The Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) dilatonic black hole, a key solution in low-energy string theory, exhibits previously unexplored chaotic dynamics for charged test particles under electromagnetic influence. While characterizing such chaos requires high-precision numerical methods, our prior research identifies the explicit symplectic algorithm as the optimal integration tool for strongly curved gravitational systems. Leveraging the Hamiltonian formulation of the GMGHS black hole, we develop an optimized fourth-order symplectic algorithm, <math altimg='si28.svg'><mrow><mi>P</mi><mi>R</mi><msub><mi>K</mi><mn>6</mn></msub><mn>4</mn></mrow></math>. This algorithm enables a systematic investigation of chaotic motion using four distinct chaos indicators: the Shannon entropy, Poincar&#233; sections, the maximum Lyapunov exponent, and the Fast Lyapunov Indicator. Our results demonstrate a critical dependence of chaos on both electric charge ( <math altimg='si1.svg'><mi>Q</mi></math>, characterized by the Coulomb parameter <math altimg='si11.svg'><msup><mi>Q</mi><mo>*</mo></msup></math>) and magnetic charge ( <math altimg='si17.svg'><msub><mi>Q</mi><mi>m</mi></msub></math>). Specifically, in electrically charged backgrounds, order-to-chaos transitions occur with increasing <math altimg='si1.svg'><mi>Q</mi></math>. Conversely, in magnetically charged backgrounds, chaos emerges with increasing <math altimg='si17.svg'><msub><mi>Q</mi><mi>m</mi></msub></math>. When <math altimg='si1.svg'><mi>Q</mi></math> and <math altimg='si11.svg'><msup><mi>Q</mi><mo>*</mo></msup></math> vary simultaneously, the chaotic dynamics exhibit greater sensitivity to changes in <math altimg='si11.svg'><msup><mi>Q</mi><mo>*</mo></msup></math>. Especially, these findings establish the Shannon entropy as a robust chaos indicator within relativistic frameworks and provide novel insights into the dynamics of string-theoretic black holes.

China

Zhen-Meng Xu

Da-Zhu Ma

Kai Li

Chaos dynamics of charged particles near Gibbons-Maeda-Garfinkle-Horowitz-Strominger black holes

It is shown that a 2D conformal field theory consisting of a central charge <math><mi>c</mi></math> Liouville theory, a chiral level one, rank <math><mi>N</mi></math> Kac-Moody algebra, and a weight <math><mo>−</mo><mn>3</mn><mo>/</mo><mn>2</mn></math> free fermion holographically generate 4D maximal helicity violating tree-level scattering amplitudes. The correlators of this 2D conformal field theory give directly the 4D leaf amplitudes associated to a single hyperbolic slice of flat space. The 4D celestial amplitudes arise in a large-<math><mi>N</mi></math> and semiclassical large-<math><mi>c</mi></math> limit, according to the holographic dictionary, as a translationally invariant combination of leaf amplitudes. A step in the demonstration is showing that the semiclassical limit of Liouville correlators are given by contact 3D anti–de Sitter Witten diagrams.

United States

Walker Melton

Atul Sharma

Andrew Strominger

Tianli Wang

Celestial Dual for Maximal Helicity Violating Amplitudes

Families of Lorentz, but not Poincare, invariant vacua are constructed for a massless scalar field in 4D Minkowski space. These are generalizations of the Rindler vacuum with a larger symmetry group. Explicit expressions are given as squeezed excitations of the Poincare vacuum. The effective reduced vacua on the 3D hyperbolic de Sitter slices are the well-known de Sitter α-vacua with antipodal singularities in the Wightman function. Several special interesting cases are discussed.

Filip Niewinski

Hyperbolic vacua in Minkowski space

Celestial amplitudes may be decomposed as weighted integrals of AdS3-Witten diagrams associated to each leaf of a hyperbolic foliation of spacetime. We show, for the Kleinian three-point MHV amplitude, that each leaf subamplitude is smooth except for the expected light-cone singularities. Moreover, we find that the full translationally-invariant celestial amplitude is simply the residue of the pole in the leaf amplitude at the point where the total conformal weights of the gluons equals three. This full celestial amplitude vanishes up to light-cone contact terms, as required by spacetime translation invariance, and reduces to the expression previously derived by Mellin transformation of the Parke-Taylor formula.

Celestial leaf amplitudes

Celestial MHV amplitudes are comprised of non-distributional leaf amplitudes associated to an AdS3 leaf of a foliation of flat spacetime. It is shown here that the leaf amplitudes are governed by the same infinite-dimensional soft ‘S-algebra’ as their celestial counterparts. Moreover, taking the soft limit of the smooth three-point MHV leaf amplitude yields a nondegenerate minus-minus two-point leaf amplitude. The two- and three-point MHV leaf amplitudes are used to compute the plus-minus-minus leaf operator product coefficients.

Soft algebras for leaf amplitudes

Recent work has shown that loop corrections from massless particles generate <math><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>log</mi><msub><mrow><mi>T</mi></mrow><mrow><mtext>Hawking</mtext></mrow></msub></mrow></math> corrections to black hole entropy which dominate the thermodynamics of cold near-extreme charged black holes. Here we adapt this analysis to near-extreme Kerr black holes. Like <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math>, the near-horizon extreme Kerr (NHEK) metric has a family of normalizable zero modes corresponding to reparametrizations of boundary time. The path integral over these zero modes leads to an infrared divergence in the one-loop approximation to the Euclidean NHEK partition function. We regulate this divergence by retaining the leading finite temperature correction in the NHEK scaling limit. This “not-NHEK” geometry lifts the eigenvalues of the zero modes, rendering the path integral infrared finite. The quantum-corrected near-extremal entropy exhibits <math><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mi>log</mi><msub><mrow><mi>T</mi></mrow><mrow><mtext>Hawking</mtext></mrow></msub></mrow></math> behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.

Daniel Kapec

Ahmed Sheta

Italy

Chiara Toldo

Logarithmic Corrections to Kerr Thermodynamics

We construct a regular bound state of two extremal black holes in type IIB supergravity with opposite charges. The bound state resembles the Schwarzschild black hole from the asymptotics to the photon ring and has the same mass and charges as the Schwarzschild black hole. On the one hand, we show that the bound-state entropy admits a microscopic description in terms of branes and antibranes in string theory. On the other hand, we demonstrate that the entropy approaches half of the Schwarzschild entropy as the mass becomes significantly larger than the Kaluza-Klein scales used to regularize the geometry. This opens up the possibility of a brane/antibrane interpretation of the Schwarzschild entropy in string theory.

Pierre Heidmann

Half the Schwarzschild entropy from Strominger-Vafa black holes

The general form of a 2D conformal field theory (CFT) correlator on a Euclidean Riemann surface, Lorentzian plane or Lorentzian cylinder is well known. This paper describes the general form of 2- and 3-point CFT correlators on the Lorentzian torus <math><mrow><msup><mrow><mi>LT</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> which arises as the conformal boundary of the group manifold <math><mrow><mi>SL</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo>)</mo><mo>≃</mo><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>/</mo><mi>Z</mi></mrow></math>. We consider only generic points, thereby omitting an analysis of contact terms, which already exhibits a surprisingly rich structure. The results are relevant to celestial holography, for which the <math><mrow><msup><mrow><mi>LT</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> at the boundary of Klein space is the home of the putative celestial CFT.

Conformal correlators on the Lorentzian torus

BFSS proposed that asymptotically flat M-theory is dual to a large N limit of the matrix quantum mechanics describing N nonrelativistic D0-branes. Recent insights on the soft symmetries of any quantum theory of gravity in asymptotically flat space are applied to the BFSS matrix model. It is shown that soft gravitons are realized by submatrices whose rank is held fixed in the large N M-theory limit, rather than the usual linear scaling with N for hard gravitons. The soft expansion is identified with the large N expansion and the soft theorem becomes a universal formula for the quantum mechanical scattering of such submatrix excitations. This formula is shown to be the Ward identity of large type IIA U(1) RR  asymptotic gauge symmetry in the matrix model, whose asymptotic boundaries are at future and past timelike infinity.

Noah Miller

Adam Tropper

Soft gravitons in the BFSS matrix model

We construct two-dimensional quantum states associated to four-dimensional linearized rotating self-dual black holes in (2, 2) signature Klein space. The states are comprised of global conformal primaries circulating on the celestial torus, the Kleinian analog of the celestial sphere. By introducing a generalized tower of Goldstone operators we identify the states as coherent exponentiations carrying an infinite tower of w1+∞  charges or soft hair. We relate our results to recent approaches to black hole scattering, including a connection to Wilson lines,   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$ -matrix results, and celestial holography in curved backgrounds.