The Sakai-Sugimoto holographic model is famous for implementing the approximate chiral symmetry of QCD and reproducing the Chiral Lagrangian in a top-down approach. In this manuscript, we revisit the model in a formalism that is somewhat different from the original work by Sakai and Sugimoto: we start by identifying boundary degrees of freedom and splitting the bulk equations of motion into dynamical ones and constraints. The former are then solved to all orders in derivatives of the boundary fields. The constraints are left unsolved, leaving the dynamical degrees of freedom off-shell. This approach enables us to systematically derive the effective action of the boundary theory. The derived effective action is very rich in physics: it contains an U($\textit{N}$ ) multiplet of massless pseudoscalars interacting (via trilinear and higher terms) with towers of massive (axial-)vector mesons. In contrast to the previous studies, our effective action is non-local. The original Chiral Lagrangian is recovered as its local expansion in small $\textit{π}$-meson momenta (derivative expansion). We particularly zoom in on the values of four derivative terms couplings, the low energy constants, and compare those with the ones reported in the literature.

Israel

Michael Lublinsky

Timofey Solomko

Sakai-Sugimoto model in an off-shell: Chiral Lagrangian to all orders

We consider the vector and the pseudovector glueball in the top-down holographic model of large-<math><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub></mrow></math> QCD of Witten and their decays into ordinary mesons described by the D8 brane construction due to Sakai and Sugimoto. At leading order, the relevant interactions are determined exclusively by the Chern-Simons action of the D8 branes and are thus rigidly connected to the chiral anomaly and the Wess-Zumino-Witten terms. As found in a previous study of the pseudovector glueball, which we revisit and complete, the resulting decay widths are surprisingly large, implying that both the pseudovector and the vector glueball are very broad resonances, with a conspicuous dominance of decays into <math><msub><mi>a</mi><mn>1</mn></msub><mi>ρ</mi></math> and <math><msub><mi>K</mi><mn>1</mn></msub><mo>(</mo><mn>1400</mn><mo>)</mo><msup><mi>K</mi><mo>*</mo></msup></math> in the case of the vector glueball. We also obtain a certain weak mixing of vector glueballs with ordinary vector mesons, but we conclude that it does not provide an explanation for the so-called <math><mi>ρ</mi><mi>π</mi></math> puzzle in charmonium decays.

Austria

Florian Hechenberger

Josef Leutgeb

Anton Rebhan

Spin-1 glueballs in the Witten-Sakai-Sugimoto model

We consider the Witten-Sakai-Sugimoto model in the approximation of smeared instantons at finite density via a homogeneous ansatz, which is known to be discontinuous in order to be able to contain a nonvanishing baryon density. The discontinuity at the infrared tip of the bulk spacetime gives rise to subtleties of discarding boundary terms that are normally discarded in the literature. We propose a reason for discarding this boundary term, by scrutinizing the currents and topological properties of the model. Along the way, we find a very effective and simple condition to compute the point of thermodynamic equilibrium.

China

Lorenzo Bartolini

Sven Bjarke Gudnason

Boundary terms in the Witten-Sakai-Sugimoto model at finite density

We utilize the top-down holographic QCD model, the Witten-Sakai-Sugimoto model, in a hybrid setting with the SLy4, soft chiral EFT and stiff chiral EFT equations of state to describe neutron stars with high precision. In particular, we employ a calibration that bootstraps the nuclear matter by fitting the Kaluza-Klein scale and the ’t Hooft coupling such that the physical saturation density and physical symmetry energy are achieved. We obtain static stable neutron star mass-radius data via the Tolman-Oppenheimer-Volkov equations that yield sufficiently large maximal masses of neutron stars to be compatible with the recently observed PSR-J0952-0607 data as well as all other known radius and tidal deformation constraints.

Sven Gudnason

Neutron stars in the Witten-Sakai-Sugimoto model

We calculate radiative decay rates of mesons and glueballs in the top-down holographic Witten-Sakai-Sugimoto model with finite quark masses. After assessing to what extent this model agrees or disagrees with experimental data, we present its predictions for so far undetermined decay channels. Contrary to widespread expectations, we obtain sizeable two-photon widths of scalar, tensor, and pseudoscalar glueballs, suggesting in particular that the observed two-photon rate of the glueball candidate <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>1710</mn><mo>)</mo></math> is not too large to permit a glueball interpretation, but could be even much higher. We also discuss the so-called exotic scalar glueball, which in the Witten-Sakai-Sugimoto model is too broad to match either of the main glueball candidates <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>1500</mn><mo>)</mo></math> and <math><msub><mi>f</mi><mn>0</mn></msub><mo>(</mo><mn>1710</mn><mo>)</mo></math> but might be of interest with regard to the alternative scenario of the so-called fragmented scalar glueball. Employing the exotic scalar glueball for the latter, much smaller two-photon rates are predicted for the ground-state glueball despite a larger total width; relatively large two-photon rates would then apply to the excited scalar glueball described by the predominantly dilatonic scalar glueball. In either case, the resulting contributions to the muon <math><mi>g</mi><mo>−</mo><mn>2</mn></math> from hadronic light-by-light scattering involving glueball exchanges are small compared to other single meson exchanges, of the order of <math><mo>≲</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>12</mn></mrow></msup></math>.

Radiative meson and glueball decays in the Witten-Sakai-Sugimoto model

We discuss all-order transseries in one of the simplest quantum mechanical systems: a U(1) symmetric single-degree-of-freedom system with a first-order time derivative term. Following the procedure of the Lefschetz thimble method, we explicitly evaluate the path integral for the generating function of the Noether charge and derive its exact transseries expression. Using the conservation law, we find all the complex saddle points of the action, which are responsible for the nonperturbative effects and the resurgence structure of the model. The all-order power-series contributions around each saddle point are generated from the one-loop determinant with the help of the differential equations obeyed by the generating function. The transseries are constructed by summing up the contributions from all the relevant saddle points, which we identify by determining the intersection numbers between the dual thimbles and the original path integration contour. We confirm that the Borel ambiguities of the perturbation series are canceled by the nonperturbative ambiguities originating from the discontinuous jumps of the intersection numbers. The transseries computed in the path-integral formalism agrees with the exact generating function, whose explicit form can be obtained in the operator formalism thanks to the integrable nature of the model. This agreement indicates the nonperturbative completeness of the transseries obtained by the semiclassical expansion of the path integral based on the Lefschetz thimble method.

Japan

Toshiaki Fujimori

Poland

Syo Kamata

Tatsuhiro Misumi

Muneto Nitta

Norisuke Sakai

All-order resurgence from complexified path integral in a quantum mechanical system with integrability

The resurgence structure of the 2d O(N) sigma model at large N is studied with a focus on an IR momentum cutoff scale a that regularizes IR singularities in the semiclassical expansion. Transseries expressions for condensates and correlators are derived as series of the dynamical scale Λ (nonperturbative exponential) and coupling λ  μ  renormalized at the momentum scale μ. While there is no ambiguity when a &gt; Λ, we find for a &lt; Λ that the nonperturbative sectors have new imaginary ambiguities besides the well-known renormalon ambiguity in the perturbative sector. These ambiguities arise as a result of an analytic continuation of transseries coefficients to small values of the IR cutoff a below the dynamical scale Λ. We find that the imaginary ambiguities are cancelled each other when we take all of them into account. By comparing the semiclassical expansion with the transseries for the exact large-N result, we find that some ambiguities vanish in the a → 0 limit and hence the resurgence structure changes when going from the semiclassical expansion to the exact result with no IR cutoff. An application of our approach to the ℂP  N−1 sigma model is also discussed. We find in the compactified model with the ℤ N  twisted boundary condition that the resurgence structure changes discontinuously as the compactification radius is varied.

Hiromichi Nishimura

Resurgence and semiclassical expansion in two-dimensional large-N sigma models

We determine exactly the phase structure of a chiral magnet in one spatial dimension with the Dzyaloshinskii-Moriya (DM) interaction and a potential that is a function of the third component of the magnetization vector, n 3, with a Zeeman (linear with the coefficient B) term and an anisotropy (quadratic with the coefficient A) term, constrained so that 2A ≤ |B|. For large values of potential parameters A and B, the system is in one of the ferromagnetic phases, whereas it is in the spiral phase for small values. In the spiral phase we find a continuum of spiral solutions, which are one-dimensionally modulated solutions with various periods. The ground state is determined as the spiral solution with the lowest average energy density. As the phase boundary approaches, the period of the lowest energy spiral solution diverges, and the spiral solutions become domain wall solutions with zero energy at the boundary. The energy of the domain wall solutions is positive in the homogeneous phase region, but is negative in the spiral phase region, signaling the instability of the homogeneous (ferromagnetic) state. The order of the phase transition between spiral and homogeneous phases and between polarized (n 3 = ±1) and canted (n 3 ≠ ±1) ferromagnetic phases is found to be second order.

United Kingdom

Calum Ross

Exact ground states and domain walls in one dimensional chiral magnets

Abstract A brane-world SU(5) grand unified theory model with global non-Abelian vortices is constructed in six-dimensional spacetime. We find a solution with a vortex associated to SU(3) separated from another vortex associated to SU(2). This 3–2 split configuration achieves a geometric Higgs mechanism for SU(5) → SU(3) × SU(2) × U(1) symmetry breaking. A simple deformation potential induces a domain wall between non-Abelian vortices, leading to a linear confining potential. The confinement stabilizes the vortex separation moduli, and ensures the vorticities of the SU(3) and SU(2) groups are identical. This dictates the equality of the numbers of fermion zero modes in the fundamental representation of SU(3) (quarks) and SU(2) (leptons), leading to quark/lepton generations. The standard model massless gauge fields are localized on the non-Abelian vortices thanks to a field-dependent gauge kinetic function. We perform fluctuation analysis with an appropriate gauge fixing and obtain a four-dimensional effective Lagrangian of unbroken and broken gauge fields at quadratic order. We find that SU(3) × SU(2) × U(1) gauge fields are localized on the vortices and exactly massless. Complications in analyzing the spectra of gauge fields with the nontrivial gauge kinetic function are neatly worked out by a vector-analysis-like method.

Masato Arai

Czechia

Filip Blaschke

Minoru Eto

Masaki Kawaguchi

Standard model gauge fields localized on non-Abelian vortices in six dimensions

Abstract We study a resurgence structure of a quantum field theory with a phase transition to uncover relations between resurgence and phase transitions. In particular, we focus on three-dimensional  supersymmetric quantum electrodynamics (SQED) with multiple hypermultiplets, where a second-order quantum phase transition has recently been proposed in the large-flavor limit. We provide interpretations of the phase transition from the viewpoints of Lefschetz thimbles and resurgence. For this purpose, we study the Lefschetz thimble structure and properties of the large-flavor expansion for the partition function obtained by the supersymmetric localization. We show that the second-order phase transition is understood as a phenomenon where a Stokes and an anti-Stokes phenomenon occur simultaneously. The order of the phase transition is determined by how saddles collide at the critical point. In addition, the phase transition accompanies an infinite number of Stokes phenomena due to the supersymmetry. These features are appropriately mapped to the Borel plane structures as the resurgence theory expects. Given the lessons from SQED, we provide a more general discussion on the relationship between the resurgence and phase transitions. In particular, we show how the information on the phase transition is decoded from the Borel resummation technique.