Under a reasonable set of ab initio assumptions, we define and chart the atlas of simple gauge theories with families of fermions whose masses are forbidden by gauge invariance. We propose a compass to navigate the atlas based on counting degrees of freedom. When searching for Grand Unification Theories with three matter generations, the free energy singles out the SU(5) Georgi-Glashow model as the minimal one, closely followed by SO(10) with spinorial matter. The atlas also defines the dryland of grand-unifiable gauge extensions of the standard model. We further provide examples relevant for gauge dual completions of the standard model as well as extensions by an additional SU(N) gauge symmetry.

France

Giacomo Cacciapaglia

Konstantinos Kollias

South Africa

Aldo Deandrea

Italy

Francesco Sannino

Selection toolkit for standard and non-standard GUTs

The presence of a topological susceptibility in the electroweak sector of the Standard Model motivates the existence of a good quality weak axion <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>W</mi></msub></math>, associated with the spontaneous breaking of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>+</mo><mi>L</mi></math>. Its anomalous couplings and tiny mass, generated from electroweak instantons, render <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>W</mi></msub></math> photophobic. We find that the strongest bound on the associated decay constant <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mi>W</mi></msub></math> stems from a loop-induced coupling to electrons, leading to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mi>W</mi></msub><mo>≳</mo><mn>1000</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> from stellar cooling. Spontaneous breaking of the Abelian <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><mo>+</mo><mi>L</mi></math> symmetry induces proton decay via higher-dimensional operators controlled by a new physics scale <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi></math>. Existing Super-Kamiokande limits on these decay channels constrain the new physics scale to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Λ</mi><mo>≳</mo><msup><mn>10</mn><mn>12</mn></msup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. The characteristic channel <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mo stretchy="false">→</mo><msup><mi>e</mi><mo>+</mo></msup><msub><mi>a</mi><mi>W</mi></msub></math> and other possible operators mediating interactions with the Standard Model fields yield signals which are not detectable within the allowed parameter space. Future proton decay searches at the next generation of neutrino experiments offer the most promising avenues to test the good qualities of the weak axion paradigm.

United Kingdom

Jessica Turner

Good qualities of the weak axion

The Swampland program, which looks for low energy theories consistent with quantum gravity, has led to the introduction of a dark dimension stemming from the cosmological constant. We show that the same argument leads to the emergence of the electroweak scale, once the dark dimension is realised in a warped background. A second warped extra dimension at the TeV scale is, therefore, postulated, where the long-standing problem of the hierarchy between the electroweak and the Planck scales can be addressed. Furthermore, standard model contributions to the cosmological constant are tamed, together with the gravitational ones. In the emergent holistic picture of gravity and gauge interactions, both Planck and the electroweak scales are emergent from a theory with two fundamental scales: 10 eV and 10 GeV, which are of geometric origin and, following the Distance Conjecture, natural. Hence, a bridge is established between the two standard models of particle physics and cosmology.

Iran

Kazem Fadafan

Denmark

The cosmological constant, dark matter and the electroweak scale meet in the Swampland

Asymptotic grand unification models can be constructed in five dimensions compactified on an orbifold. We demonstrate that the parameter space of such models admit solutions that naturally achieve the baryon asymmetry via leptogenesis, these solutions indicating that the scale of the extra dimensions is much higher than the TeV scale.

Timothé Alezraa

Leptogenesis in five-dimensional asymptotic grand unification models

Gravitational wave observation has provided numerous insights into the merger of astrophysical black holes. In contrast to other violent events ( <italic>e.g.</italic> supernovae), they are, however, not expected to lead to significant emissions of photons and neutrinos. In this paper we discuss a scenario that would lead to characteristic observable gamma ray bursts, which would provide numerous hints to physics beyond General Relativity. Starting from the hypothesis that micro-black holes (called <italic>morsels</italic>) are formed during the merger process, we show that it is possible to observe their Hawking radiation, which takes the form of gamma ray bursts of a uniquely characteristic form: with energies in the TeV range, their temporal structure is unlike that stemming from any other astrophysical event. Notably, the time delay from the gravitational wave event is correlated to the mass distribution of the morsels. The integrated mass of the morsels, allowed by the unaccounted merger mass, leads to a Hawking radiation in photons that is above the sensitivity of atmospheric Cherenkov telescopes such as HESS, LHAASO and HAWC, and gamma ray space telescopes, such as Fermi-LAT. This renders the hypothesis of morsel creation experimentally testable, and we provide the first concrete bounds on the total mass of morsels formed in specific events.

Stefan Hohenegger

Looking for black hole morsels in astrophysical mergers via Hawking radiation

We examine the vacuum stability of gauge symmetry breaking in five dimensions, compactified on the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>/</mo><mo stretchy="false">(</mo><msub><mrow><mi mathvariant="double-struck">Z</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>×</mo><msubsup><mrow><mi mathvariant="double-struck">Z</mi></mrow><mrow><mn>2</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo stretchy="false">)</mo></mrow></math> orbifold. We consider <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>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Sp</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SO</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo stretchy="false">)</mo></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SO</mi><mo stretchy="false">(</mo><mn>2</mn><mi>N</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo></math> theories in the bulk, and provide an exhaustive classification of possible parity assignments that lead to stable orbifolds and of the corresponding symmetry breaking patterns. We use these results in the search for viable asymptotic grand unification theories (aGUT), testing the stability criteria on models based on SU(6) and SU(8). As a result, we identify two viable aGUTs: a unique SU(6) pathway down to the Standard Model, and one SU(8) model leading to an intermediate Pati-Salam partial unification.

Alan S. Cornell

Wanda Isnard

Sweden

Roman Pasechnik

Anca Preda

China

Zhi-Wei Wang

General vacuum stability of orbifold gauge breaking and application to asymptotic grand unification

In analysing five dimensional orbifolds with exceptional gauge groups, we seek to find stable vacua configurations which satisfy the minimal requirements for asymptotic grand unified models. In this respect we show that no minimal asymptotic grand unified theory can be built. Our results point towards non-minimal models based on $$E_6$$ : one featuring supersymmetry, and the other needing a modification of the Coleman–Weinberg potential to stabilise the breaking of $$E_6$$ to the standard model gauge group.

Alan Cornell

Are there minimal exceptional aGUTs from stable 5D orbifolds?

We investigate high and low energy implications of a gauge dual description of the Standard Model. The high energy electric theory features gauge dynamics involving only fermionic matter fields, while the low energy magnetic description features a quasisupersymmetric spectrum testable at colliders. The flavor theory is constructed via operators generated at the Planck scale, possibly by gravitational global symmetry breaking interactions. We further show that duality opens novel avenues for theories of grand unification.

Charting standard model duality and its signatures

Strong dynamics for composite Higgs models predict spin-1 resonances which are expected to be in the same mass range as the usually considered top-partners. We study here QCD-coloured vector and axial-vector states stemming from composite Higgs dynamics in several relevant models based on an underlying gauge-fermion description. These states can come as triplet, sextet and octet representation. All models considered have a colour octet vector state in common which can be singly produced at hadron colliders as it mixes with the gluon. We explore the rich and testable phenomenology of these coloured spin-1 states at the LHC and future colliders.

Germany

Manuel Kunkel

Werner Porod

Coloured spin-1 states in composite Higgs models

The ultimate dream of unification models consists in combining both gauge and Yukawa couplings into one unified coupling. This is achieved by using a supersymmetric exceptional <math><msub><mrow><mi>E</mi></mrow><mrow><mn>6</mn></mrow></msub></math> gauge symmetry together with asymptotic unification in compact five-dimensional space-time. The ultraviolet fixed point requires exactly three fermion generations: one in the bulk, and the two light ones localised on the <math><mrow><mi>SO</mi></mrow><mo>(</mo><mn>10</mn><mo>)</mo></math> boundary in order to cancel gauge anomalies. A second option allows to preserve baryon number and to lower the compactification scale down to the typical scales of the intermediate Pati-Salam gauge theory.