We provide the first example of a geometric transition that resolves the Schwarzschild black hole into a smooth microstructure in eleven-dimensional supergravity on a seven-torus. The geometry is indistinguishable from a Schwarzschild black hole dressed with a scalar field in four dimensions, referred to as a Schwarzschild scalarwall. In eleven dimensions, the scalar field arises as moduli of the torus. The resolution occurs at an infinitesimal scale above the horizon, set by the size of the internal torus, where it transitions to a smooth bubbling spacetime supported by M2-brane flux.

United States

Ibrahima Bah

Pierre Heidmann

Geometric resolution of the Schwarzschild horizon

We study the Symmetry Topological Field Theory in holography associated with 4d 𝒩 = 1 Super Yang-Mills theory with gauge algebra 𝔰𝔲(M). From this, all the bulk symmetry operators are computed and matched to various D-brane configurations. The fusion algebra of the operators emerges from brane dynamics. In particular, we show that the symmetry operators are purely determined from the center-of-mass modes of the branes. We identify the TQFT fusion coefficients with the relative motion of the branes. We also establish the origin of condensation defects, arising from fusion of non-invertible operators, as the consequence of tachyon condensation in brane-anti-brane pairs.

Enoch Leung

Thomas Waddleton

Non-invertible symmetries, brane dynamics, and tachyon condensation

We consider the scattering of high energy and ultra relativistic spherically symmetric shells in asymptotically AdS D  spacetimes. We analyze an exclusive amplitude where a single spherically symmetric shell goes in and a single one comes out, such that the two have different global symmetry charges of the effective gravity theory. We study a simple wormhole configuration that computes the square of the amplitude and analyze its properties.

Yiming Chen

Juan Maldacena

Estimating global charge violating amplitudes from wormholes

We propose a systematic approach to deriving symmetry generators of quantum field theories in holography. Central to this analysis are the Gauss law constraints in the Hamiltonian quantization of symmetry topological field theories (SymTFTs), which are obtained from supergravity. In turn, we realize the symmetry generators from world-volume theories of D-branes in holography. Our main focus is on noninvertible symmetries, which have emerged in the past year as a new type of symmetry in <math><mi>d</mi><mo>≥</mo><mn>4</mn></math> QFTs. We exemplify our proposal in the holographic confinement setup, dual to 4D <math><mi>N</mi><mo>=</mo><mn>1</mn></math> Super-Yang Mills. In the brane picture, the fusion of noninvertible symmetries naturally arises from the Myers effect on D-branes. In turn, their action on line defects is modeled by the Hanany-Witten effect.

Switzerland

Fabio Apruzzi

United Kingdom

Federico Bonetti

Sakura Schäfer-Nameki

Noninvertible Symmetries from Holography and Branes

We construct large classes of non-BPS smooth horizonless geometries that are asymptotic to AdS3 × S3 × T4 in type IIB supergravity. These geometries are supported by electromagnetic flux corresponding to D1-D5 charges. We show that Einstein equations for systems with eight commuting Killing vectors decompose into a set of Ernst equations, thereby admitting an integrable structure. This feature, which can a priori be applied to other   <math> <msub> <mi>AdS</mi> <mi>D</mi> </msub> <mo>×</mo> <mi>C</mi> </math>  $$ {\textrm{AdS}}_D\times \mathcal{C} $$  settings in supergravity, allows us to use solution-generating techniques associated with the Ernst formalism. We explicitly derive solutions by applying the charged Weyl formalism that we have previously developed. These are sourced internally by a chain of bolts that correspond to regions where the orbits of the commuting Killing vectors collapse smoothly. We show that these geometries can be interpreted as non-BPS T4 and S3 deformations on global AdS3 × S3 × T4 that are located at the center of AdS3. These non-BPS deformations can be made arbitrarily small and should therefore correspond to non-supersymmetric operators in the D1-D5 CFT. Finally, we also construct interesting bound states of non-extremal BTZ black holes connected by regular bolts.

Non-BPS bubbling geometries in AdS3

We present new families of AdS 5 solutions in M-theory preserving 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 supersymmetry. We perform a systematic analysis of holographic observables for these solutions, providing evidence for an interpretation in terms of 4d superconformal field theories (SCFTs) of Argyres-Douglas type, realized in class   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$  via a sphere with one irregular, and one regular puncture. The gravity solutions exhibit internal M5-brane sources that correspond to the irregular puncture. For a family of solutions, we identify explicitly the class   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$  puncture data and perform a detailed match, including Higgs branch operators. For other families we comment on proposed field theory duals, based on irregular punctures labeled by nested Young tableaux.

Japan

Emily Nardoni

Aspects of irregular punctures via holography

We analyze the global symmetries and anomalies of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 field theories that arise from a stack of N M5-branes probing a class of flux backgrounds. These backgrounds consist of a resolved ℂ2 /ℤ k  singularity fibered over a smooth Riemann surface of genus g ≥ 2, supported by a non-trivial G 4-flux configuration labeled by a collection of 2(k − 1) flux quanta, {N  i }. For k = 2, this setup defines a non-trivial superconformal field theory (SCFT) in the IR, which is holographically dual to an explicit AdS5 solution first described by Gauntlett, Martelli, Sparks, and Waldram. The generalization to k ≥ 3 is hard to tackle directly within holography. Instead, in this paper we lay the groundwork for a systematic analysis of such a generalization by adopting anomaly inflow methods to identify continuous and discrete global symmetries of the 4d field theories. We also compute the ’t Hooft anomalies for continuous symmetries at leading order in the limit of large N, N  i .

Peter Weck

M5-branes probing flux backgrounds

We consider 4d field theories obtained by reducing the 6d (1,0) SCFT of N M5-branes probing a ℂ2 /ℤ k  singularity on a Riemann surface with fluxes. We follow two different routes. On the one hand, we consider the integration of the anomaly polynomial of the parent 6d SCFT on the Riemann surface. On the other hand, we perform an anomaly inflow analysis directly from eleven dimensions, from a setup with M5-branes probing a resolved ℂ2 /ℤ k  singularity fibered over the Riemann surface. By comparing the 4d anomaly polynomials, we provide a characterization of a class of modes that decouple along the RG flow from six to four dimensions, for generic N, k, and genus. These modes are identified with the flip fields encountered in the Lagrangian descriptions of these 4d models, when they are available. We show that such fields couple to operators originating from M2-branes wrapping the resolution cycles. This provides a geometric origin of flip fields. They interpolate between the 6d theory in the UV, where the M2-brane operators are projected out, and the 4d theory in the IR, where these M2-brane operators are part of the spectrum.

The geometry of decoupling fields

We construct the first class of topological solitons in gravity that are supported by internal electromagnetic flux with vanishing net charges. The solutions are obtained in a six-dimensional Einstein-Maxwell theory with a three-form flux, and admit an uplift to type IIB supergravity on T4. They are asymptotic to a torus fibration over four-dimensional Minkowski spacetime. An interesting class corresponds to solitons with a BPS particle and its anti-BPS partner held apart by a vacuum bubble. In type IIB, they correspond to bound states of BPS and anti-BPS D1-D5 extremal black holes. These metrics are a particular limit of a larger class of axially symmetric metrics that we construct and that describe smooth horizonless topological solitons. They correspond to bound states of three non-BPS bubbles on a line. An important achievement is that the outer bubbles can carry arbitrary D1-D5 charges that we can tune to vanishing net charges. We discuss their properties and compare them to a four-dimensional Schwarzschild black hole of the same mass. We show that they have a long throat with a large redshift, and that they are ultra-compact with a characteristic size of 1.52 times the Schwarzschild radius.

Schwarzschild-like topological solitons

We study the existence of smooth topological solitons and black strings as locally-stable saddles of the Euclidean gravitational action of five dimensional Einstein-Maxwell theory. These objects live in the Kaluza-Klein background of four dimensional Minkowski with an S 1. We compute the off-shell gravitational action in the canonical ensemble with fixed boundary data corresponding to the asymptotic radius of S 1, and to the electric and magnetic charges that label the solitons and black strings. We show that these objects are locally-stable in large sectors of the phase space with varying lifetime. Furthermore, we determine the globally-stable phases for different regimes of the boundary data, and show that there can be Hawking-Page transitions between the locally-stable phases of the topological solitons and black strings. This analysis demonstrates the existence of a large family of globally-stable smooth solitonic objects in gravity beyond supersymmetry, and presents a mechanism through which they can arise from the black strings.