Changes in magnetic helicity are often discussed across a variety of fields, from condensed matter physics to early universe cosmology. It is frequently stated that the helicity change is given by the integral of the gauge field strength tensor and its dual over spacetime, ∫ $\textit{F}$ ∧ $\textit{F}$. However, this is incorrect when magnetic monopoles once existed in the spacetime. In this paper, we show the correct formula of the helicity change in such a case for the Maxwell theory with the magnetic monopoles. We also discuss what happens when we embed the Maxwell theory with magnetic monopoles into non-Abelian gauge theories. We show that a similar formula holds for the ’t Hooft-Polyakov monopole. In particular, we find the winding numbers and the zeroes of the Higgs field in the non-Abelian gauge theory play a crucial role in the helicity change. The same discussion is also applicable to the electroweak theory, and we discuss the implication of our findings to the baryon number change via the chiral anomaly in the early universe.

Japan

Hajime Fukuda

Yuta Hamada

China

Kohei Kamada

Kyohei Mukaida

South Korea

Fumio Uchida

Magnetic helicity, magnetic monopoles, and Higgs winding

We determine the maximal gauge groups arising in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mn>8</mn></msub></math> heterotic string theory on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>T</mi><mn>2</mn></msup></math>. Our analysis proceeds along two approaches. First, we start the moduli space of the supersymmetric heterotic string theory on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>T</mi><mn>2</mn></msup></math> focusing on points of maximal gauge enhancement. At these special points, the charge lattice can exhibit a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="double-struck">Z</mi><mn>2</mn></msub></math> outer automorphism corresponding to the bulk gauge symmetry. By orbifolding the worldsheet theory by it with the fermion parity, we obtain the maximal gauge group of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mn>8</mn></msub></math> theory. Second, we directly study the toroidal compactification of 10D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>E</mi><mn>8</mn></msub></math> heterotic string. Both approaches agree, yielding a classification of 22 maximal gauge groups. For each case, we present the corresponding massless spectrum. In light of the no global symmetry/cobordism conjecture in quantum gravity, our result also offers a classification of nonsupersymmetric branes in 8D supersymmetric heterotic string theories.

Arata Ishige

Yuichi Koga

More on 8D nonsupersymmetric branes and heterotic strings

We revisit the electroweak crossover of the Standard Model (SM) in the early Universe, focusing on the interplay between generalized global symmetries, magnetic flux dynamics, and baryogenesis. Employing the dimensionally reduced 3d effective field theory of the SM at high temperature, we identify the symmetry structure — including higher-form and magnetic symmetries — and analyze their spontaneous breaking patterns across the crossover. We further define a gauge-invariant mixing angle that interpolates between U(1) and U(1) magnetic fields. Based on this framework, we examine baryogenesis via decaying magnetic helicity and identify three key effects: the baryon asymmetry is modified by an $$\mathcal{O}(1)$$ factor due to (1) the gauge-invariant definition of the mixing angle and (2) the approximate conservation of the unconfined magnetic flux; (3) a novel non-perturbative process in the presence of magnetic flux, which has been overlooked in previous analyses. Our findings suggest that the previous estimation of baryon asymmetry from the magnetic helicity decay may have sizable uncertainties, and we caution against relying on it, calling for further investigation.

Symmetries of hot SM, magnetic flux baryogenesis from helicity decay

We investigate the extent to which the swampland conjecture can be employed to constrain large-field inflationary models from the perspective of quantum gravity consistency. In particular, we focus on the swampland distance conjecture, which imposes an upper bound on the amplitude of primordial gravitational waves predicted by large-field inflation scenarios. This provides a striking contrast with the well-known Lyth bound, which yields a lower bound on the tensor-to-scalar ratio in such models. The two bounds thus play complementary roles in assessing the viability of inflationary scenarios. We demonstrate that, for certain representative large-field inflation models, the swampland distance conjecture alone can impose more stringent upper limits on the tensor-to-scalar ratio than current observational constraints from the cosmic microwave background. These findings highlight the utility of swampland criteria as a theoretical discriminator among competing inflationary models, independent of empirical data.

Yuma S. Furuta

Kazunori Kohri

Inflation models selected by the swampland distance conjecture with the Lyth bound

The Swampland cobordism conjecture [<a href="http://arXiv.org/abs/1909.10355">arXiv:1909.10355</a>.] predicts various new objects in a theory with dynamical gravity. Applying this idea to the Standard Model of particle physics, a string object is predicted. We numerically constructed such an object as a black string solution.

Germany

Yu Hamada

Hayate Kimura

Black string in the standard model

We consider heterotic string theories in nine and eight dimensions. We identify the disconnected part of the spacetime gauge group by studying the outer automorphism of the charge lattices. The absence of the global symmetry indicates the existence of non-supersymmetric codimension two branes. Moreover, we provide a list of gauge groups and matter contents of non-supersymmetric rank-reduced heterotic string theories (a branch corresponding to the $\textit{E}$ string on $\textit{S}$ ) from the orbifolding of the outer automorphism as well as the fermion parity. We also provide examples in eight dimensions.

Investigating 9d/8d non-supersymmetric branes and theories from supersymmetric heterotic strings

We consider a six-dimensional U(1) gauge theory compactified on two-dimensional manifolds. The number of chiral fermions is determined by the flux quantization number on the two-dimensional compact manifolds. Using the Swampland Conjectures, we find constraints among the parameters of the theory: the flux quantization number, the compactification scale, and the string scale. Specifically, the Weak Gravity Conjecture and the Trans-Planckian Censorship Conjecture give non-trivial bounds.

Maki Takeuchi

Swampland bounds on magnetized extra dimensions

The space of 6D supergravities with minimal supersymmetry is greatly constrained by anomaly cancellation. Nevertheless, a large number of models satisfy all low-energy consistency conditions and in this work we make progress towards exhaustively enumerating all anomaly-free models with at most one tensor multiplet. Generalizing previous techniques, we describe a general algorithm using multi-hypergraphs and simplicial complexes to systematically enumerate anomaly-free models with gauge groups of any number of simple factors and with hypermultiplets falling into any representations. Using these new ideas, we obtain a $\textit{complete}$ list of anomaly-free models for $\textit{T}$ ≤ 1, the only simplifying assumption being that the gauge group contains no U(1), SU(2), SU(3) or Sp(2) factors. We also study which and how many models in this ensemble satisfy several UV and swampland bounds which have been proposed and previously utilized to great effect, finding that none are ruled out for $\textit{T}$ = 0 and ≈ 50% are inconsistent with quantum gravity for $\textit{T}$ = 1.

Gregory Loges

Enumerating 6D supergravities with $\textit{T}$ ≤ 1

The six-derivative conformal scalar operator was originally found by Hamada in its critical dimension of spacetime, $$d=6$$ <math> <mrow> <mi>d</mi> <mo>=</mo> <mn>6</mn> </mrow> </math> . We generalize this construction to arbitrary dimensions d by adding new terms cubic in gravitational curvatures and by changing its coefficients of expansion in various curvature terms. The consequences of global scale-invariance and of infinitesimal local conformal transformations are derived for the form of this generalized operator. The system of linear equations for coefficients is solved giving explicitly the conformal Hamada operator in any d. Some singularities in construction for dimensions $$d=2$$ <math> <mrow> <mi>d</mi> <mo>=</mo> <mn>2</mn> </mrow> </math> and $$d=4$$ <math> <mrow> <mi>d</mi> <mo>=</mo> <mn>4</mn> </mrow> </math> are noticed. We also prove a general theorem that a scalar conformal operator with n derivatives in $$d=n-2$$ <math> <mrow> <mi>d</mi> <mo>=</mo> <mi>n</mi> <mo>-</mo> <mn>2</mn> </mrow> </math> dimensions is impossible to construct. Finally, we compare our explicit construction with the one that uses conformal covariant derivatives and conformal curvature tensors. We present new results for operators built with different orders of conformal covariant derivatives.

Brazil

Lesław Rachwał

Públio Vale

Generalization of conformal Hamada operators

In this work we study interesting corners of the quantum gravity landscape with 8 supercharges pushing the boundaries of our current understanding. Calabi-Yau threefolds compactifications of F/M/type II theories to 6, 5 and 4 dimensions are the most prominent examples of this class, and these always lead to a universal hypermultiplet coming from the volume/string coupling constant. We find new examples of asymmetric orbifold constructions which have no hypermultiplets in 4 or 5 dimensions and no neutral hypers in 6d. We argue that these theories can also be obtained by going to strong coupling/small volume regions of geometric constructions where a new Coulomb branch opens up and moving in this direction freezes the volume/string coupling constant. Interestingly we find that the Kodaira condition encountered in geometric limits of F-theory compactifications to 6 dimensions is violated in these corners of the landscape due to strong quantum corrections. We also construct a theory in 3 dimensions which if it were to arise by toroidal compactifications from 5d, it would have to come from pure <math> <mi>N</mi> </math> $$ \mathcal{N} $$ = 1 supergravity with no massless scalar fields.