<p>We construct a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">d</mi></mrow></math> gapless theory which has Haagerup <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">H</mi><mn>3</mn></msub></math> symmetry. The construction relies on the recent exploration of the categorical Landau paradigm applied to fusion category symmetries. First, using the symmetry topological field theory, we construct all gapped phases with Haagerup symmetry. Extending this construction to gapless phases, we study the second order phase transition between gapped phases, and determine analytically a Haagerup-symmetric conformal field theory. This is given in terms of two copies of the three-state Potts model, on which we realize the full <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">H</mi><mn>3</mn></msub></math> symmetry action and determine the relevant deformations to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi mathvariant="script">H</mi><mn>3</mn></msub></math>-symmetric gapped phases. This continuum analysis is corroborated by a lattice model construction of the gapped and gapless phases, using the anyon chain.</p>

United Kingdom

Lea E. Bottini

Sakura Schäfer-Nameki

Construction of a Gapless Phase with Haagerup Symmetry

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 States

Ibrahima Bah

Federico Bonetti

Noninvertible Symmetries from Holography and Branes

We derive the Symmetry Topological Field Theories (SymTFTs) for 3d supersymmetric quantum field theories (QFTs) constructed in M-theory either via geometric engineering or holography. These 4d SymTFTs encode the symmetry structures of the 3d QFTs, for instance the generalized global symmetries and their ’t Hooft anomalies. Using differential cohomology, we derive the SymTFT by reducing M-theory on a 7-manifold Y 7, which either is the link of a conical Calabi-Yau four-fold or part of an AdS4 × Y 7 holographic solution. In the holographic setting we first consider the 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 6 ABJ(M) theories and derive the BF-couplings, which allow the identification of the global form of the gauge group, as well as 1-form symmetry anomalies. Secondly, we compute the SymTFT for 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 quiver gauge theories whose holographic duals are based on Sasaki-Einstein 7-manifolds of type Y 7 = Y  p,k (  <math> <mi>CP</mi> </math>  $$ \mathbbm{CP} $$  2). The SymTFT encodes 0- and 1-form symmetries, as well as potential ’t Hooft anomalies between these. Furthermore, by studying the gapped boundary conditions of the SymTFT we constrain the allowed choices for U(1) Chern-Simons terms in the dual field theory.

Marieke Beest

Dewi Gould

China

Yi-Nan Wang

Symmetry TFTs for 3d QFTs from M-theory

Compactification of M-theory and of IIB string theory on threefold canonical singularities gives rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. The resolutions and deformations of the singularities encode salient features of the SCFTs and of their moduli spaces. In this paper, we build on Part 0 of this series [1] and further explore the physics of SCFTs arising from isolated hypersurface singularities. We study in detail these canonical isolated hypersurface singularities that admit a smooth Calabi-Yau (crepant) resolution. Their 5d and 4d physics is discussed and their 3d reduction and mirrors (the magnetic quivers) are determined in many cases. As an explorative tool, we provide a Mathematica code which computes key quantities for any canonical isolated hypersurface singularity, including the 5d rank, the 4d Coulomb branch spectrum and central charges, higher-form symmetries in 4d and 5d, and crepant resolutions.

Cyril Closset

Coulomb and Higgs branches from canonical singularities. Part I. Hypersurfaces with smooth Calabi-Yau resolutions

We study confinement in 4d <math><mi>N</mi><mo>=</mo><mn>1</mn></math> <math><mi>S</mi><mi>U</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> Super-Yang Mills (SYM) from a holographic point of view, focusing on the 1-form symmetry and its relation to chiral symmetry breaking (<math><msub><mi>χ</mi><mi>SB</mi></msub></math>). We identify the topological couplings in the 5d truncation of the Klebanov-Strassler solution that determine the 1-form symmetry and its ’t Hooft anomalies. One coupling is a mixed 0-/1-form symmetry anomaly related to <math><msub><mi>χ</mi><mi>SB</mi></msub></math> in gapped confining vacua. In the gravity dual we also identify the infrared 4d topological field theory which realizes <math><msub><mi>χ</mi><mi>SB</mi></msub></math> and matches the mixed anomaly. Finally, complementing this, we derive the chiral and mixed anomalies from the little string theory realization of pure SYM.

Marieke van Beest

Dewi S. W. Gould

Holography, 1-form symmetries, and confinement

Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of ‘trinion’ singularities which exhibit these properties. In Type IIB, they give rise to 4d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 SCFTs that we call   <math> <msubsup> <mi>D</mi> <mi>p</mi> <mi>b</mi> </msubsup> </math>  $$ {D}_p^b $$ (G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as ‘ugly’ components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver ‘bad’. We propose a way to redeem the badness of these quivers using a class   <math> <mi>S</mi> </math>  $$ \mathcal{S} $$  realization. We also discover new S-dualities between different   <math> <msubsup> <mi>D</mi> <mi>p</mi> <mi>b</mi> </msubsup> </math>  $$ {D}_p^b $$ (G)-trinions. For instance, a certain E 8 gauging of the E 8 Minahan-Nemeschansky theory is S-dual to an E 8-shaped Lagrangian quiver SCFT.

Simone Giacomelli

5d and 4d SCFTs: canonical singularities, trinions and S-dualities

5d superconformal field theories (SCFTs) can be obtained from 6d SCFTs by circle compactification and mass deformation. Successive decoupling of hypermultiplet matter and RG-flow generates a decoupling tree of descendant 5d SCFTs. In this paper we determine the magnetic quivers and Hasse diagrams, that encode the Higgs branches of 5d SCFTs, for entire decoupling trees. Central to this undertaking is the approach in [1], which, starting from the generalized toric polygons (GTPs) dual to 5-brane webs/tropical curves, provides a systematic and succinct derivation of magnetic quivers and their Hasse diagrams. The decoupling in the GTP description is straightforward, and generalizes the standard flop transitions of curves in toric polygons. We apply this approach to a large class of 5d KK-theories, and compute the Higgs branches for their descendants. In particular we determine the decoupling tree for all rank 2 5d SCFTs. For each tree, we also identify the flavor symmetry algebras from the magnetic quivers, including non-simply-laced flavor symmetries.

Antoine Bourget

Julius Eckhard

(5d RG-flow) trees in the tropical rain forest

We describe general methods for determining higher-form symmetry groups of known 5d and 6d superconformal field theories (SCFTs), and 6d little string theories (LSTs). The 6d theories can be described as supersymmetric gauge theories in 6d which include both ordinary non-abelian 1-form gauge fields and also abelian 2-form gauge fields. Similarly, the 5d theories can also be often described as supersymmetric non-abelian gauge theories in 5d. Naively, the 1-form symmetry of these 6d and 5d theories is captured by those elements of the center of ordinary gauge group which leave the matter content of the gauge theory invariant. However, an interesting subtlety is presented by the fact that some massive BPS excitations, which includes the BPS instantons, are charged under the center of the gauge group, thus resulting in a further reduction of the 1-form symmetry. We use the geometric construction of these theories in M/F-theory to determine the charges of these BPS excitations under the center. We also provide an independent algorithm for the determination of 1-form symmetry for 5d theories that admit a generalized toric construction (i.e. a 5-brane web construction). The 2-form symmetry group of 6d theories, on the other hand, is captured by those elements of the center of the abelian 2-form gauge group that leave all the massive BPS string excitations invariant, which is much more straightforward to compute as it is encoded in the Green-Schwarz coupling associated to the 6d theory.

Lakshya Bhardwaj

Higher-form symmetries of 6d and 5d theories

Five- and four-dimensional superconformal field theories with eight supercharges arise from canonical threefold singularities in M-theory and Type IIB string theory, respectively. We study their Coulomb and Higgs branches using crepant resolutions and deformations of the singularities. We propose a relation between the resulting moduli spaces, by compactifying the theories to 3d, followed by 3d   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 4 mirror symmetry and an S-type gauging of an abelian flavor symmetry. In particular, we use this correspondence to determine the Higgs branch of some 5d SCFTs and their magnetic quivers from the geometry. As an application of the general framework, we observe that singularities that engineer Argyres-Douglas theories in Type IIB also give rise to rank-0 5d SCFTs in M-theory. We also compute the higher-form symmetries of the 4d and 5d SCFTs, including the one-form symmetries of generalized Argyres-Douglas theories of type (G, G′).

Coulomb and Higgs branches from canonical singularities. Part 0

We derive the structure of the Higgs branch of 5d superconformal field theories or gauge theories from their realization as a generalized toric polygon (or dot diagram). This approach is motivated by a dual, tropical curve decomposition of the (p, q) 5-brane-web system. We define an edge coloring, which provides a decomposition of the generalized toric polygon into a refined Minkowski sum of sub-polygons, from which we compute the magnetic quiver. The Coulomb branch of the magnetic quiver is then conjecturally identified with the 5d Higgs branch. Furthermore, from partial resolutions, we identify the symplectic leaves of the Higgs branch and thereby the entire foliation structure. In the case of strictly toric polygons, this approach reduces to the description of deformations of the Calabi-Yau singularities in terms of Minkowski sums.