We discuss the AdS/CFT correspondence from the viewpoint of gravity as a broken phase of conformal gauge symmetry. In AdS <inline-formula><tex-math id='TM0001' notation='LaTeX'>$_2$</tex-math></inline-formula>/CFT <inline-formula><tex-math id='TM0002' notation='LaTeX'>$_1$</tex-math></inline-formula>, the Schwarzian structure is related to the boundary extrinsic curvature. In AdS <inline-formula><tex-math id='TM0003' notation='LaTeX'>$_4$</tex-math></inline-formula>/CFT <inline-formula><tex-math id='TM0004' notation='LaTeX'>$_3$</tex-math></inline-formula>, the gauge-theoretic formulation of four-dimensional gravity contains a boundary-sensitive Euler sector whose descent structure leads to the Cotton tensor characterizing the three-dimensional boundary conformal geometry. At the structural and kinematical level considered here, these results suggest a unified geometrical interpretation of holography in terms of boundary remnants of broken bulk conformal gauge symmetry.

Japan

Takeshi Fukuyama

Gauge Theory of Gravity and the AdS/CFT Correspondence

The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough elucidation. We introduce a novel probabilistic interpretation scheme for complex compositeness of resonances, in which resonances with large decay widths fall outside the domain where their internal structure can be interpreted probabilistically. Employing this scheme to analyze resonances via the effective range expansion, we demonstrate that narrow interpretable near-threshold resonances have a small composite fraction, in sharp contrast to shallow bound states below the threshold.

Tomona Kinugawa

Tetsuo Hyodo

Compositeness of Near-Threshold <italic>s</italic>-Wave Resonances

We investigate stringy constraints on moduli spaces in modular flavor models by analyzing moduli-dependent threshold corrections in heterotic string vacua. While moduli play a crucial role in determining the flavor structure of fermions predicted by modular flavor models, the parameter space in which their vacuum expectation values are allowed has not been fully explored. In this work, within the framework of perturbative heterotic string theory on toroidal orbifolds, we derive the constraints on the moduli space and study their systematic behavior. We characterize the stringy constraints in terms of the dilaton, the beta function coefficients, and the ratio between the complex-structure modulus and Kähler modulus. It is found that a large value of the modulus controlling the flavor structure, i.e. <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\tau \simeq i \infty$</tex-math></inline-formula>, is inconsistent within perturbative string theory, and the self-dual point <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\tau =i$</tex-math></inline-formula> is also disfavored in the large-volume regime of toroidal backgrounds. In addition, we discuss the phenomenological implications of these stringy constraints.

Keiya Ishiguro

Takafumi Kai

Tatsuo Kobayashi

Hajime Otsuka

Stringy Constraints on Modular Flavor Models

In this work, Bogomol’nyi–Prasad–Sommerfield (BPS) models built from the coupling of the Yang–Mills–Higgs Lagrangian to impurities are investigated. We first consider scalar impurities, which in the BPS limit generate monopoles similar to those obtained in a previously considered class of <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\mathrm{SU(2)}\times \mathrm{Z}_2$</tex-math></inline-formula> or <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\mathrm{SU(2)}\times \mathrm{SU(2)}$</tex-math></inline-formula> models. We then focus on the coupling to non-Abelian impurities, defined as fixed backgrounds produced by fields transforming under the adjoint representation of SU(2), with a coupling chosen to preserve half of the BPS sectors. The nature of this coupling, the ensuing Bogomol&#8217;nyi bound and BPS equations, as well as the effect of these impurities on the abelianization that leads to the emergence of a U(1) gauge group are investigated. We also verify that these impurity models can be derived as effective theories from a homogeneous <inline-formula><tex-math id='TM0003' notation='LaTeX'>$\rm {SU(2)}\times \widetilde{\rm {SU}}(2)$</tex-math></inline-formula> Yang&#8211;Mills&#8211;Higgs parent model with a bridge field. In this interpretation, the SU(2) impurities of the effective impurity-doped theory are produced by frozen antimonopoles from the <inline-formula><tex-math id='TM0004' notation='LaTeX'>$\widetilde{\rm {SU}}(2)$</tex-math></inline-formula> sector. We study in greater detail impurities with spherical symmetry, and examine the manner in which impurity coupling changes the asymptotic behavior and range of monopole interactions. Moreover, we introduce a method that can be used to approximate solutions with the use of small perturbations around the Prasad&#8211;Sommerfield monopole. In order to exemplify the most important properties of the theory, several specific impurity models are presented, and the corresponding monopole solutions are found numerically. These solutions present novel internal structure and multiple features that would not be possible in the original theory.

Brazil

D Bazeia

M A Liao

M A Marques

Magnetic Monopoles in Yang–Mills–Higgs Theory with Impurities

We study black-hole quasinormal modes by applying the complex-scaling method (CSM) to the perturbation equations of Schwarzschild and Reissner–Nordström black holes. The method converts the outgoing-wave boundary condition into a non-Hermitian eigenvalue problem, allowing quasinormal-mode frequencies to be computed within a common spectral framework. We first benchmark the method for the Schwarzschild Regge–Wheeler equation and then extend it to the Reissner–Nordström family, including the extremal limit. Our results show that CSM provides a unified and flexible approach to the computation of black-hole quasinormal frequencies.

Shoya Ogawa

Takuya Hirose

Okuto Morikawa

Complex-Scaling Approach to Quasinormal Modes of Schwarzschild and Reissner–Nordström Black Holes

The extensive list of 4+4-dimensional Manin triples that was presented recently can be used to find new solutions of Supergravity Equations via Poisson–Lie T-plurality. To obtain the solutions, we start with 1+3-dimensional flat backgrounds on Poisson–Lie groups corresponding to semi-Abelian Manin triples. For application of the Poisson–Lie T-plurality, we identify Manin triples that form various decompositions of the same Drinfeld double. Besides flat backgrounds and plane-parallel waves for solving Supergravity Equations, plurality transformation also produces curved backgrounds with torsion satisfying (Generalized) Supergravity Equations. Many of the Poisson–Lie transformations can be understood as homogeneous Yang–Baxter deformations. Of special interest are the non-unimodular deformations leading to solutions of Generalized Supergravity Equations.

Czechia

Ladislav Hlavatý

Petr Novotný

Ivo Petr

Eight-Dimensional Manin Triples, Yang–Baxter Deformations, and Solutions of Supergravity Equations

By performing a field redefinition via a cohomomorphism on the Maurer–Cartan action of the <inline-formula><tex-math id='TM0001' notation='LaTeX'>$A_\infty$</tex-math></inline-formula> algebra, we construct an action that reproduces the characteristic structure of boundary string field theory (BSFT), which we refer to as the BSFT-like action. We show that the form and several properties of this BSFT-like action closely resemble those of BSFT. Our results suggest that this approach provides a systematic framework to derive the BSFT action from the open string field theory based on <inline-formula><tex-math id='TM0002' notation='LaTeX'>$A_\infty$</tex-math></inline-formula> algebras.

Jojiro Totsuka-Yoshinaka

Boundary String Field Theory–like Action from Cohomomorphism

The Lorentzian type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In this model, the eigenvalue distribution of the <inline-formula><tex-math id='TM0001' notation='LaTeX'>$N\times N$</tex-math></inline-formula> bosonic matrices <inline-formula><tex-math id='TM0002' notation='LaTeX'>$A_\mu$</tex-math></inline-formula> <inline-formula><tex-math id='TM0003' notation='LaTeX'>$(\mu = 0 , \ldots , 9)$</tex-math></inline-formula> represents an emergent spacetime, which is determined by the dynamics of the model in the large- <italic>N</italic> limit. Here we perform numerical simulations of the model overcoming the sign problem by the complex Langevin method with the matrix size <italic>N</italic> up to 128. In order to avoid the singular drift problem due to the Pfaffian, which appears after integrating out the fermionic matrices, we deform the model in a manner inspired by the supersymmetric deformation, which is used to define the &#8220;polarized type IIB matrix model&#8221; in the Euclidean case. We find that the deformed model exhibits a phase in which (3+1)D expanding spacetime emerges with both space and time being smooth and real.

Greece

Konstantinos N Anagnostopoulos

Takehiro Azuma

Italy

Mitsuaki Hirasawa

Jun Nishimura

Stratos Papadoudis

Asato Tsuchiya

The Emergence of (3+1)D Expanding Spacetime from Complex Langevin Simulations of the Lorentzian Type IIB Matrix Model with Deformations

Understanding the novel QCD phenomenon under high external magnetic fields of a hot and dense medium help us to develop a better understanding of the underlying quark dynamics of baryons. Using a hybrid approach based on the effective field theory that treats quarks as the fundamental degrees of freedom and calculating the individual contributions from valence, sea, and the orbital angular moments of sea quarks, the magnetic moment of a given baryon of the decuplet family is calculated. The incorporation of Landau quantization in the vector and scalar densities of baryons help us to obtain the impact of an external magnetic field on the properties of baryons within the chiral SU(3) quark mean field model (CQMF). In the present study, effective masses of the baryons are calculated using CQMF while the framework of the chiral constituent quark model ( <inline-formula><tex-math id='TM0001' notation='LaTeX'>$\chi$</tex-math></inline-formula>CQM), extended to the SU(4) sector, is used to obtain the effective magnetic moments of decuplet baryons under the influence of a magnetic field.

India

Utsa Dastidar

Arvind Kumar

Harleen Dahiya

Suneel Dutt

Magnetic Moments of Decuplet Baryons in Asymmetric Magnetized Nuclear Matter

Strongly motivated by a mathematical result by Lin and Yamashita, we describe a long exact sequence formed by groups of equivalence classes of two-dimensional <inline-formula><tex-math id='TM0002' notation='LaTeX'>$\mathcal {N}{=}(0,1)$</tex-math></inline-formula> supersymmetric quantum field theories (SQFTs) with and without <inline-formula><tex-math id='TM0003' notation='LaTeX'>$SU(2)$</tex-math></inline-formula> symmetry. As an application, we study chiral fermions in heterotic compactifications with an&#160; <inline-formula><tex-math id='TM0004' notation='LaTeX'>$SU(2)$</tex-math></inline-formula> symmetry of level one to four dimensions, and show that each even-dimensional irreducible representation of <inline-formula><tex-math id='TM0005' notation='LaTeX'>$SU(2)$</tex-math></inline-formula> appears even times, assuming the conjectural relation between topological modular forms and SQFTs. This implies the absence of the Witten anomaly, but contains more information than that.

Yuji Tachikawa

On a Long Exact Sequence of Groups of Equivalence Classes of 2d 𝒩 = (0,1) SQFTs