We introduce a new class of non-compact backgrounds of Type IIB string theory preserving eight supercharges by combining S-folds and non-perturbative 7-branes wrapping orbifolds, and study the four-dimensional superconformal field theories arising at low energy on $\textit{D}$3-branes probing them. We draw a precise correspondence between this setup and the torus compactification of six-dimensional orbi-instanton theories with a Stiefel-Whitney twist, and use it to determine the main features of such strongly-coupled systems, like central charges, spectra of Coulomb-branch operators, networks of Higgs-branch flows. Finally, with the aim to improve our understanding of the landscape of $$ \mathcal{N} $$ = 2 superconformal field theories, and possibly to extend their classification beyond rank two, we provide a detailed catalogue of all the rank-three theories that our framework gives access to.

Italy

Simone Giacomelli

Raffaele Savelli

Gianluca Zoccarato

$$ \mathcal{N} $$ = 2 Orbi-S-Folds

The center-flavor symmetry of a gauge theory specifies the global form of consistent gauge and flavor bundle background field configurations. For 6D gauge theories which arise from a tensor branch deformation of a superconformal field theory (SCFT), we determine the global structure of such background field configurations, including possible continuous Abelian symmetry and R-symmetry bundles. Proceeding to the conformal fixed point, this provides a prescription for reading off the global form of the continuous factors of the zero-form symmetry, including possible nontrivial mixing between flavor and R-symmetry. As an application, we show that this global structure leads to a large class of 4D <math><mi>N</mi><mo>=</mo><mn>2</mn></math> SCFTs obtained by compactifying on a <math><msup><mi>T</mi><mn>2</mn></msup></math> in the presence of a topologically nontrivial flat flavor bundle characterized by an ’t Hooft magnetic flux. The resulting “Stiefel-Whitney twisted” compactifications realize several new infinite families of 4D <math><mi>N</mi><mo>=</mo><mn>2</mn></math> SCFTs, and also furnish a 6D origin for a number of recently discovered rank one and two 4D <math><mi>N</mi><mo>=</mo><mn>2</mn></math> SCFTs.

United States

Jonathan J. Heckman

Germany

Craig Lawrie

CERN

Ling Lin

Hao Y. Zhang

Belgium

6D SCFTs, center-flavor symmetries, and Stiefel-Whitney compactifications

We use Higgs bundles to study the 3D <math><mi>N</mi><mo>=</mo><mn>1</mn></math> vacua obtained from M-theory compactified on a local <math><mrow><mi>S</mi><mi>p</mi><mi>i</mi><mi>n</mi><mo>(</mo><mn>7</mn><mo>)</mo></mrow></math> space given as a four-manifold <math><msub><mi>M</mi><mn>4</mn></msub></math> of ADE singularities with further generic enhancements in the singularity type along one-dimensional subspaces. There can be strong quantum corrections to the massless degrees of freedom in the low energy effective field theory, but topologically robust quantities such as “parity” anomalies are still calculable. We show how geometric reflections of the compactification space descend to 3D reflections and discrete symmetries. The parity anomalies of the effective field theory descend from topological data of the compactification. The geometric perspective also allows us to track various perturbative and nonperturbative corrections to the 3D effective field theory. We also provide some explicit constructions of well-known 3D theories, including those which arise as edge modes of 4D topological insulators, and 3D <math><mi>N</mi><mo>=</mo><mn>1</mn></math> analogs of grand unified theories. An additional result of our analysis is that we are able to track the spectrum of extended objects and their transformations under higher-form symmetries.

Slovenia

Mirjam Cvetič

Ethan Torres

Reflections on the matter of 3D <math><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></math> vacua and local <math><mstyle><mrow><mstyle><mrow><mi>S</mi><mi>p</mi><mi>i</mi><mi>n</mi></mrow></mstyle><mo>(</mo><mn>7</mn><mo>)</mo></mrow></mstyle></math> compactifications

<math><mi>S</mi></math>-folds are a nonperturbative generalization of orientifold 3-planes which figure prominently in the construction of four-dimensional (4D) <math><mi>N</mi><mo>=</mo><mn>3</mn></math> superconformal field theories (SCFTs) and have also recently been used to realize examples of 4D <math><mi>N</mi><mo>=</mo><mn>2</mn></math> SCFTs. In this paper, we develop a general procedure for reading off the flavor symmetry experienced by D3-branes probing 7-branes in the presence of an <math><mi>S</mi></math>-fold. We develop an <math><mi>S</mi></math>-fold generalization of orientifold projection which applies to nonperturbative string junctions. This procedure leads to a different 4D flavor symmetry algebra depending on whether the <math><mi>S</mi></math>-fold supports discrete torsion. We also show that this same procedure allows us to read off admissible representations of the flavor symmetry in the associated 4D <math><mi>N</mi><mo>=</mo><mn>2</mn></math> SCFTs. Furthermore, this provides a prescription for how to define F-theory in the presence of <math><mi>S</mi></math>-folds with discrete torsion.

Thomas B. Rochais

<math><mi>S</mi></math>-folds, string junctions, and 4D <math><mi>N</mi><mo>=</mo><mn>2</mn></math> SCFTs

Higgs bundles are a central tool used to study a range of intersecting brane systems in string compactifications. Solutions to the internal gauge theory equations of motion for the corresponding worldvolume theories of branes give rise to different low energy effective field theories. This has been heavily used in the study of M-theory on local <math><msub><mi>G</mi><mn>2</mn></msub></math> spaces and F-theory on local elliptically fibered Calabi-Yau fourfolds. In this paper we show that the 3D <math><mi>N</mi><mo>=</mo><mn>1</mn></math> effective field theory defined by M-theory on a local spin(7) space unifies the Higgs bundle data associated with 4D <math><mi>N</mi><mo>=</mo><mn>1</mn></math> M- and F-theory vacua. This 3D system appears as an interface with finite thickness between different 4D vacua. We develop the general formalism of M-theory on such local spin(7) spaces and build explicit interpolating solutions. This provides a complementary local gauge theory analysis of a recently proposed approach to constructing spin(7) spaces from generalized connected sums.

Geometric unification of Higgs bundle vacua

Compactification of M-string theory on manifolds with <math><msub><mi>G</mi><mn>2</mn></msub></math> structure yields a wide variety of 4D and 3D physical theories. We analyze the local geometry of such compactifications as captured by a gauge theory obtained from a three-manifold of ADE singularities. Generic gauge theory solutions include a nontrivial gauge field flux as well as normal deformations to the three-manifold captured by noncommuting matrix coordinates, a signal of T-brane phenomena. Solutions of the 3D gauge theory on a three-manifold are given by a deformation of the Hitchin system on a marked Riemann surface which is fibered over an interval. We present explicit examples of such backgrounds as well as the profile of the corresponding zero modes for localized chiral matter. We also provide a purely algebraic prescription for characterizing localized matter for such T-brane configurations. The geometric interpretation of this gauge theory description provides a generalization of twisted connected sums with codimension seven singularities at localized regions of the geometry. It also indicates that geometric codimension six singularities can sometimes support 4D chiral matter due to physical structure “hidden” in T-branes.

Rodrigo Barbosa

T-branes and <math><msub><mi>G</mi><mn>2</mn></msub></math> backgrounds

We argue that global F-theory compactifications to four dimensions gener- ally exhibit higher rank Yukawa matrices from multiple geometric contributions known as Yukawa points. The holomorphic couplings furthermore have large hierarchies for generic complex structure moduli. Unlike local considerations, the compact setup realizes these features all through geometry, and requires no instanton corrections. As an example, we consider a concrete toy model with SU(5) × U(1) gauge symmetry. From the geometry, we find two Yukawa points for the     <math> <mn>1</mn> <msub> <mn>0</mn> <mrow> <mo>−</mo> <mn>2</mn> </mrow> </msub> <msub> <mover> <mn>5</mn> <mo>¯</mo> </mover> <mn>6</mn> </msub> <msub> <mover> <mn>5</mn> <mo>¯</mo> </mover> <mrow> <mo>−</mo> <mn>4</mn> </mrow> </msub> </math> $$ \mathbf{1}{\mathbf{0}}_{-2}{\overline{\mathbf{5}}}_6{\overline{\mathbf{5}}}_{-4} $$  coupling, producing a rank two Yukawa matrix. Our methods allow us to track all complex structure dependencies of the holomorphic couplings and study the ratio numerically. This reveals hierarchies of     <math> <mi>O</mi> </math> $$ \mathcal{O} $$ (105) and larger on a full-dimensional subspace of the moduli space.

Muyang Liu

Hao Zhang

Yukawa hierarchies in global F-theory models

We establish a brane-brane duality connecting T-branes to collections of ordinary D-branes. T-branes are intrinsically non-Abelian brane configurations with worldvolume flux, whereas their duals consist of Abelian brane systems that encode the T-brane data in their curvature. We argue that the new Abelian picture provides a reliable description of T-branes when their non-Abelian fields have large expectation values in string units. To confirm this duality, we match the energy density and all the electromagnetic couplings on both sides. A key step in this derivation is a non-trivial factorization of the symmetrized-trace non-Abelian Dirac-Born-Infeld action when evaluated on solutions of the α′ -corrected Hitchin system.

France

Iosif Bena

Johan Blåbäck

The two faces of T-branes

We compute the full classical 4d scalar potential of type IIA Calabi-Yau orientifolds in the presence of fluxes and D6-branes. We show that it can be written as a bilinear form V = Z  AB  ρ  A  ρ  B , where the ρ  A  are in one-to-one correspondence with the 4-form fluxes of the 4d effective theory. The ρ  A  only depend on the internal fluxes, the axions and the topological data of the compactification, and are fully determined by the Freed-Witten anomalies of branes that appear as 4d string defects. The quadratic form Z  AB  only depends on the saxionic partners of these axions. In general, the ρ  A  can be seen as the basic invariants under the discrete shift symmetries of the 4d effective theory, and therefore the building blocks of any flux-dependent quantity. All these polynomials may be obtained by derivation from one of them, associated to a universal 4-form. The standard  <math><mi>N</mi><mo>=</mo><mn>1</mn></math> $$ \mathcal{N}=1 $$ supergravity flux superpotential is uniquely determined from this master polynomial, and vice versa.

Spain

Alvaro Herráez

Luis Ibáñez

Fernando Marchesano

Hong Kong

The type IIA flux potential, 4-forms and Freed-Witten anomalies

String theory models of axion monodromy inflation exhibit scalar potentials which are quadratic for small values of the inflaton field and evolve to a more complicated function for large field values. Oftentimes the large field behaviour is gentler than quadratic, lowering the tensor-to-scalar ratio. This effect, known as flattening, has been observed in the string theory context through the properties of the DBI+CS D-brane action. We revisit such flattening effects in type IIB flux compactifications with mobile D7-branes, with the inflaton identified with the D7-brane position. We observe that, with a generic choice of background fluxes, flattening effects are larger than previously observed, allowing to fit these models within current experimental bounds. In particular, we compute the cosmological observables in scenarios compatible with closed-string moduli stabilisation, finding tensor-to-scalar ratios as low as r ∼ 0 . 04. These are models of single field inflation in which the inflaton is much lighter than the other scalars through a mild tuning of the compactification data.