We study soliton and black hole solutions with scalar hair in AdS in a theory with a Maxwell field and a charged scalar field with double trace boundary conditions, which can trigger the dual boundary theory to become a superconductor. We investigate the phase diagram as a function of the temperature $\textit{T}$ and of the double trace coupling $\textit{κ}$ and we find a rich pattern of phase transitions, which can be of the Hawking-Page kind or can be due to the condensation of the order parameter. We also find a transition between vortex solutions and the zero temperature limit of the black hole for a critical value of the double trace coupling $\textit{κ}$. The Little-Park periodicity is realized for the dual of the black hole solution with hair as a shift in the winding number and in the gauge field.

Italy

Roberto Auzzi

Stefano Bolognesi

Giuseppe Nardelli

Chile

Gianni Tallarita

Japan

Nicolò Zenoni

Solitonic vortices and black holes with vortex hair in AdS

We study the strong-interaction dynamics of a class of 4$\textit{D}$ chiral SU($\textit{N}$) gauge theories with a fermion in a symmetric second-rank tensor representation and a number of fermions in an anti-antisymmetric tensor representation, extending the previous work on chiral gauge theories such as the Bars-Yankielowicz and the generalized Georgi-Glashow models. The main tool of our analysis is the anomalies obstructing the gauging of certain 1-form color-flavor-locked center symmetry, together with some flavor symmetries. The matching requirement for these mixed-anomalies strongly favors dynamical Higgs phases caused by bifermion condensate formation, against a confinement phase with no condensates and no symmetry breaking, or a confinement phase with multifermion color-singlet condensates only. Dynamical gauge symmetry breaking and the spontaneous breaking of a U(1) symmetry caused by such condensates mean that the color-flavor-locked 1-form center symmetry itself is lost in the infrared. One is led to a solution, if not unique, which satisfies fully the conventional as well as the new, generalized ’t Hooft anomaly matching requirements.

Kenichi Konishi

Andrea Luzio

Matteo Orso

Chiral gauge theories, generalized anomalies and breakdown of the color-flavor-locked center symmetry

We propose a generalization of the theory of magnetic Skyrmions in chiral magnets in two dimensions to a higher-dimensional theory with magnetic Skyrmions in three dimensions and an target space, requiring a 4-dimensional magnetization vector. A physical realization of our theory could be made using a synthetic dimension, recently promoted and realized in condensed matter physics. In the simplest incarnation of the theory, we find a Skyrmion and a sphaleron — the latter being an unstable soliton. Including also the Skyrme term in the theory enriches the spectrum to a small metastable Skyrmion, an unstable sphaleron and a large stable Skyrmion.

China

Sven Gudnason

Roberto Menta

Higher-dimensional magnetic Skyrmions

In a large class of chiral gauge theories in four dimensions it was found that certain natural assumption about the bifermion condensates leads to the infrared effective theory where the ’t Hooft anomaly matching conditions are satisfied in an entirely evident fashion, without need of verifying arithmetic equations. This is due to the fact that in these systems, characterized by dynamical color (and flavor) symmetry breaking, the quantum numbers and multiplicities of the low-energy massless fermions match exactly those of the fermions in the UV theory which do not condense and remain massless, with respect to the unbroken symmetries. This means also that the stronger constraints following from the matching request of mixed anomalies involving certain generalized 1-form center symmetries, as well as some global anomalies such as Witten’s <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> anomaly, are all fully satisfied. It is the aim of this note to clarify better the working of this phenomenon (which we call natural anomaly matching), correct some earlier statements made about it, and illustrate it further with a few new examples.

Natural anomaly matching

The scattering of electrically charged fermions on magnetic monopole leads to the Callan-Rubakov effect. We discuss some aspects of this problem for Abelian gauge theories with chiral fermions in a Dirac monopole background. In some cases, it is possible to embed the theory in a non-Abelian gauge theory where the monopole is regularized as a ’t Hooft-Polyakov monopole. One theory of this kind is the <math><mrow><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></math> chiral gauge theory with fermions in the representation <math><mrow><mo>□</mo><mspace height="0.0ex" width="-4pt"></mspace><mo>□</mo><mo>⊕</mo></mrow></math> <math><mover><mtable frame="solid" align="bottom"><mtr><mtd><mi> </mi></mtd></mtr><mtr><mtd><mi> </mi></mtd></mtr></mtable><mo>¯</mo></mover></math><math><mi> </mi><mo>⊕</mo><mi> </mi><mn>8</mn><mi> </mi><mo>×</mo><mi> </mi><mover><mrow><mi>□</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>, also called the “<math><mi>ψ</mi><mi>χ</mi><mi>η</mi></math>” model, with an extra adjoint scalar that induces the abelianization of the gauge group. We examine this model in detail and provide a possible solution for the condensates around the monopole, the symmetry preserving boundary conditions, and discuss the particle scattering problem.

Bruno Bucciotti

Monopole-fermion scattering in a chiral gauge theory

We discuss how the quark masses and their mass splitting affect the baryons in the Skyrme model as well as the Witten-Sakai-Sugimoto (WSS) model. In both cases, baryons are described by solitonic objects, i.e., Skyrmions and instantons, respectively. After the quantization of their zero modes, the nucleons become quantum states of a rotor. We show how the quark mass affects the moment of inertia and we provide a semianalytic approach valid in the small-mass limit. Additionally, we show how the two lightest quarks’ mass splitting affects the moments of inertia of the Skyrmion and induces an isospin breaking effect. This effect turns out not to be enough to split the degeneracy in the neutron-proton multiplet, but it splits some of the states in the <math><mi>Δ</mi></math> multiplet. Unlike the basic Skyrme model, the WSS model already includes vector mesons and another mechanism to transfer isospin breaking from quark masses to the solitons is known. We compute the splitting of the moment of inertia in the small-mass limit in the WSS model and combine the two effects on the spectrum of baryons, in particular the <math><mi>Δ</mi></math>’s.

Lorenzo Bartolini

Sven Bjarke Gudnason

United States

Tommaso Rainaldi

Mass and isospin breaking effects in the Skyrme model and in holographic QCD

We revisit the simplest Bars-Yankielowicz (BY) model (the ψη model), starting from a model with an additional Dirac pair of fermions in the fundamental representation, together with a complex color-singlet scalar ϕ coupled to them through a Yukawa interaction. This model possesses a color-flavor-locked 1-form ℤ N  symmetry, due to the intersection of the color SU(N) and two nonanomalous U(1) groups. In the bulk, the model reduces to the ψη model studied earlier when ϕ acquires a nonzero vacuum expectation value and the extra fermions pair up, get massive and decouple (thus we will call our extended theory as the “X-ray model”), while it provides a regularization of the ℤ2 fluxes needed to study the ℤ2 anomaly. The anomalies involving the 1-form ℤ N  symmetry reduce, for N even, exactly to the mixed ℤ2 anomaly found earlier in the ψη model. The present work is a first significant step to clarify the meaning of the mixed ℤ2 − [  <math> <msubsup> <mi>ℤ</mi> <mi>N</mi> <mfenced> <mn>1</mn> </mfenced> </msubsup> </math>  $$ {\mathbb{Z}}_N^{(1)} $$ ]2 anomaly found in the ψη and in other BY and Georgi-Glashow type SU(N) models with even N.

The ℤ2 anomaly in some chiral gauge theories

We consider certain aspects of the electroweak Skyrmion (EWS). We discuss the case of EWS with dynamical Higgs and find numerical solutions for various values of the cutoff scale. Our results are qualitatively similar to the ones present in the literature, but we find a considerable lower mass than previous studies. We discuss the quantization of the light degrees of freedom and prove that the EWS is a boson. We consider the interaction between fermions and the EWS and the transfer of fermionic charge onto the soliton. We consider the large distance structure of the soliton and the interaction between two well separated EWSs. We find that the classical EWS has a magnetic dipole moment. We discuss the lifetime of the metastable soliton. Finally, we discuss some phenomenological and cosmological consequences of our results.

Giacomo Santoni

Aspects of the electroweak Skyrmion

We explore the idea that in some class of strongly-coupled chiral SU(N) gauge theories the infrared dynamics might be characterized by a bifermion condensate in the ad- joint representation of the color gauge group. As an illustration, in this work we revisit an SU(N) chiral gauge theory with Weyl fermions in a symmetric (ψ) and anti-antisymmetric (χ) tensor representations, together with eight fermions in the anti-fundamental representations (η), which we called ψχη model in the previous investigations. We study the infrared dynamics of this system more carefully, by assuming dynamical Abelianization, a phenomenon familiar from 𝒩 = 2 supersymmetric gauge theories, and by analyzing the way various continuous and discrete symmetries are realized at low energies. We submit then these ideas to a more stringent test, by taking into account some higher-form symmetries and the consequent mixed anomalies. A detailed analysis of the mixed anomalies involving certain 0-form U(1) symmetries and the color-flavor locked 1-form ℤ N  symmetry in the ψχη system shows that the proposed infrared dynamics is consistent with it.

Dynamical Abelianization and anomalies in chiral gauge theories

We consider the Skyrme model in the near-BPS limit. The BPS part is made of the sextic term plus a potential and the deformation is made of the standard massive Skyrme model controlled by a small parameter ϵ ≪ 1. In order to keep the perturbation under theoretical and computational control, we find a model for which BPS Skyrmions have compact support, henceforth denoted as compactons, and the spherically symmetric B = 1 Skyrmion represents the most stable solution. We use the ϵ-expansion scheme to systematically calculate the corrections to the energy and compare with the exact numerical computations in the B = 1 sector. Finally, we use the ϵ-expansion scheme to calculate the bound state of two B = 1 Skyrmions and its binding energy, which corresponds, prior to quantization, to the deuteron in our model.