Publications

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Inverted pendulum driven by a horizontal random force: statistics of the never-falling trajectory and supersymmetry

Nikolai A. Stepanov, Mikhail A. Skvortsov

SciPost Phys. 13, 021 (2022) · published 16 August 2022 | · pdf

We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction (Whitney's problem). Considered on the entire time axis, the problem admits a unique solution that always remains in the upper half plane. We formulate the problem of statistical description of this never-falling trajectory and solve it by a field-theoretical technique assuming a white-noise driving. In our approach based on the supersymmetric formalism of Parisi and Sourlas, statistic properties of the never-falling trajectory are expressed in terms of the zero mode of the corresponding transfer-matrix Hamiltonian. The emerging mathematical structure is similar to that of the Fokker-Planck equation, which however is written for the "square root" of the probability distribution function. Our results for the statistics of the non-falling trajectory are in perfect agreement with direct numerical simulations of the stochastic pendulum equation. In the limit of strong driving (no gravitation), we obtain an exact analytical solution for the instantaneous joint probability distribution function of the pendulum's angle and its velocity.
Recent progress on two-loop massless pentabox integrals with one off-shell leg

D. Canko, A. Kardos, C. G. Papadopoulos, A. V Smirnov, N. Syrrakos, C. Wever

SciPost Phys. Proc. 7, 037 (2022) · published 21 June 2022 | · pdf

Analytic expressions in terms of polylogarithmic functions for all three families of planar two-loop five-point Master Integrals with one off-shell leg are presented. The Simplified Differential Equations approach is the only known way to fulfil this task due to its unique factorisation property of the symbols of the canonical differential equation. The results are relevant to the study of many $2\to 3$ scattering processes of interest at the LHC.
Laudatio of Dr. Erik Panzer, 2020 Hermann Weyl Prize

María Antonia Lledó Barrena

SciPost Phys. Proc. 14, 002 (2023) · published 23 November 2023 | · pdf

Erik Panzer, from the University of Oxford, has been awarded the 2020 Hermann Weyl Prize of the International Colloquium on Group Theoretical Methods in Physics, for "his pioneering achievements in the calculation of amplitudes in gauge theories, for developing new mathematical structures that exploit the language of symmetries, and for his contribution to the description of important physical phenomena present in nature."
The acceptance speech of the 2022 Weyl-Wigner award

Nicolai Reshetikhin

SciPost Phys. Proc. 14, 003 (2023) · published 23 November 2023 | · pdf

This is the acceptance speech for the 2022 Weyl-Wigner award.
Algebraic Bethe Ansatz for spinor R-matrices

Vidas Regelskis

SciPost Phys. 12, 067 (2022) · published 17 February 2022 | · pdf

We present a supermatrix realisation of $q$-deformed spinor-spinor and spinor-vector $R$-matrices. These $R$-matrices are then used to construct transfer matrices for $U_{q^2}(\mathfrak{so}_{2n+1})$- and $U_{q}(\mathfrak{so}_{2n+2})$-symmetric closed spin chains. Their eigenvectors and eigenvalues are computed.
Adiabatic gauge potential and integrability breaking with free fermions

Balázs Pozsgay, Rustem Sharipov, Anastasiia Tiutiakina, István Vona

SciPost Phys. 17, 075 (2024) · published 9 September 2024 | · pdf

We revisit the problem of integrability breaking in free fermionic quantum spin chains. We investigate the so-called adiabatic gauge potential (AGP), which was recently proposed as an accurate probe of quantum chaos. We also study the so-called weak integrability breaking, which occurs if the dynamical effects of the perturbation do not appear at leading order in the perturbing parameter. A recent statement in the literature claimed that integrability breaking should generally lead to an exponential growth of the AGP norm with respect to the volume. However, afterwards it was found that weak integrability breaking is a counter-example, leading to a cross-over between polynomial and exponential growth. Here we show that in free fermionic systems the AGP norm always grows polynomially, if the perturbation is local with respect to the fermions, even if the perturbation strongly breaks integrability. As a by-product of our computations we also find, that in free fermionic spin chains there are operators which weakly break integrability, but which are not associated with known long range deformations.
On a $\mathbb{Z}_3$-valued discrete topological term in 10d heterotic string theories

Yuji Tachikawa, Hao Y. Zhang

SciPost Phys. 17, 077 (2024) · published 11 September 2024 | · pdf

We show that the low-energy effective actions of two ten-dimensional supersymmetric heterotic strings are different by a $\mathbb{Z}_3$-valued discrete topological term even after we turn off the $E_8×E_8$ and $Spin(32)/\mathbb{Z}_2$ gauge fields. This will be demonstrated by considering the inflow of normal bundle anomaly to the respective NS5-branes from the bulk. This result will be used to show further that the $Spin(16)×Spin(16)$ non-tachyonic non-supersymmetric heterotic string has the same non-zero $\mathbb{Z}_3$-valued discrete topological term. We will also explain the relation of our findings to the theory of topological modular forms. The paper is written as a string theory paper, except for an appendix translating the content in mathematical terms. We will explain there that our finding identifies a representative of the $\mathbb{Z}/3$-torsion element of $\pi_{-32}\mathrm{TMF}$ as a particular self-dual vertex operator superalgebra of $c=16$ and how we utilize string duality to arrive at this statement.
Jordan meets Freudenthal. A black hole exceptional story

Alessio Marrani

SciPost Phys. Proc. 14, 009 (2023) · published 23 November 2023 | · pdf

Within the extremal black hole attractors arising in ungauged $\mathcal{N}≥ 2$-extended Maxwell Einstein supergravity theories in $3+1$ space-time dimensions, we provide an overview of the stratification of the electric-magnetic charge representation space into "large" orbits and related "moduli spaces", under the action of the (continuous limit of the) non-compact $U$-duality Lie group. While each "large" orbit of the $U$-duality supports a class of attractors, the corresponding " moduli space" is the proper subspace of the scalar manifold spanned by those scalar fields on which the Attractor Mechanism is inactive. We present the case study concerning $\mathcal{N}=2$ supergravity theories with symmetric vector multiplets' scalar manifold, which in all cases (with the exception of the minimally coupled models) have the electric-magnetic charge representation of $U$-duality fitting into a reduced Freudenthal triple system over a cubic (simple or semi-simple) Jordan algebra.
Kurt Bernardo Wolf memorial lecture

George Pogosyan, Mariano A. del Olmo

SciPost Phys. Proc. 14, 010 (2023) · published 23 November 2023 | · pdf

A personal view of the Mexican mathematical physicist Kurt Bernardo Wolf (1942-2022) is presented here.
Tchavdar Dimitrov Palev - In memoriam

N. I. Stoilova

SciPost Phys. Proc. 14, 011 (2023) · published 23 November 2023 | · pdf

Tchavdar Dimitrov Palev – In memoriam

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