Cascading RG flows are characteristic of $$ \mathcal{N} $$ = 1 gauge theories realized by D3-branes probing singularities in the presence of fractional branes. A celebrated example is the Klebanov-Strassler model, which exhibits an infinite cascade that ends with confinement. In this work, we explore a related setup where the addition of an orientifold plane modifies the cascade structure: the RG flow now consists of a finite number of steps, originating from a UV fixed point with a finite number of degrees of freedom. We provide a supergravity solution dual to this flow, that reproduces all its salient features. The string frame curvature can be kept small up to parametrically large values of the holographic coordinate, larger than the one at which the first cascade step occurs.

Italy

Fabrizio Aramini

Belgium

Riccardo Argurio

Matteo Bertolini

Eduardo García-Valdecasas

Pietro Moroni

Gravity, finite duality cascades and confinement

Global variants of four-dimensional gauge theories are specified by their spectrum of genuine Wilson-’t Hooft line operators. The choice of global variant has significant consequences when spacetime is taken to be $\textit{ℝ}$ × $\textit{S}$ . We focus on $$ \mathcal{N} $$ = 1 theories, which are closely connected to twisted elliptic Calogero-Moser systems. We establish, on general grounds, how this gauge-theoretic topological data manifests itself on the integrable system side by introducing a notion of global variants for complex many-body integrable systems associated with Lie algebras. Focusing on $$ \mathcal{N} $$ = 1 theories of type $\textit{A}$ and $\textit{B}$ , we elucidate the implications for the structure of gapped vacua, the emergent (generalized) symmetries realized in each vacuum, and the action of spontaneously broken modular invariance.

Argentina

Spain

Jeremías Damia

France

Antoine Bourget

Germany

Valdo Tatitscheff

Romain Vandepopeliere

Global variants of $$ \mathcal{N} $$ = 1

We revisit the construction of the duality group for $$\mathcal{N}$$ = 2 $${\widehat{A}}_{n}$$ -shaped quivers SCFTs and generalize it to the previously unexplored case of $${\widehat{D}}_{n}$$ -shaped quivers. We then provide a systematic description of non-invertible duality symmetries in both classes. Furthermore, we characterize the $$\mathcal{N}$$ = 1 mass deformations of these theories that preserve such symmetries, thereby identifying a large class of $$\mathcal{N}$$ = 1 SCFTs with non-invertible duality symmetries inherited from their parent $$\mathcal{N}$$ = 2 theories.

Andrés Collinucci

Salvo Mancani

Sweden

Shani Meynet

Louan Mol

Inherited non-invertible duality symmetries in quiver SCFTs

We revisit the possibility of constructing noninvertible topological defects for the axial symmetry of massless quantum electrodynamics (QED), despite its Adler-Bell-Jackiw anomaly. Dressing the defects with a topological quantum field theory with mixed <math><mrow><mi>U</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math> and <math><mi>R</mi></math>-valued gauge fields, we are able to describe axial rotations of any rational or irrational angle. We confront our results with the existing proposals, in particular those that concern rational angles. We also provide the symmetry topological field theory that reproduces the action of all such symmetry defects of QED. Finally, we discuss how similar techniques allow the study of condensation defects for a <math><mi>R</mi></math> global symmetry.

Adrien Arbalestrier

Luigi Tizzano

Noninvertible axial symmetry in QED comes full circle

Three-dimensional Yang-Mills-Chern-Simons theory has the peculiar property that its one-form symmetry defects have nontrivial braiding, namely they are charged under the same symmetry they generate, which is then anomalous. This poses a few puzzles in describing the corresponding Symmetry TFT in a four-dimensional bulk. First, the braiding between lines at the boundary seems to be ill-defined when such lines are pulled into the bulk. Second, the Symmetry TFT appears to be too trivial to allow for topological boundary conditions encoding all the different global variants. We show that both of these puzzles can be solved by including endable (tubular) surfaces in the class of bulk topological operators one has to consider. In this way, we are able to reproduce all global variants of the theory, with their symmetries and their anomalies. We check the validity of our proposal also against a top-down holographic realization of the same class of theories.

Francesco Benini

Giovanni Galati

United States

Pierluigi Niro

On the symmetry TFT of Yang-Mills-Chern-Simons theory

We investigate theories of Nambu-Goldstone bosons where the spontaneously broken continuous symmetry is non-invertible. In such theories, the vacua generically parameterize an orbifold. We study in detail the simplest example of a single free scalar with shift symmetry, modded by reflection symmetry. At singular points of the vacuum manifold, we show that the spectrum of NG excitations is reduced, in particular there are no single-particle states. At the smooth points, on the other hand, single NG modes are present. We show that this is a consequence of the fact that at those points one can construct invertible operators implementing the continuous symmetry on the Hilbert space.

Jeremias Damia

Soumyadeep Chaudhuri

When the moduli space is an orbifold: spontaneous breaking of continuous non-invertible symmetries

We explore novel examples of RG flows preserving a non-invertible self-duality symmetry. Our main focus is on   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 quadratic superpotential deformations of 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 super-Yang-Mills theory with gauge algebra   <math> <mi>su</mi> <mfenced> <mi>N</mi> </mfenced> </math>  $$ \mathfrak{su}(N) $$ . A theory that can be obtained in this way is the so-called   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1* SYM where all adjoint chiral multiplets have a mass. Such IR theory exhibits a rich structure of vacua which we thoroughly examine. Our analysis elucidates the physics of spontaneous breaking of self-duality symmetry occurring in the degenerate gapped vacua. The construction can be generalized, taking as UV starting point a theory of class   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$ , to demonstrate how non-invertible self-duality symmetries exist in a variety of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 SCFTs. We finally apply this understanding to prove that the conifold theory has a non-invertible self-duality symmetry.

Sergio Benvenuti

Christian Copetti

Non-invertible symmetries along 4d RG flows

We study non-abelian gauge theories with fermions in a representation such that the surviving electric 1-form symmetry is ℤ2. This includes SU(N) gauge theories with matter in the (anti)symmetric and N even, and USp(2N) with a Weyl fermion in the adjoint, i.e.   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 SYM. We study the mixed ’t Hooft anomaly between the discrete axial symmetry and the 1-form symmetry and show that when it is non-trivial, it leads to non-invertible symmetries upon gauging the ℤ2. The TQFT dressing the non-invertible symmetry defects is universal to all the cases we study, namely it is always a U(1)2 CS theory coupled to the ℤ2 2-form gauge field. We uncover a pattern where the presence or not of non-invertible defects depends on the rank of the gauge group.

When ℤ2 one-form symmetry leads to non-invertible axial symmetries

We present a class of three-dimensional quantum field theories whose ordinary global symmetries mix with higher-form symmetries to form a continuous 2-group. All these models can be obtained by performing a gauging procedure in a parent theory revealing a ’t Hooft anomaly in the space of coupling constants when suitable compact scalar background fields are activated. Furthermore, the gauging procedure also implies that our main example has infinitely many non-invertible global symmetries. These can be obtained by dressing the continuous symmetry operators with topological quantum field theories. Finally, we comment on the holographic realization of both 2-group global symmetries and non-invertible symmetries discussed here by introducing a corresponding four-dimensional bulk description in terms of dynamical gauge fields.

Continuous generalized symmetries in three dimensions

Recently, the first instance of a model of D-branes at Calabi-Yau singularities where supersymmetry is broken dynamically into stable vacua has been proposed. This construction was based on a system of N regular and M = 1 fractional branes placed at the tip of the so-called (orientifolded) Octagon singularity. In this paper we show that this model admits a large M generalization, having the same low energy effective dynamics. This opens up the possibility that the effect on geometry is smooth, and amenable to describing the gauge theory all along the RG flow, including the deep IR, in terms of a weakly coupled gravity dual background. The relevance of this result in the wider context of the string landscape and the Swampland program is also discussed.

Sebastián Franco

Antoine Pasternak

The Octagon at large M