<p>M-theory frozen singularities are (locally) <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>- or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi></math>-type orbifold singularities with a background fractional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mn>3</mn></msub></math>-monodromy surrounding them. In this paper, we revisit such backgrounds and address several puzzling features of their physics. We first give a top-down derivation of how the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>- or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi></math>-type 7D <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>1</mn></math> gauge theory directly “freezes” to a lower-rank gauge theory due to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mn>3</mn></msub></math> background. This relies on a Hanany-Witten effect of fractional M5 branes and the presence of a gauge anomaly of fractional <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">D</mi><mi>p</mi></mrow></math> probes in the circle reduction. Additionally, we compute defect groups and 8D symmetry topological field theories of the 7D frozen theories in several duality frames. We apply our results to understanding the evenness condition of strings ending on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">O</mi><msup><mrow><mn>7</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> planes, and calculating the global forms of supergravity gauge groups of M-theory compactified on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>T</mi><mn>4</mn></msup><mo>/</mo><mi mathvariant="normal">Γ</mi></math> with frozen singularities. We also revisit IIA <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>A</mi><mi>D</mi><mi>E</mi></math> singularities with a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>C</mi><mn>1</mn></msub></math>-monodromy along a 1-cycle in the boundary lens space and show that this freezes the gauge degrees of freedom via confinement.</p>

United States

Slovenia

Mirjam Cvetič

CERN

Germany

Markus Dierigl

Italy

Ling Lin

Ethan Torres

Japan

Hao Y. Zhang

Frozen generalized symmetries

In this work we explore the effect of a non-Abelian dark sector gauge group that couples to the axion field. In particular, we analyze effects that arise if the dark sector gauge group mixes topologically with the Standard Model. This is achieved by gauging a subgroup of the global center 1-form symmetries which embeds non-trivially in both the visible as well as the dark sector gauge groups. Leaving the local dynamics unchanged, this effect modifies the quantization conditions for the topological couplings of the axion, which enter the estimate of a lower bound on the axion-photon coupling. In the presence of a dark sector this lower bound can be reduced significantly, which might open up interesting new parameter regions for axion physics. We further determine the allowed exotic matter representations in the presence of topological mixing with a dark sector, explore the generalized categorical symmetries of such axion theories, and comment on other model-independent phenomenological consequences.

Dušan Novičić

The axion is going dark

R7-branes are a class of recently discovered nonsupersymmetric real codimension-two duality defects in type IIB string theory predicted by the swampland cobordism conjecture. For type IIB realizations of 6D SCFTs with <math><mi>N</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo>)</mo></math> supersymmetry, wrapping an R7-brane “at infinity” leads to a topological operator associated with a zero-form charge conjugation symmetry that squares to the identity. Similar considerations hold for those theories obtained from further toroidal compactification, but this can be obstructed by bundle curvature effects. Using some minimal data on the topological sector of the R7-branes, we extract the associated fusion rules for these charge conjugation operators. More broadly, we sketch a top down realization of various topological operators/interfaces associated with <math><mi>C</mi></math>, <math><mi>R</mi></math>, and <math><mi>T</mi></math> transformations. We also use holography to provide strong evidence for the existence of the R7-brane which is complementary to the cobordism conjecture. Similar considerations apply to other string-realized QFTs with symmetry operators constructed via nonsupersymmetric branes which carry a conserved charge.

Jonathan J. Heckman

Spain

Miguel Montero

R7-branes as charge conjugation operators

The swampland cobordism conjecture successfully predicts the supersymmetric spectrum of 7-branes of IIB/F-theory. Including reflections on the F-theory torus, it also predicts the existence of new nonsupersymmetric objects, which we dub reflection 7-branes (R7-branes). We present evidence that these R7-branes only exist at strong coupling. R7-branes serve as end of the world branes for 9D theories obtained from type IIB asymmetric orbifold and Dabholkar-Park orientifold backgrounds, and an anomaly inflow analysis suggests the existence of a gapless Weyl fermion, which would have the quantum numbers of a goldstino. Using general arguments, we conclude that different kinds of branes are able to end on the R7, and accounting for their charge requires exotic localized degrees of freedom, for which the simplest possibility is a massless 3-form field on the R7-brane worldvolume. We also show how to generalize the standard F-theory formalism to account for reflections.

IIB string theory explored: Reflection 7-branes

We study global anomalies of discrete gauge symmetries in six-dimensional supergravities and their realizations in F-theory. We explicitly construct a discrete Green-Schwarz mechanism that depends on the choice of a coupling constant and on a certain quadratic refinement in differential cohomology. By geometrically engineering theories with G = ℤ3 gauge symmetry and no tensor multiplets, we observe that a particular choice of the quadratic refinement is singled out in F-theory. This implies new Swampland constraints on the discrete charge spectra of 6d supergravities. On the other hand, the discrete Green-Schwarz coupling depends on the geometry of the Calabi-Yau. We use anomaly inflow to relate this to a ’t Hooft anomaly of the induced global symmetry in the worldsheet theories of non-critical strings. Using topological symmetry lines, we further relate this anomaly to the modular properties of twisted-twined elliptic genera. We then argue that the latter are encoded in the A-model topological string partition functions on different torus fibrations that are equipped with a flat torsional B-field. This allows us to derive a geometric expression for the global discrete anomaly in terms of the height-pairing of a multi-section on a genus one fibered Calabi-Yau.

Paul-Konstantin Oehlmann

France

Thorsten Schimannek

The discrete Green-Schwarz mechanism in 6D F-theory and elliptic genera of non-critical strings

In this paper we discuss black hole solutions parametrized by their entropy   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$  and temperature   <math> <mi>T</mi> </math>  $$ \mathcal{T} $$  in gravitational effective theories. We are especially interested in the analysis of the boundary regions in the   <math> <mi>T</mi> </math>  $$ \mathcal{T} $$  −   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$  diagram, i.e. large/small values of entropy and temperature, and their relation to Swampland constraints. To explore this correlation, we couple the gravitational theories to scalar fields and connect limits of thermodynamic quantities of black holes to scalar field excursions in the corresponding solutions. Whenever the scalar fields traverse an infinite field distance, the Swampland Distance Conjecture allows for a reformulation in terms of entropy- or temperature-distance. The effective theories with scalars we investigate are Einstein-Maxwell-dilaton theory as well as   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supergravity in four dimensions. The relation of the latter to type II string theory compactified on Calabi-Yau 3-folds often allows for a direct identification of the corresponding light tower of states. These setups also point towards various dualities between asymptotic regions of the black hole solution. In the context of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supergravity black holes, these thermodynamic dualities have an interpretation in terms of T- and S-dualities along the internal directions and their natural action on Kaluza-Klein and winding states.

Niccolò Cribiori

Alessandra Gnecchi

Dieter Lüst

Marco Scalisi

Large and small non-extremal black holes, thermodynamic dualities, and the Swampland

String and 5-brane junctions are shown to succinctly classify all known 8D <math><mi>N</mi><mo>=</mo><mn>1</mn></math> string vacua. This requires an extension of the description for ordinary <math><mo>[</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>]</mo></math>-7-branes to consistently include <math><mrow><mi>O</mi><msup><mrow><mn>7</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow></math> planes, which then naturally encodes the dynamics of <math><msub><mi>sp</mi><mi>n</mi></msub></math> gauge algebras, including their <math><mi>p</mi></math>-form center symmetries. Central to this analysis are loop junctions, i.e., strings/5-branes which encircle stacks of 7-branes and <math><mrow><mrow><mi>O</mi><msup><mrow><mn>7</mn></mrow><mrow><mo>+</mo></mrow></msup></mrow><mi>s</mi></mrow></math>. Loop junctions further signal the appearance of affine symmetries of emergent 9D descriptions at the 8D moduli space’s boundaries. Such limits reproduce all 9D string vacua, including the two disconnected rank (1,1) moduli components.

All eight- and nine-dimensional string vacua from junctions

We explore higher-form symmetries of M- and F-theory compactified on elliptic fibrations, determined by the topology of their asymptotic boundaries. The underlying geometric structures are shown to be equivalent to known characterizations of the gauge group topology in F-theory via Mordell-Weil torsion and string junctions. We further study dimensional reductions of the 11d Chern-Simons term in the presence of torsional boundary <math><mrow><msub><mrow><mi>G</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math>-fluxes, which encode background gauge fields of center one-form symmetries in the lower-dimensional effective gauge theory. We find contributions that can be interpreted as ’t Hooft anomalies involving the one-form symmetry which originate from a fractionalization of the instanton number of non-Abelian gauge theories in F-/M-theory compactifications to <math><mrow><mn>8</mn><mi>d</mi><mo>/</mo><mn>7</mn><mi>d</mi></mrow></math> and <math><mrow><mn>6</mn><mi>d</mi><mo>/</mo><mn>5</mn><mi>d</mi></mrow></math>.

Higher-form symmetries and their anomalies in M-/F-theory duality

Compactifications of the Chaudhuri-Hockney-Lykken (CHL) string to eight dimensions can be characterized by embeddings of root lattices into the rank 12 momentum lattice <math><msub><mi>Λ</mi><mi>M</mi></msub></math>, the so-called Mikhailov lattice. Based on these data, we devise a method to determine the global gauge group structure including all <math><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></math> factors. The key observation is that, while the physical states correspond to vectors in the momentum lattice, the gauge group topology is encoded in its dual. Interpreting a nontrivial <math><msub><mi>π</mi><mn>1</mn></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>≡</mo><mi>Z</mi></math> for the non-Abelian gauge group <math><mi>G</mi></math> as having gauged a <math><mi>Z</mi></math> 1-form symmetry, we also prove that all CHL gauge groups are free of a certain anomaly [1] that would obstruct this gauging. We verify this by explicitly computing <math><mi>Z</mi></math> for all 8D CHL vacua with <math><mrow><mi>rank</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mn>10</mn></mrow></math>. Since our method applies also to <math><msup><mi>T</mi><mn>2</mn></msup></math> compactifications of heterotic strings, we further establish a map that determines any CHL gauge group topology from that of a “parent” heterotic model.

Gauge group topology of 8D Chaudhuri-Hockney-Lykken vacua

We study the cobordism conjecture of McNamara and Vafa which asserts that the bordism group of quantum gravity is trivial. In the context of type IIB string theory compactified on a circle, this predicts the presence of D7-branes. On the other hand, the non-Abelian structure of the IIB duality group <math><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>Z</mi><mo>)</mo></math> implies the existence of additional <math><mo>[</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>]</mo></math> 7-branes. We find that this additional information is instead captured by the space of closed paths on the moduli space of elliptic curves parameterizing distinct values of the type IIB axio-dilaton. This description allows to recover the full structure of non-Abelian braid statistics for 7-branes. Combining the cobordism conjecture with an earlier Swampland conjecture by Ooguri and Vafa, we argue that only certain congruence subgroups <math><mi>Γ</mi><mo>⊂</mo><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>Z</mi><mo>)</mo></math> specifying genus zero modular curves can appear in 8D F-theory vacua. This leads to a successful prediction for the allowed Mordell–Weil torsion groups for 8D F-theory vacua.