We derive the explicit embedding of the effective Kerr spacetimes, which are pertinent to the vanishing of static Love numbers, soft hair descriptions of Kerr black holes, and low-frequency scalar-Kerr scattering amplitudes, as solutions within <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>2</mn></math> supergravity. These spacetimes exhibit a hidden <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo stretchy="false">)</mo><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>4</mn><mo>,</mo><mn>2</mn><mo stretchy="false">)</mo></math> symmetry resembling the so called subtracted geometries with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>L</mi><mo stretchy="false">(</mo><mn>2</mn><mo>,</mo><mi>R</mi><mo stretchy="false">)</mo></math> symmetry, which accurately represent the near-horizon geometry of Kerr black holes and, as we will argue most accurately represents the internal structure of the Kerr black hole. To quantify the differences among the effective Kerr spacetimes, we compare their physical quantities, internal structures, and geodesic equations. Although their thermodynamic properties, including entropy, match those of Kerr, our study uncovers significant differences in the interiors of these effective Kerr solutions. A careful examination of the internal structure of the spacetimes highlights the distinctions between various effective Kerr geometries and their quasinormal spectra.

United States

Slovenia

Mirjam Cvetič

Spain

Nelson Hernández Rodríguez

Maria J. Rodriguez

Oscar Varela

Kerr effective black hole geometries in supergravity

The symmetry data of a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math>-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory. In top-down (i.e., stringy) realizations of this structure, the QFT in question is localized in a higher-dimensional bulk. In many cases of interest, however, the associated (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></math>)-dimensional bulk is not fully gapped and one must instead consider a filtration of theories to reach a gapped bulk in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><mo>=</mo><mi>d</mi><mo>+</mo><mi>m</mi></math> dimensions. Overall, this leads us to a nested structure of relative symmetry theories which descend to coupled edge modes, with the original QFT degrees of freedom localized at a corner of this <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math>-dimensional bulk system. We present a bottom-up characterization of this structure and also show how it naturally arises in a number of string-based constructions of QFTs with both finite and continuous symmetries.

Ron Donagi

Jonathan J. Heckman

Max Hübner

CERN

Ethan Torres

Cornering relative symmetry theories

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.

Germany

Markus Dierigl

Italy

Ling Lin

Japan

Hao Y. Zhang

Frozen generalized symmetries

We investigate the interior of the moduli space of four-dimensional <math><mi>N</mi><mo>=</mo><mn>1</mn></math> theories of gravity arising from compactifications of the <math><msub><mi>E</mi><mn>8</mn></msub><mo>×</mo><msub><mi>E</mi><mn>8</mn></msub></math> heterotic string on Calabi-Yau threefolds. By studying the threshold corrections to the coupling of the heterotic gauge groups, we infer the existence of a strong coupling singularity for one of the perturbative heterotic gauge groups, which effectively yields an additional finite distance boundary of the classical scalar field space. In heterotic M-theory, this boundary maps to a domain wall solution for which the gauge coupling and the warp factor on one of the Horava-Witten 9-branes diverge, thus highlighting the gravitational origin of the classical strong coupling singularity. The divergence of the warp factor is, however, regulated once nonperturbative effects are taken into account, as we demonstrate by studying the instanton corrections to the 5D BPS domain wall equations. This regularization implies that the classical strong coupling boundary of the scalar field 4D <math><mi>N</mi><mo>=</mo><mn>1</mn></math> heterotic M-theory is resolved, indicating that, at the quantum level, the field space can be extended beyond this classical boundary.

Max Wiesner

Nonperturbative resolution of strong coupling singularities in 4D <math><mi>N</mi><mo>=</mo><mn>1</mn></math> heterotic M-theory

The stringy realization of generalized symmetry operators involves wrapping “branes at infinity”. We argue that in the case of continuous (as opposed to discrete) symmetries, the appropriate objects are fluxbranes. We use this perspective to revisit the phase structure of Verlinde’s monopole, a proposed particle satisfies the Bogomol’nyi-Prasad-Sommerfield (BPS) condition when gravity is decoupled, but is non-BPS and metastable when gravity is switched on. Geometrically, this monopole is obtained from branes wrapped on locally stable but globally trivial cycles of a compactification geometry. The fluxbrane picture allows us to characterize electric (respectively magnetic) confinement (respectively screening) in the 4D theory as a result of monopole decay. In the presence of the fluxbrane, this decay also creates lower-dimensional fluxbranes, which in the field theory is interpreted as the creation of an additional topological field theory sector.

Fluxbranes, generalized symmetries, and Verlinde’s metastable monopole

Generalized global symmetries are a common feature of many quantum field theories decoupled from gravity. By contrast, in quantum gravity/the Swampland program, it is widely expected that all global symmetries are either gauged or broken, and this breaking is in turn related to the expected completeness of the spectrum of charged states in quantum gravity. We investigate the fate of such symmetries in the context of 7D and 5D vacua realized by compact Calabi-Yau spaces with localized singularities in M theory. We explicitly show how gravitational backgrounds support additional dynamical degrees of freedom which trivialize (i.e., “break”) the higher symmetries of the local geometric models. Local compatibility conditions across these different sectors lead to gluing conditions for gauging higher-form and (in the 5D case) higher-group symmetries. This also leads to a preferred global structure of the gauge group and higher-form gauge symmetries. In cases based on a genus-one fibered Calabi-Yau space, we also get an F-theory model in one higher dimension with corresponding constraints on the global form of the gauge group.

Generalized symmetries, gravity, and the swampland

Orbifold singularities of M-theory constitute the building blocks of a broad class of supersymmetric quantum field theories (SQFTs). In this paper we show how the local data of these geometries determine global data on the resulting higher symmetries of these systems. In particular, via a process of cutting and gluing, we show how local orbifold singularities encode the 0-form, 1-form, and 2-group symmetries of the resulting SQFTs. Geometrically, this is obtained from the possible singularities that extend to the boundary of the noncompact geometry. The resulting category of boundary conditions then captures these symmetries and is equivalently specified by the orbifold homology of the boundary geometry. We illustrate these general points in the context of a number of examples, including five-dimensional (5D) superconformal field theories engineered via orbifold singularities, 5D gauge theories engineered via singular elliptically fibered Calabi-Yau threefolds, as well as four-dimensional supersymmetric quantum chromodynamics-like theories engineered via M-theory on noncompact <math><msub><mi>G</mi><mn>2</mn></msub></math> spaces.

0-form, 1-form, and 2-group Symmetries via Cutting and Gluing of Orbifolds

Root bundles appear prominently in studies of vector-like spectra of 4d F-theory compactifications. Of particular importance to phenomenology are the Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze a superset of the physical root bundles whose cohomologies encode the vector-like spectra for the matter representations (3 , 2)1/6, ( <math> <mover> <mn>3</mn> <mo>¯</mo> </mover> </math> $$ \overline{\textbf{3}} $$ , 1) −2/3 and (1 , 1)1. For the family B 3( <math> <msubsup> <mtext>∆</mtext> <mn>4</mn> <mo>°</mo> </msubsup> </math> $$ {\Delta }_4^{{}^{\circ}} $$ ) consisting of <math> <mi>O</mi> </math> $$ \mathcal{O} $$ (1011) F-theory QSM geometries, we argue that more than 99.995% of the roots in this superset have no vector-like exotics. This indicates that absence of vector-like exotics in those representations is a very likely scenario in the <math> <mi>O</mi> </math> $$ \mathcal{O} $$ (1011) QSM geometries B 3( <math> <msubsup> <mtext>∆</mtext> <mn>4</mn> <mo>°</mo> </msubsup> </math> $$ {\Delta }_4^{{}^{\circ}} $$ ).

Martin Bies

Marielle Ong

Brill-Noether-general limit root bundles: absence of vector-like exotics in F-theory Standard Models

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 argue for the quantum-gravitational inconsistency of certain 6D <math><mrow><mi>N</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math> supergravity theories, whose anomaly-free gauge algebra <math><mrow><mi>g</mi></mrow></math> and hypermultiplet spectrum <math><mi>M</mi></math> were observed by Raghuram et al. [J. High Energy Phys. 07 (2021) 048] to be realizable only as part of a larger gauge sector <math><mrow><mo>(</mo><msup><mrow><mi>g</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>⊃</mo><mi>g</mi><mo>,</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>⊃</mo><mi>M</mi><mo>)</mo></mrow></math> in F-theory. To detach any reference to a string theoretic method of construction, we utilize flavor symmetries to provide compelling reasons why the vast majority of such <math><mrow><mo>(</mo><mi>g</mi><mo>,</mo><mi>M</mi><mo>)</mo></mrow></math> theories are not compatible with quantum gravity constraints, and how the “automatic enhancement” to <math><mrow><mo>(</mo><msup><mrow><mi>g</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>,</mo><msup><mrow><mi>M</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>)</mo></mrow></math> remedies this. In the first class of models, with <math><mrow><msup><mrow><mi>g</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mi>g</mi><mo>⊕</mo><mi>h</mi></mrow></math>, we show that there exists an unbroken flavor symmetry <math><mi>h</mi></math> acting on the matter <math><mi>M</mi></math>, which, if ungauged, would violate the no-global-symmetries hypothesis. This argument also applies to 1-form center symmetries, which govern the gauge group topology and massive states in representations different from those of massless states. In a second class, we find that <math><mi>g</mi></math> is incompatible with the flavor symmetry of certain supersymmetric strings that must exist by the completeness hypothesis.