We investigate baryogenesis in Standard Model (SM) extensions with new SU(2) multiplet fields. We focus on sphalerogenesis, in which the baryon asymmetry of the Universe (BAU) is generated through the gradual decoupling of CP-violating electroweak sphaleron-like processes. We show that the observed BAU can be reproduced when the new fields possess CP-violating Yukawa interactions, which leave a CP-violating dimension-six operator involving the SU(2) gauge fields at low energies. As representative examples, we study models with fermionic SU(2) quintuplets and septuplets, and find that these field masses should be $$ \mathcal{O}(1) $$ TeV to explain the BAU. We also show that viable parameter regions for the BAU are consistent with current bounds on the electron electric dipole moment and thoroughly probed by future measurements such as ACME III and by mono-lepton searches at the HL-LHC. Our results provide a concrete and phenomenologically testable ultraviolet completion of sphalerogenesis.

Japan

Kiyoto Ogawa

China

Masanori Tanaka

Baryogenesis in SU(2) $\textit{L}$ multiplet models

In this paper we study the IR dynamics of SU($\textit{N}$) gauge theories with four supercharges in 3d in presence of symmetric or antisymmetric tensor. Using the tensor deconfinement technique we provide some proofs of results previously claimed in the literature about confining dualities for SU($\textit{N}$) with two antisymmetric tensors. Furthermore we study 3d confining dualities with symmetric tensors and linear monopole superpotentials. These confining dualities have been obtained by applying the duplication formula for the hyperbolic Gamma functions on effective dualities on ℝ $\textit{× S}$ with SU($\textit{N}$) gauge groups and antisymmetric tensors. We conclude the analysis providing an alternative derivation, again using the tensor deconfinement technique.

Italy

Antonio Amariti

Germany

Fabio Mantegazza

Simone Rota

Rank-two tensors and deconfinement in 3d 𝒩 = 2 SU($\textit{N}$) gauge theories

Flavourful extensions of the Standard Model aimed at explaining its fermionic mass structure typically rely on symmetries, broken at high-energy scales far beyond the reach of foreseeable direct collider searches. We illustrate, using a SU(2) flavour gauge group, that the breaking of these symmetries up to scales as high as 10 GeV could generate a gravitational wave signal potentially observable by future observatories. We use dimensional reduction techniques to obtain the finite-temperature effective potential and study the possible first-order phase transitions. We match these transitions to steady-state hydrodynamical solutions in order to determine the corresponding gravitational-wave spectra. We observe that order-one gauge couplings are always required for a first-order phase transition to occur. On the other hand, adding leptoquarks (as an example of particles that are typically present in a complete flavour theory) significantly extends the testable parameter space. We find excellent prospects at the Einstein Telescope for future gravitational-wave detection of flavoured SU(2) early-universe phase transitions.

France

Anna Chrysostomou

South Africa

Philippines

Alan Cornell

Luc Darmé

Aldo Deandrea

Thibault Demartini

Gravitational waves from flavoured SU(2) early-universe phase transitions

We investigate string configurations in the deconfined phase of SU(3) gauge theory, which arise from the spontaneous breaking of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>3</mn></msub></math> center symmetry. These configurations form at the junctions of domain walls of the theory. The complex phase of the Polyakov loop changes by multiples of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>2</mn><mi>π</mi></math> on large spatial loops around the string, rendering them topologically stable. Using the Monte Carlo simulations of the partition function, we compute the free energy associated with these configurations. The simulations are performed on lattices with spatial dimensions <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></msub><mo>=</mo><mn>60</mn><mo>,</mo><msub><mi>N</mi><mi>z</mi></msub><mo>=</mo><mn>4</mn></math>, and temporal extent <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>2</mn></math>, 4. Our results show that the free energy of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>3</mn></msub></math> strings is dominated by the domain walls. Further near the transition point, thermal fluctuations cause the decay of domain walls as well as the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>Z</mi><mn>3</mn></msub></math> strings into confined-deconfined interfaces.

India

Sanatan Digal

Sumit Shaw

Vinod Mamale

Topological strings in SU(3) gauge theory at finite temperature

In a recent work, we argued that the net quark number gained by a bath of quarks and gluons upon bringing an external static quark probe, while being equal to 1 in the high temperature, deconfined phase, is equal to 0 or 3 in the low temperature, confined phase, depending on the value of the quark chemical potential. This establishes a clear-cut connection between the confinement of a medium as probed by order parameters such as the Polyakov loop, and the ability of that same medium to screen the quark probe into states with the same net quark content as mesons or baryons. In this work, we extend these findings to the SU(<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math>) color group, consider color probes in various (fundamental and nonfundamental) representations, and conjecture a rationale of how these results could be recovered from a purely thermodynamic argument that shortcuts the use of the Euclidean functional framework, while emphasizing the role of color <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math>-ality as a proxy for center symmetry within the Minkowskian framework.

V. Tomas Mari Surkau

Urko Reinosa

SU(<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math>) confinement and color <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>c</mi></msub></math>-ality

Mixed oriented and nonoriented center vortices are known to generate nontrivial topological charge. However, most previous analyses have been restricted to Abelian-projected thin configurations. Studies of thick vortices have so far focused on the <italic>SU</italic>(2) case and on the intersection of a single pair of oriented objects. In this work, we construct mixed oriented and nonoriented thick center-vortex gauge fields in <italic>SU</italic>( <italic>N</italic>) with smooth profiles and explicit non-Abelian phases. These phases ensure a smooth interpolation between different Cartan fluxes at monopole junctions. We analyze the resulting topological charge density and visualize its morphology, elucidating the color structures responsible for fractional lumps that together yield a nonvanishing global charge.

Brazil

David R. Junior

Luis E. Oxman

Gustavo M. Simões

Thick oriented and nonoriented center-vortex <italic>SU</italic>( <italic>N</italic>) configurations with fractional topological charge lumps

Generalised spin structures are necessary for placing fermions on manifolds that do not admit a standard spin structure. This is especially relevant in a dimensional reduction on such a manifold, which can then be compensated by using fermions that are appropriately charged under some Maxwell or Yang-Mills field defined on the internal manifold. A well known example in the physics literature is $$ {\mathbbm{CP}}^2 $$ , which has four real dimensions and is the coset SU(3)/U(2). In this paper we focus on a five-dimensional coset space, namely the Wu manifold SU(3)/SO(3) , where SO(3) is maximal in SU(3). Intriguingly, the Wu manifold does not admit a spin structure or spin structure, it does admit a spin structure. We provide a physical interpretation of the spin structure by considering spinors that are coupled to an SO(3) Yang-Mills field defined on the Wu manifold, but which carry half-integer “isospin,” thereby canceling the minus sign in the holonomy for uncharged spinors that provides the original obstruction to an ordinary spin structure. We also construct a gauge-covariantly constant spinor in the Wu manifold, and we show how this can be employed in order to construct spin spinor harmonics from scalar harmonics. We provide a very explicit construction of all the scalar and spin harmonics. In a follow-up paper, we shall employ the results we obtain here in order to discuss dimensional reductions and consistent reductions on the Wu manifold.

United States

Cameron Gibson

Okan Günel

Gabriel Larios

C. Pope

Spin $\textit{h}$ structure, scalar and charged spinor eigenfunctions on the SU(3)/SO(3) Wu manifold

We revisit the fermion mass problem of the <italic>SU</italic>(5) grand unified theory using machine learning techniques. The original <italic>SU</italic>(5) model proposed by Georgi and Glashow is incompatible with the observed fermion mass spectrum. Two remedies are known to resolve this discrepancy, one is through introducing a new interaction via a 45-dimensional field, and the other via a 24-dimensional field. We investigate which modification is more beautiful, defining the beauty as proximity to the original Georgi-Glashow <italic>SU</italic>(5) model. Our analysis shows that, in both supersymmetric and non-supersymmetric scenarios, the model incorporating the interaction with the 24-dimensional field is more beautiful under this criterion. We then generalise these models by introducing a continuous parameter <italic>y</italic>, which takes the value 3 for the 45-dimensional field and 1.5 for the 24-dimensional field. Numerical optimisation reveals that <italic>y</italic>&#8239;&#8776;&#8239;0.8 yields the closest match to the original <italic>SU</italic>(5) model, indicating that this value corresponds to the most beautiful model according to our definition.

Fayez Abu-Ajamieh

Shinsuke Kawai

Nobuchika Okada

Good flavor search in SU(5): A machine learning approach

We consider electric flux tube solutions in SU(3) gauge theory with scalar fields in the fundamental representation. Such solutions can possibly be constructed in two classes, corresponding to the two maximally commuting generators <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mn>3</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mn>8</mn></msub></math> of SU(3). We successfully construct the 3-type solution with two scalar fields and show that it is immune to decay through Schwinger pair production of gauge bosons, but we have not been able to construct an 8-type solution.

Jude Pereira

Tanmay Vachaspati

Electric flux tube solutions in SU(3) gauge theory

We investigate the (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-dimensional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math>-deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><msub><mo stretchy="false">)</mo><mi>k</mi></msub></math> Yang-Mills theory in the lattice Hamiltonian formalism, which is characterized by three parameters: the number of colors <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>, the coupling constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>g</mi></math>, and the level <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi></math>. By treating these as tunable parameters, we explore how key properties of the theory, such as confinement and topological order, emerge in different regimes. Employing a variational mean-field analysis that interpolates between the strong- and weak-coupling regimes, we determine the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> phase structure in terms of the ’t Hooft coupling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>λ</mi><mi>tH</mi></msub><mo>=</mo><msup><mi>g</mi><mn>2</mn></msup><mi>N</mi></math> and the ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>k</mi><mo>/</mo><mi>N</mi></math>. We find that the topologically ordered phase remains robust at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> under appropriate scalings of these parameters. This result indicates that the continuum limit of large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> gauge theory may be more intricate than naively expected, and it motivates studies beyond the mean-field theory, both to achieve a further understanding of confinement in gauge theories and to guide quantum simulations of large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math> gauge theories.

Tomoya Hayata

Yoshimasa Hidaka

Hiromasa Watanabe

Phases of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math>-deformed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math> Yang-Mills theory at large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi></math>