We investigate the scalar perturbation around a rotating Einstein-bumblebee BTZ black hole under Robin boundary conditions. It is shown that the relationship curves between real and imaginary parts of scalar quasinormal modes in the complex plane depend on the black hole spin parameter <italic>j</italic> and the Lorentz symmetry breaking parameter <italic>s</italic>. The shapes of these curves are similar for different <italic>s</italic>, but heavily depend on the spin parameter <italic>j</italic>. With the increase of <italic>j</italic>, the symmetry of these curves with respect to the imaginary axis in the complex plane is gradually broken for different <italic>s</italic>. We also discuss the energy and angular momentum fluxes across the black hole horizon under Robin boundary conditions, and probe the changes of the threshold parameter related to the superradiance in Robin boundary conditions with the symmetry breaking parameter and the spin parameter. The combination of the Lorentz symmetry violation and the Robin boundary condition provides richer physics in the scalar perturbation around a rotating Einstein-bumblebee BTZ black hole.

China

Chengjia Chen

Fengkai Ge

Qiyuan Pan

Jiliang Jing

Scalar perturbation around rotating Einstein-bumblebee BTZ black holes under Robin boundary conditions: Quasinormal modes and superradiance

The maximal cut of the nonplanar crossed box diagram with all massive internal propagators was long ago shown to encode a hyperelliptic curve of genus 3 in momentum space. Surprisingly, in Baikov representation, the maximal cut of this diagram only gives rise to a hyperelliptic curve of genus 2. To show that these two representations are in agreement, we identify a hidden involution symmetry that is satisfied by the genus 3 curve, which allows it to be algebraically mapped to the curve of genus 2. We then argue that this is just the first example of a general mechanism by means of which hyperelliptic curves in Feynman integrals can drop from genus <math><mi>g</mi></math> to <math><mo>⌈</mo><mi>g</mi><mo>/</mo><mn>2</mn><mo>⌉</mo></math> or <math><mo>⌊</mo><mi>g</mi><mo>/</mo><mn>2</mn><mo>⌋</mo></math>. We find an algorithm to test for the presence of genus drop, and highlight further instances of this mechanism in Feynman integrals.

Switzerland

Robin Marzucca

CERN

United States

Andrew J. McLeod

Ben Page

Germany

Sebastian Pögel

Stefan Weinzierl

Genus drop in hyperelliptic Feynman integrals

In this paper, we delve into the gravitational path integral of Gauss-Bonnet gravity in four spacetime dimensions, in the mini-superspace approximation. Our primary focus lies in investigating the transition amplitude between distinct boundary configurations. Of particular interest is the case of Robin boundary conditions, known to lead to a stable Universe in Einstein-Hilbert gravity, alongside Neumann boundary conditions. To ensure a consistent variational problem, we supplement the bulk action with suitable surface terms. This study leads us to compute the necessary surface terms required for Gauss-Bonnet gravity with the Robin boundary condition, which wasn’t known earlier. Thereafter, we perform an exact computation of the transition amplitude. Through ħ → 0 analysis, we discover that the Gauss-Bonnet gravity inherently favors the initial configuration, aligning with the Hartle-Hawking no-boundary proposal. Remarkably, as the Universe expands, it undergoes a transition from the Euclidean (imaginary time) to the Lorentzian signature (real time). To further reinforce our findings, we employ a saddle point analysis utilizing the Picard-Lefschetz methods. The saddle point analysis allows us to find the initial configurations which lead to Hartle-Hawking no-boundary Universe that agrees with the exact computations. Our study concludes that for positive Gauss-Bonnet coupling, initial configurations corresponding to the Hartle-Hawking no-boundary Universe gives dominant contribution in the gravitational path-integral.

India

Manishankar Ailiga

Shubhashis Mallik

Gaurav Narain

Lorentzian Robin Universe

We study hairy black holes in Einstein-Maxwell-complex scalar theory in four-dimensional asymptotically global anti-de Sitter (AdS) spacetime when the Robin boundary conditions are imposed on the scalar field. This setup is dual to the double trace deformation of strongly interacting field theory on R × S 2 by charged scalar operators. We identify the instability of the Reissner-Nordström-AdS (RNAdS) black holes under the Robin boundary conditions and construct backreacted geometries branching at the onset of the instability. Also considering associated horizonless geometries called boson stars, we obtain phase diagrams with fairly rich structure in the grand canonical ensemble depending on the boundary condition parameter or the deformation parameter, where phase transition occurs between thermal AdS, RNAdS, charged boson stars, and hairy black holes.

Japan

Tomohiro Harada

Takaaki Ishii

Denmark

Takuya Katagiri

Norihiro Tanahashi

Hairy black holes in AdS with Robin boundary conditions

We consider the case of a two-loop five-point pentagon-box integral configuration with one internal massive propagator that contributes to top-quark pair production in association with a jet at hadron colliders. We construct the system of differential equations for all the master integrals in a canonical form where the analytic form is reconstructed from numerical evaluations over finite fields. We find that the system can be represented as a sum of d-logarithmic forms using an alphabet of 71 letters. Using high precision boundary values obtained via the auxiliary mass flow method, a numerical solution to the master integrals is provided using generalised power series expansions.

Italy

Simon Badger

Matteo Becchetti

France

Ekta Chaubey

Two-loop master integrals for a planar topology contributing to pp →   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>j</mi> </math>  $$ t\overline{t}j $$

We compute helicity amplitudes for the one-loop QCD corrections to top-quark pair production analytically in terms of a set of uniformly transcendental master integrals. We provide corrections up to O(ε 2) in the dimensional regulator for the first time which are relevant at NNLO. Four independent pentagon integral topologies appear in the complete description of the colour structure for which we provide numerical solutions using canonical form differential equations and the method of generalised power series expansions. Analytic forms of the boundary values are obtained in all cases except one where we find a one-dimensional integral representation.

Francesco Sarandrea

One-loop QCD helicity amplitudes for pp →   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>j</mi> </math>  $$ t\overline{t}j $$  to O(ε 2)

We compute the three-loop leading-colour corrections to the Yang-Mills Regge trajectory and gluon impact factor. Conjecturing that, in analogy with   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super Yang-Mills (SYM), in a suitable scheme N  c -subleading terms are absent from the three-loop Regge trajectory, we understand our result as the first computation of the pure gauge, or n  f  = 0, part of the QCD three-loop Regge trajectory. The results are presented both for the bare and renormalised amplitudes and are consistent with predictions from infrared factorisation along with reproducing known results in planar   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 SYM through a maximal weight truncation. We also include the dependence on a Regge factorisation scale to facilitate future applications in BFKL theory at next-to-next-to leading logarithmic accuracy.

Vittorio Duca

Sweden

Bram Verbeek

The gluon Regge trajectory at three loops from planar Yang-Mills theory

We perform a systematic study of the Maxwell quasinormal spectrum in a mirror-like cavity following the generic Robin type vanishing energy flux principle, by starting with the Schwarzschild black holes in this paper. It is shown that, for black holes in a cavity, the vanishing energy flux principle leads to two different sets of boundary conditions. By solving the Maxwell equations with these two boundary conditions both analytically and numerically, we observe two distinct sets of modes. This indicates that the vanishing energy flux principle may be applied not only to asymptotically anti-de Sitter (AdS) black holes but also to black holes in a cavity. In the analytic calculations, the imaginary part of the Maxwell quasinormal modes are derived analytically for both boundary conditions, which match well with the numeric results. While in the numeric calculations, we complete a thorough study on the two sets of the Maxwell spectrum by varying the mirror radius  $$r_m$$  <math> <msub> <mi>r</mi> <mi>m</mi> </msub> </math>  , the angular momentum quantum number  $$\ell $$  <math> <mi>ℓ</mi> </math>  , and the overtone number N. In particular, we proclaim that the Maxwell spectrum may bifurcate for both modes when the mirror is placed around the black hole event horizon, which is analogous to the spectrum bifurcation effects found for the Maxwell fields on asymptotically AdS black holes. This observation provides another example to exhibit the similarity between black holes in a cavity and the AdS black holes.

Yunhe Lei

Mengjie Wang

Maxwell perturbations in a cavity with Robin boundary conditions: two branches of modes with spectrum bifurcation on Schwarzschild black holes

Within quantum field theory on a global monopole spacetime, we study thermal effects on a naked singularity and their relation to boundary conditions. We first obtain the two-point functions for the ground state and for thermal states of a massive, arbitrarily coupled, free scalar field compatible with Robin boundary conditions at the singularity. We then probe these states using a static Unruh-Dewitt particle detector. The transition rate is analyzed for the particular cases of massless minimally or conformally coupled fields at finite temperature. To interpret the detector’s behavior, we compute the thermal contribution to the ground-state fluctuations and to the energy density. We verify that the behavior of the transition rate, the fluctuations, and the energy density are closely intertwined. In addition, we find that these renormalized quantities remain finite at the singularity for, and only for, the Dirichlet boundary condition.

Lissa de Souza Campos

Brazil

João Paulo M. Pitelli

Thermal effects on a global monopole with Robin boundary conditions

We compute the transition rate of an Unruh-DeWitt detector coupled both to a ground state and to a KMS state of a massless, conformally coupled scalar field on a static BTZ black hole with Robin boundary conditions. We observe that, although the anti-Hawking effect is manifest for the ground state, this is not the case for the KMS state. In addition, we show that our analysis applies with minor modifications also to the anti-Unruh effect on Rindler-AdS$_{3}$ spacetime.

Claudio Dappiaggi

The anti-Hawking effect on a BTZ black hole with Robin boundary conditions