arXiv subjects

Gleb Aminov

Publications and source records attributed to Gleb Aminov.

6 recordsLinked to original sources

arXiv2026

Non-Abelian and Type-A Conformal Anomalies from Euler Descent

We classify the non-Abelian anomaly of the Euclidean conformal group $SO(2n+1,1)$ in $2n$ dimensions via Stora-Zumino descent from its Euler invariant polynomial in $2n+2$ dimensions. In this way, we place the conformal anomaly on the same footing as ordinary perturbative 't Hooft anomalies. We also explore the relation of the non-Abelian anomaly to the known \textit{type-A Weyl anomaly}, which involves projecting into a Weyl cocycle. We discuss implications for anomaly inflow, and 't Hooft anomaly matching for the full conformal group with a Wess-Zumino-Witten term. In 4d, this enables the construction of a dilaton effective action matching the full non-Abelian $SO(5,1)$ conformal anomaly.

hep-th↗

arXiv2024

Black hole scattering amplitudes via analytic small-frequency expansion and monodromy

We utilize three complementary approaches to pinpoint the exact form of scattering amplitudes in Schwarzschild spacetime. First, we solve the Regge-Wheeler equation perturbatively in the small-frequency regime. We use the obtained solutions to determine the monodromy in the near-spatial infinity region, which leads to a specific partial differential equation on the elements of the scattering matrix. As a result, it can be written in terms of the elements of the infinitesimal generator of the monodromy transformation and an integration constant. This constant is further related to the Nekrasov-Shatashvili free energy through the resummation of infinitely many instantons. The quasinormal mode frequencies are also studied in the small-frequency approximation.

hep-th↗

arXiv2024

Basics of Multiple Polyexponential Integrals

We introduce a set of special functions called multiple polyexponential integrals, defined as iterated integrals of the exponential integral $\text{Ei}(z)$. These functions arise in certain perturbative expansions of the local solutions of second-order ODEs around an irregular singularity. In particular, their recursive definition describes the asymptotic behavior of these local solutions. To complement the study of the multiple polyexponential integrals on the entire complex plane, we relate them with two other sets of special functions - the undressed and dressed multiple polyexponential functions - which are characterized by their Taylor series expansions around the origin.

math.CA↗

arXiv2023

Black hole perturbation theory and multiple polylogarithms

We study black hole linear perturbation theory in a four-dimensional Schwarzschild (anti) de Sitter background. When dealing with a positive cosmological constant, the corresponding spectral problem is solved systematically via the Nekrasov-Shatashvili functions or, equivalently, classical Virasoro conformal blocks. However, this approach can be more complicated to implement for certain perturbations if the cosmological constant is negative. For these cases, we propose an alternative method to set up perturbation theory for both small and large black holes in an analytical manner. Our analysis reveals a new underlying recursive structure that involves multiple polylogarithms. We focus on gravitational, electromagnetic, and conformally coupled scalar perturbations subject to Dirichlet and Robin boundary conditions. The low-lying modes of the scalar sector of gravitational perturbations and its hydrodynamic limit are studied in detail.

hep-th↗

arXiv2020

Black Hole Quasinormal Modes and Seiberg-Witten Theory

We present new analytic results on black hole perturbation theory. Our results are based on a novel relation to four-dimensional $\mathcal{N}=2$ 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 $Ω$-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.

hep-th↗

arXiv2020

Spontaneous symmetry breaking in pure 2D Yang-Mills theory

We consider purely topological $2$d Yang-Mills theory on a torus with the second Stiefel-Whitney class added to the Lagrangian in the form of a $θ$-term. It will be shown, that at $θ=π$ there exists a class of $SU(2 N)/\mathbb{Z}_2$ ($N>1$) gauge theories with a two-fold degenerate vacuum, which spontaneously breaks the time reversal and charge conjugation symmetries. The corresponding order parameter is given by the generator $\mathcal{O}$ of the $\mathbb{Z}_N$ one-form symmetry.

hep-th↗