describing spherical symmetric quantum mechanical systems in a given angular momentum sector. We show that the thermodynamic Bethe ansatz (TBA) equations that govern the quantum periods undergo nontrivial monodromies as the angular momentum is analytically continued between integer values in the complex plane. The TBA equations together with the EQC are checked numerically against Hamiltonian truncation at real angular momenta and couplings, and are used to explore the analytic continuation of the spectrum on the complex angular momentum plane in examples.
We construct, for the first time, Abelian-Higgs vortices on certain compact surfaces of constant negative curvature. Such surfaces are represented by a tessellation of the hyperbolic plane by regular polygons. The Higgs field is given implicitly in terms of Schwarz triangle functions and analytic solutions are available for certain highly symmetric configurations.
We consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized eta function a more systematic version of the derivative expansion for spectral assymmetry and that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in a multiflavour extension of the Goldstone-Wilczek model.We also propose an improved expansionof the heat kernelthat allows the tackling ofthe convergence issues and permits an automated computation of the coefficients
It has been recently shown that every SCFT living on D3 branes at a toric Calabi-Yau singularity surprisingly also describes a complete integrable system. In this paper we use the Master Space as a bridge between the integrable system and the underlying field theory and we reinterpret the Poisson manifold of the integrable system in term of the geometry of the field theory moduli space.
We study weak coupling perturbative series in 4d N=2 and 5d N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in zero instanton sector are Borel summable for various observables. Our result for 4d $mathcal{N}=2$ case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N=2 theories and the perturbative series are unambiguous, namely Borel summable. We also prove that the perturbative series in arbitrary number of instanton sector are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations in each number of instanton sector.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
