<p>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.</p>

Germany

Japan

Yu Hamada

Yuta 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 string on ) from the orbifolding of the outer automorphism as well as the fermion parity. We also provide examples in eight dimensions.

Arata Ishige

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 complete list of anomaly-free models for 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 T = 0 and ≈ 50% are inconsistent with quantum gravity for T = 1.

Gregory Loges

Enumerating 6D supergravities with 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.

United States

Zihni Baykara

Houri-Christina Tarazi

Cumrun Vafa

On the string landscape without hypermultiplets

The constraints arising from anomaly cancellation are particular strong for chiral theories in six dimensions. We make progress towards a complete classification of 6D supergravities with minimal supersymmetry and non-abelian gauge group. First, we generalize a previously known infinite class of anomaly-free theories which has 𝑇 ≫ 9 to essentially any semi-simple gauge group and infinitely many choices for hypermultiplets. The construction relies on having many decoupled sectors all selected from a list of four simple theories which we identify. Second, we use ideas from graph theory to rephrase the task of finding anomaly-free theories as constructing cliques in a certain multigraph. A branch-and-bound type algorithm is described which can be used to explicitly construct, in a 𝑇-independent way, anomaly-free theories with an arbitrary number of simple factors in the gauge group. We implement these ideas to generate an ensemble of   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (107) irreducible cliques from which anomaly-free theories may be easily built, and as a special case obtain a complete list of 19,847 consistent theories for 𝑇 = 0, for which the maximal gauge group rank is 24. Modulo U(1), SU(2) and SU(3) simple factors and the new infinite families, we give a complete characterization of anomaly-free theories and show that the bound 𝑇 ≤ 273 is sharp.

Towards a complete classification of 6D supergravities

We initiate the program of bottom-up derivation of string theory dualities using Swampland principles. In particular, we clarify the relation between Swampland arguments and all the string theory dualities in d ≥ 9 dimensional supersymmetric theories. Our arguments center around the sharpened distance conjecture and rely on various other Swampland principles.

Alek Bedroya

Dualities from Swampland principles

We present a model to explain the Standard Model flavor hierarchy. Our model is based on explicit smooth confinement (namely confinement without chiral symmetry breaking in a supersymmetric gauge theory) at an intermediate energy scale, before the electroweak symmetry breaking by the Higgs condensation at lower energy. In our context, the smooth confinement preserves the SU(3) and the chiral <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mi>L</mi></msub><mo>×</mo><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>Y</mi></msub></mrow></mrow></math> symmetry in a supersymmetric Standard Model, while this internal symmetry becomes dynamically gauged in the end. In contrast to Razamat-Tong’s symmetric mass generation model also preserving the <math><msub><mi>G</mi><mrow><mi>SM</mi></mrow></msub><mo>≡</mo><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>C</mi></msub><mo>×</mo><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mi>L</mi></msub><mo>×</mo><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mi>Y</mi></msub></mrow></mrow></mrow></math> internal symmetry, our model introduces different matter contents with a different kind of superpotential deformation irrelevant at UV, which further induces Yukawa-Higgs terms marginal at IR, breaking the <math><msub><mi>G</mi><mrow><mi>SM</mi></mrow></msub></math> down to <math><mrow><msub><mrow><mi>SU</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow><mi>C</mi></msub></mrow></math> and the electromagnetic <math><mrow><msub><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>EM</mi></mrow></msub></mrow></math> only when Higgs condenses. In our model, the IR fermions in the first and second families are composite of UV fields, while the third-family elementary fermions match between UV and IR. The smallness of the first- and second-family fermion masses is explained by the exponential hierarchy between the cutoff scale and the smooth confinement scale via dimensional transmutation. As a result, our UV Lagrangian only contains the natural parameters close to the order one.

Juven Wang

Flavor hierarchy from smooth confinement

We study positivity bounds in the presence of gravity. We first review the gravitational positivity bound at the tree-level, where it is known that a certain amount of negativity is allowed for the coefficients of higher-derivative operators. The size of these potentially negative contributions is estimated for several tree-level, Reggeized gravitational amplitudes which are unitary at high energies and feature the t-channel pole characteristic of graviton exchange. We also argue for the form of the one-loop Regge amplitude assuming that the branch cut structure associated with the exchange of the graviton and higher-spin particles is reflected. We demonstrate how the one-loop Regge amplitude appears by summing over Feynman diagrams. For our one-loop amplitude proposal, the positivity bounds generically receive a finite contribution from the Regge tower and do not lead to a parametrically small bound on the cut-off scale of the low-energy EFT, consistent with recent studies based on sum rules of the amplitude.