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

France

Ruben Minasian

Italy

Raffaele Savelli

Germany

Andreas Schachner

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

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.

Simone Giacomelli

Gianluca Zoccarato

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

We study four-dimensional superconformal field theories living on the worldvolume of D3 branes probing minimally-supersymmetric F-theory backgrounds, focusing on the case of orbi-orientifold setups with and without 7-branes. We observe that these theories are closely related to compactifications of six-dimensional 𝒩 = (1, 0) theories on a torus with flux, where the flux quanta is mapped in Type IIB to the defining data of the orbifold group. We analyze the cases of class 𝒮 k  theories as well as of compactifications of the E-string and of orbi-instanton theories. We also classify 𝒮-fold configurations in F-theory preserving minimal supersymmetry in four dimensions and their mass deformations.

𝒩 = 1 SCFTs from F-theory on Orbifolds

The computation of the partition function in certain quantum field theories, such as those of the Argyres-Douglas or Minahan-Nemeschansky type, is problematic due to the lack of a Lagrangian description. In this paper, we use the holomorphic anomaly equation to derive the gravitational corrections to the prepotential of such theories at rank one by deforming them from the conformal point. In the conformal limit, we find a general formula for the partition function as a sum of hypergeometric functions. We show explicit results for the round sphere and the Nekrasov-Shatashvili phases of the Ω background. The first case is relevant for the derivation of extremal correlators in flat space, whereas the second one has interesting applications for the study of anharmonic oscillators.

Francesco Fucito

CERN

Switzerland

Alba Grassi

Jose Morales

Partition functions of non-Lagrangian theories from the holomorphic anomaly

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.

United Kingdom

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

D3 branes in the vicinity of an E6, E7, or E8 stack of 7-branes in flat space are known to host at low energy a famous class of strongly-coupled   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 superconformal field theories featuring exceptional global symmetry. What if, instead, the 7-branes wrap an orbifold? We give a systematic characterization of such theories in the case of ℂ2 /ℤ n , and determine their main properties, like global symmetries, spectra of Coulomb-branch operators, and patterns of Higgs-branch flows. We put forward a set of rules to construct their magnetic quivers, which directly generalize what happens in the perturbative case, and later derive them using the duality with M5 branes probing M9 walls.

Marina Moleti

Probing 7-branes on orbifolds

We consider regular polystable Higgs pairs (E, ϕ) on compact complex manifolds. We show that a non-trivial Higgs field ϕ ∈ H 0(End(E) ⊗ K  S ) restricts the Ricci curvature of the manifold, generalising previous results in the literature. In particular ϕ must vanish for positive Ricci curvature, while for trivial canonical bundle it must be proportional to the identity. For Kähler surfaces, our results provide a new vanishing theorem for solutions to the Vafa-Witten equations. Moreover they constrain supersymmetric 7-brane configurations in F-theory, giving obstructions to the existence of T-branes, i.e. solutions with [ϕ, ϕ †] ≠ 0. When non-trivial Higgs fields are allowed, we give a general characterisation of their structure in terms of vector bundle data, which we then illustrate in explicit examples.

Spain

Fernando Marchesano

Canada

Ruxandra Moraru

A vanishing theorem for T-branes

We provide a precise geometric picture that demystifies the phenomenon of supersymmetry enhancement along certain RG flows of four-dimensional field theories, recently discovered by Maruyoshi and Song. It applies to theories of arbitrary rank and it is based on a hyperkähler-structure restoration on the moduli space of solutions of (twisted) Hitchin systems, which underly the class-  <math> <mi>S</mi> </math>  $$ \mathcal{S} $$  construction we use as an engineering tool. Along the way, we formulate a necessary algebraic condition for supersymmetry enhancement, and, when enhancement occurs, we are able to derive the Seiberg-Witten geometry and all conformal dimensions of Coulomb-branch operators for the infrared theory, without using a-maximization.

Federico Carta

Japan

Hirotaka Hayashi

The geometry of SUSY enhancement

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.

Iosif Bena

Johan Blåbäck

The two faces of T-branes

We use the F-theoretic engineering of four-dimensional rank-one superconformal field theories to provide a geometric understanding of the phenomenon of supersymmetry enhancement along the RG flow, recently observed by Maruyoshi and Song. In this context, the superpotential deformations responsible for such flows are interpreted as T-brane backgrounds and encoded in the geometry of elliptically-fibered fourfolds. We formulate a simple algebraic criterion to select all supersymmetry-enhancing flows and, without any maximization process, derive the main features of the corresponding   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 theories in the infrared.