<p>We unify the dynamics of massive vector (Proca) fields in Schwarzschild spacetime with supersymmetric gauge theories through the Seiberg-Witten/quasinormal mode (SW/QNM) duality. By mapping Proca perturbations—specifically monopole and odd-parity modes governed by confluent Heun equations—to the quantum Seiberg-Witten curve, we establish a gauge-gravity correspondence. Leveraging instanton counting, we analytically compute QNM and quasibound state frequencies to high precision, resolving spectral properties nonperturbatively. Our results align with numerical benchmarks while extending the SW framework beyond scalar fields.</p>

China

Xian-Hui Ge

Japan

Masataka Matsumoto

Kilar Zhang

Massive vector field perturbations in the Schwarzschild spacetime from supersymmetric gauge theory

For neutron stars, there exist universal relations insensitive to the equation of states, the so called I-Love-Q relations, which show the connections among the moment of inertia, tidal Love number and quadrupole moment. In this paper, we show that these relations also apply to dark stars, bosonic or fermionic. The relations can be extended to higher ranges of the variables, clarifying the deviations for dark stars in the literature, as those curves all approximate the ones generated by a polytropic equation of state, when taking the low density (pressure) limit. Besides, we find that for equation of states with scaling symmetries, the I-Love-Q curves do not change when adjusting the scaling parameters.

Jing-Yi Wu

Wei Li

Xin-Han Huang

Dark I-Love-Q

AGT conjecture reveals a connection between 4D   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 gauge theory and 2D conformal field theory. Though some special instances have been proven, others remain elusive and the attempts on its full proof never stop. When the Ω background parameters satisfy −ϵ 1/ϵ 2 ≡ β = 1, the story can be simplified a bit. A proof of the correspondence in the case of A 1 gauge group was given in 2010 by Mironov et al., while the A  n  extension is verified by Matsuo and Zhang in 2011, with an assumption on the Selberg integral of n + 1 Schur polynomials. Then in 2020, Albion et al. obtained the rigorous result of this formula. In this paper, we show that the conjecture on the Selberg integral of Schur polynomials is formally equivalent to their result, after applying a more complicated complex contour, thus leading to the proof of the A  n  case at β = 1. To perform a double check, we also directly start from this formula, and manage to show the identification between the two sides of AGT correspondence.

Qing-Jie Yuan

Shao-Ping Hu

Zi-Hao Huang

Proof of A  n  AGT conjecture at β = 1

In this paper, we give a proof of 5D A  n  AGT conjecture at β = 1, where the gauge theory side is one dimension higher than the original 4D case, and corresponds to the q-deformation of the 2D conformal field theory side. We define a q-deformed A  n  Selberg integral, which generalizes the A  n  Selberg integral and the q-deformed A 1 Selberg integral in the literature. A q-deformed A  n  Selberg average formula with n + 1 Schur polynomials is proposed and proved to complete the proof.

Qian Shen

Hong Kong

Sweden

Proof of 5D A  n  AGT conjecture at β = 1

The newly established Seiberg-Witten (SW)/Quasinormal Modes (QNM) correspondence offers an efficient analytical approach to calculate the QNM frequencies, which was only available numerically before. This is based on the fact that both sides are characterized by Heun-type equations. We find that a similar duality exists between Seiberg-Witten theory and black hole superradiance, since the latter can also be linked to confluent Heun equation after proper transformation. Then a dictionary is constructed, with the superradiance frequencies written in terms of gauge parameters. Further by instanton counting, and taking care of the boundary conditions through connection formula, the relating frequencies are obtained analytically, which show consistency with known numerical results.

Duality between Seiberg-Witten theory and black hole superradiance

We study the quasinormal modes (QNM) of the charged C-metric, which physically stands for a charged accelerating black hole, with the help of Nekrasov’s partition function of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 superconformal field theories (SCFTs). The QNM in the charged C-metric are classified into three types: the photon-surface modes, the accelerating modes and the near-extremal modes, and it is curious how the single quantization condition proposed in [1] can reproduce all the different families. We show that the connection formula encoded in terms of Nekrasov’s partition function captures all these families of QNM numerically and recovers the asymptotic behavior of the accelerating and the near-extremal modes analytically. Using the connection formulae of different 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 SCFTs, one can solve both the radial and the angular parts of the scalar perturbation equation respectively. The same algorithm can be applied to the de Sitter (dS) black holes to calculate both the dS modes and the photon-sphere modes.

Yang Lei

Hongfei Shu

Rui-Dong Zhu

Quasinormal modes of C-metric from SCFTs

The qq-characters are powerful tools to reveal symmetries and integrabilities of Seiberg-Witten theories. The goal of this paper is to provide analytic expressions of qq-characters based on Young diagrams in 5d 𝒩 = 1 pure Yang-Mills theories with BCD-type gauge groups, by focusing on the unrefined limit. Using these expressions, we investigate the relationships among qq-characters of classical gauge groups. For SO(n) gauge groups, we construct a quantum-toroidal-like algebra via the Ward-identity approach, which allows us to derive the qq-characters.

Satoshi Nawata

ABCD of qq-characters

We propose three scenarios for compact hybrid stars composed of nuclear and dark matter. These hybrid stars could provide alternative interpretations to the LIGO/Virgo events GW170817 and GW190425. To demonstrate our proposal, we solve the Tolman–Oppenheimer–Volkoff configurations of hybrid stars by using the SLy4, APR4, and SKb equations of state (EoS) for nuclear matter, and an EoS for a bosonic self interacting dark matter (SIDM) proposed by Colpi et al. (Phys Rev Lett 57:2485, 1986). We then obtain their mass–radius and tidal Love number (TLN)-mass relations, and further examine the possible saddle instability of these compact objects by the generalized Bardeen–Thorne–Meltzer (BTM) criteria. Our results show that the hybrid star scenarios are able to explain GW170817 and GW190425. Some hybrid stars can have compact neutron or mixed cores around 10 km while possessing thick dark matter shells, thus they can be more massive than the maximum mass of the typical neutron stars but are electromagnetically detected with about the same size of neutron stars. Reversely, we also infer the dark matter model from the parameter estimation of GW190425. Our proposed hybrid stars can be further tested by the coming LIGO/Virgo O3 events.

Taiwan

Guo-Zhang Huang

Jie-Shiun Tsao

Feng-Li Lin

GW170817 and GW190425 as hybrid stars of dark and nuclear matter

We use a holographic model of quantum chromodynamics to extract the equation of state (EoS) for the cold nuclear matter of moderate baryon density. This model is based on the Sakai-Sugimoto model in the deconfined Witten's geometry with the additional point-like D4-brane instanton configuration as the holographic baryons. Our EoS takes the following doubly-polytropic form: <math><mi>ϵ</mi><mo>=</mo><mn>2.629</mn><msup><mrow><mi>A</mi></mrow><mrow><mo>−</mo><mn>0.192</mn></mrow></msup><msup><mrow><mi>p</mi></mrow><mrow><mn>1.192</mn></mrow></msup><mo>+</mo><mn>0.131</mn><msup><mrow><mi>A</mi></mrow><mrow><mn>0.544</mn></mrow></msup><msup><mrow><mi>p</mi></mrow><mrow><mn>0.456</mn></mrow></msup></math> with <math><mi>A</mi></math> a tunable parameter of order <math><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, where ϵ and p are the energy density and pressure, respectively. The sound speed satisfies the causality constraint and breaks the sound barrier. We solve the Tolman-Oppenheimer-Volkoff equations for the compact stars and obtain the reasonable compactness for the proper choices of <math><mi>A</mi></math>. Based on these configurations we further calculate the tidal deformability of the single and binary stars. We find our results agree with the inferred values of LIGO/Virgo data analysis for GW170817.

Takayuki Hirayama

Ling-Wei Luo

Compact star of holographic nuclear matter and GW170817

Some BPS quantities of <math><mi>N</mi><mo>=</mo><mn>1</mn></math> 5D quiver gauge theories, like instanton partition functions or qq-characters, can be constructed as algebraic objects of the Ding–Iohara–Miki (DIM) algebra. This construction is applied here to <math><mi>N</mi><mo>=</mo><mn>2</mn></math> super Yang–Mills theories in four dimensions using a degenerate version of the DIM algebra. We build up the equivalent of horizontal and vertical representations, the first one being defined using vertex operators acting on a free boson's Fock space, while the second one is essentially equivalent to the action of Vasserot–Shiffmann's Spherical Hecke central algebra. Using intertwiners, the algebraic equivalent of the topological vertex, we construct a set of <math><mi>T</mi></math>-operators acting on the tensor product of horizontal modules, and the vacuum expectation values of which reproduce the instanton partition functions of linear quivers. Analysing the action of the degenerate DIM algebra on the <math><mi>T</mi></math>-operator in the case of a pure <math><mi>U</mi><mo>(</mo><mi>m</mi><mo>)</mo></math> gauge theory, we further identify the degenerate version of Kimura–Pestun's quiver W-algebra as a certain limit of q-Virasoro algebra. Remarkably, as previously noticed by Lukyanov, this particular limit reproduces the Zamolodchikov–Faddeev algebra of the sine-Gordon model.