<p>A deeper understanding of QCD matter at strong coupling remains challenging due to its nonperturbative nature. To this end, we study a two-flavor holographic hard-wall model to investigate the properties of QCD at finite-density and zero temperature with a nonvanishing quark mass. A dense matter phase is described by a classical solution of the equations of motion in a homogeneous ansatz. We apply holographic renormalization to formulate the holographic dictionary that relates UV boundary data in the bulk with the physical quantities in QCD. We emphasize a role played by an IR boundary action on the hard wall when analyzing the QCD phase structures in this holographic setup. It is found that a baryonic matter phase is manifested in this model with a high baryon number density and a nearly vanishing chiral condensate. We derive the equation of state for the resulting phase and use it to work out the mass-radius relation for neutron stars. We find that the maximum mass of neutron stars can exceed two solar masses for a wide range of free parameters in this model. We also comment on an alternative scenario about the phase structure such that the baryonic matter phase arises at a baryon number chemical potential greater than a critical value.</p>

Daisuke Fujii

Atsushi Hosaka

Akihiro Iwanaka

Tadakatsu Sakai

Motoi Tachibana

Dense matter in a holographic hard-wall model of QCD

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 analyze higher-group structure of a 6d model coupled with a self-dual 2-form gauge field. This model is defined from 6d axion-electrodynamics with a 1-form Chern-Weil(CW) symmetry gauged dynamically. The gauging leads to a Green-Schwarz-West-Sagnotti(GSWS) term, which gives rise to an anomaly through a GSWS transformation acting on the 2-form gauge field. We cancel this anomaly by gauging a 3-form CW symmetry in 6d axion-electrodynamics. We find out the global symmetries in the resultant model and derive the gauge invariant action in the presence of the background gauge fields. It is argued that a discrete 1-form symmetry is anomalous because turning on the associated background gauge field causes quantum inconsistency due to an operator-valued ambiguity. Higher-group structure in this model that is manifested as a Green-Schwarz-like transformation for CW background gauge fields is discussed.

Japan

Tatsuki Nakajima

Kikyo Nakamura

Note on higher-group structure in 6d self-dual gauge theory

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 the BCF anomaly of massless QCD-like theories, first obtained by Anber and Poppitz, from the viewpoint of the low energy effective theories. We assume that the QCD-like theories exhibit spontaneous chiral symmetry breaking due to a quark bilinear condensate. Using the ’t Hooft anomaly matching condition for the BCF anomaly, we find that the low energy effective action is composed of a chiral Lagrangian and a Wess-Zumino-Witten term together with an interaction term of the η′ meson with the background gauge field for a discrete one-form symmetry. It is shown that the low energy effective action cancels the quantum inconsistencies associated with η′ due to an ambiguity of how to uplift the action to a five-dimensional spacetime with a boundary. The η′ term plays a substantial role in exploring the emergent higher-group structure at low energies.

Ryo Yokokura

BCF anomaly and higher-group structure in the low energy effective theories of mesons

We investigate 2n-dimensional axion electrodynamics for the purpose of exploring a higher-group structure underlying it. This is manifested as a Green-Schwarz transformation of the background gauge fields that couple minimally to the conserved currents. The n = 3 case is studied most intensively. We derive the identities of correlation functions among the global symmetry generators by using a gauge transformation that maps two correlation functions with each other. A key ingredient in this computation is given by the Green-Schwarz transformation and the ’t Hooft anomalies associated with the gauge transformation. The algebraic structure of these results and its physical interpretations are discussed in detail. In particular, we find that the higher-group structure for n = 3 is endowed with a multi-ary operation among the symmetry generators.

Higher-group structure in 2n-dimensional axion-electrodynamics

Abstract We study the contact terms that appear in the correlation functions of exactly marginal operators using the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. It is known that CFT with an exactly marginal deformation requires the existence of the contact terms with their coefficients having a geometrical interpretation in the context of conformal manifolds. We show that the AdS/CFT correspondence captures properly the mathematical structure of the correlation functions that is expected from the CFT analysis. For this purpose, we employ a holographic renormalization group to formulate a most general setup in the bulk for describing an exactly marginal deformation. The resultant bulk equations of motion are nonlinear and solved perturbatively to obtain the on-shell action. We compute three- and four-point functions of the exactly marginal operators using the GKP–Witten prescription, and show that they match the expected results precisely. The cut-off surface prescription in the bulk serves as a regularization scheme for conformal perturbation theory in the boundary CFT. As an application, we examine a double OPE limit of the four-point functions. The anomalous dimensions of double trace operators are written in terms of the geometrical data of a conformal manifold.