Topological defects and operators give a far-reaching generalization of symmetries of quantum fields. An auxiliary topological field theory in one dimension higher than the QFT of interest, known as the SymTFT, provides a natural way for capturing such operators. This gives a new perspective on several applications of symmetries, but fails to capture continuous non-Abelian symmetries. The main aim of this work is to fill this gap. Guided by geometric engineering and holography, we recover various known features of representation theory of the non-Abelian symmetry from a SymTFT viewpoint. Central to our approach is a duality between the flat sector of Yang-Mills at zero coupling and non-Abelian BF theories. Our results extend naturally to models without supersymmetry.

United Kingdom

Federico Bonetti

Sweden

Michele Del Zotto

France

Ruben Minasian

SymTFTs for continuous non-Abelian symmetries

We study the Type IIB eight-derivative effective Lagrangian beyond the quartic level, focusing on interactions involving gravitons and axio-dilatons. We show how to translate five-point scattering amplitudes into genuine five-point contact terms and extract all perturbative contributions to the effective action. Our result is consistent with T-duality predictions at tree level in the NSNS sector. We find that couplings with an even/odd number of scalars are neutral/charged under SL(2, $\textit{ℤ}$), and use this feature to deduce their non-perturbative completion. The mixed NSNS/RR structures that cannot be deduced from the pure NSNS sector allow us to unambiguously fix the kinematics, which turns out to be the same for tree level and one loop. In Type IIA, these structures are essential for establishing agreement of string-theoretic corrections with the circle reduction of M-theory higher-derivative couplings.

United States

James Liu

Italy

Raffaele Savelli

Germany

Andreas Schachner

Type IIB at eight derivatives: five-point axio-dilaton couplings

We revisit 6d (2,0) SCFTs of type $\textit{D}$ and their realization in M-theory, focusing on absolute variants of these theories and on their global finite 0- and 2-form symmetries. We derive the 7d SymTFT capturing these global symmetries from M-theory, both from the point of view of the low-energy supergravity action on × and from M2- and M5-branes giving rise to its topological operators. Along the way, results by Gukov, Hsin, and Pei are extended by keeping track of an additional 7d $\textit{ℤ}$ gauge field, associated to the outer automorphism of the $\textit{D}$ algebra. In particular, we find an interplay of non-invertible symmetries and mixed anomalies for absolute 6d (2,0) $\textit{D}$ SCFTs with $\textit{k}$ ≥ 1. We highlight several subtle points related to the non-orientability of , the half-integral $\textit{G}$ -flux that threads it, and the non-commutativity of fluxes. All these also play an essential role in a holographic derivation of the anomaly polynomial of 6d (2,0) $\textit{D}$ SCFTs.

Spain

Michele Zotto

SymTFTs and non-invertible symmetries of 6d (2,0) SCFTs of type $\textit{D}$ from M-theory

We investigate the interrelation between topology and Narain T-duality of heterotic flux vacua. We present evidence that all 5 and 4-dimensional Minkowski space heterotic flux backgrounds with 8 supercharges have a locus in the moduli space with a T-dual description in terms of a compactification on the product of a K3 surface with a circle or a torus. A test of this equivalence is provided by calculating the new supersymmetric index on both sides of the duality. We examine the implications of these dualities for CHL-like orbifolds that reduce the rank of the gauge group, as well as those that lead to minimal supersymmetry in 4 dimensions. We also discuss properties of flux vacua that preserve minimal supersymmetry in 4 dimensions that cannot be related to conventional compactifications by Narain T-duality. Along the way we point out a number of properties of these vacua, including the role played by non-trivial flat gerbes, the appearance of rational worldsheet CFTs in decompactification limits, and the role of attractive K3 surfaces in backgrounds with minimal supersymmetry. Finally, we discuss the dual pairs from the perspective of M-theory/heterotic duality.

Dan Israël

Ilarion Melnikov

Yann Proto

Topology change and heterotic flux vacua

We reexamine the question of quantum consistency of supergravities in eight dimensions. Theories with 16 supercharges suffer from the anomalies under the action of its discrete modular groups. In minimally supersymmetric theory coupled to Yang-Mills multiples of rank l with the moduli space given by SO(2, l)/(U(1) × SO(l)), the existence of a counterterm together with the requirement that its poles and zeros correspond to the gauge symmetry enhancement imposes nontrivial constraints on the lattice. The counterterms needed for anomaly cancellation for all cases, that are believed to lead to consistent theories of quantum gravity (l = 2, 10, 18), are discussed.

Bing-Xin Lao

Consistency of eight-dimensional supergravities: anomalies, lattices and counterterms

We discuss F-theory backgrounds associated to flat torus bundles over Ricci-flat manifolds. In this setting the F-theory background can be understood as a IIB orientifold with a large radius limit described by a supersymmetric compactification of IIB supergravity on a smooth, Ricci flat, but in general non-spin geometry. When compactified on an additional circle these backgrounds are T-dual to IIA compactifications on smooth non-orientable manifolds with a Pin− structure.

Peng Cheng

Flat F-theory and friends

In this paper, we present a unified perspective on sphere consistent truncations based on the classical geometric properties of sphere bundles. The backbone of our approach is the global angular form for the sphere. A universal formula for the Kaluza-Klein ansatz of the flux threading the n-sphere captures the full nonabelian isometry group SO(n + 1) and scalar deformations associated to the coset SL(n + 1, ℝ)/SO(n + 1). In all cases, the scalars enter the ansatz in a shift by an exact form. We find that the latter can be completely fixed by imposing mild conditions, motivated by supersymmetry, on the scalar potential arising from dimensional reduction of the higher dimensional theory. We comment on the role of the global angular form in the derivation of the topological couplings of the lower-dimensional theory, and on how this perspective could provide inroads into the study of consistent truncations with less supersymmetry.

Valentí Camell

Peter Weck

Consistent truncations from the geometry of sphere bundles

We examine the role of global topological data associated to choices of holonomy for flat gauge fields in string compactification. Our study begins with perturbative string compactification on compact flat manifolds preserving 8 supercharges in 5 dimensions. By including non-trivial holonomy for Wilson lines in the heterotic string and for the B-field gerbe in the type II string we find worldsheet dualities that relate these backgrounds to other string compactifications. While our simple examples allow for explicit analysis, the concepts and some of the methods extend to a broader class of compactifications and have implications for string dualities, perturbative and otherwise.

Flat equivariant gerbes: holonomies and dualities

We study the non-linear structure of Type IIB eight-derivative couplings involving the metric and the complexified three-form G 3. We show that, at the level of five-point string amplitudes, the kinematics in the maximally R-symmetry-violating sector is fully matched by standard superspace integrals and by superparticle amplitudes in M-theory on a two-torus. The latter approach is used to determine the complete effective action in this sector and to verify its invariance under SL(2, ℤ) duality. We further comment on the general structure of the higher-point kinematics. Compactifications to lower dimensions provide both tests for our results and the arena for their applications. We verify that K3 reductions are fully consistent with the constraints of six-dimensional supersymmetry, and derive the four-dimensional flux scalar potential and axion kinetic terms at order (α′)3 in Calabi-Yau threefold reductions.

Type IIB at eight derivatives: insights from Superstrings, Superfields and Superparticles

We revisit quantum field theory anomalies, emphasizing the interplay with diffeomorphisms and supersymmetry. The Ward identities of the latter induce Noether currents of all continuous symmetries, and we point out how these consistent currents are replaced by their covariant form through the appearance of the Bardeen-Zumino currents, which play a central role in our study. For supersymmetry Ward identities, two systematic methods for solving the Wess-Zumino consistency conditions are discussed: anomaly inflow and anomaly descent. The simplest inflows are from supersymmetric Chern-Simons actions in one dimension higher, which are used to supersymmetrize flavor anomalies in <math><mi>d</mi><mo>=</mo><mn>4</mn></math> and, for <math><mi>d</mi><mo>=</mo><mn>2</mn></math> <math><mi>N</mi><mo>=</mo><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math>, flavor anomalies with <math><mrow><mi>p</mi></mrow></math>, <math><mrow><mi>q</mi><mo>≤</mo><mn>3</mn></mrow></math> and Lorentz-Weyl anomalies with <math><mrow><mi>p</mi></mrow></math>, <math><mrow><mi>q</mi><mo>≤</mo><mn>6</mn></mrow></math>. Finally, we extend the Becchi-Rouet-Stora-Tyutin algebra and the subsequent descent, a necessity for the diffeomorphism anomaly in retrospect. The same modification computes the supersymmetrized anomalies and determines the above Chern-Simons actions when these exist.